Comparative verification of discrete and smeared numerical approaches for the simulation of hydraulic fracturing View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-12

AUTHORS

Keita Yoshioka, Francesco Parisio, Dmitri Naumov, Renchao Lu, Olaf Kolditz, Thomas Nagel

ABSTRACT

The numerical treatment of propagating fractures as embedded discontinuities is a challenging task for which an analyst has to select a suitable numerical method from a range of options. Since their inception in the mid-80s, smeared approaches for fracture simulation such as non-local damage, gradient damage or more lately phase-field modelling have steadily gained popularity. One of the appeals of a smeared implicit fracture representation, the ability to handle complex topologies with unknown crack paths in relatively coarse meshes as well as multiple-crack interaction and multiphysics, is a fundamental requirement for the numerical simulation of hydraulic fracturing in complex situations which is technically more difficult to achieve with many other methods. However, in hydraulic fracturing simulations, not only the prediction of the fracture path but also the computation of fracture width and propagation pressure (frac pressure) is crucial for reliable and meaningful applications of the simulation tool; how to determine some of these quantities in smeared representations is not immediately obvious. In this study, two of the most popular smeared approaches of recent, namely non-local damage and phase-field models, and an approach in which the solution space is locally enriched to capture a strong discontinuity combined with a cohesive-zone model are verified against fundamental hydraulic fracture propagation problems in the toughness-dominated regime. The individual theoretical foundations of each approach are discussed and differences in the treatment of physical and numerical properties of the methods when applied to the same physical problems are highlighted through examples. More... »

PAGES

13

References to SciGraph publications

  • 2003-12. Manuel Rocha Medal Recipient Rock Fracture and Collapse Under Low Confinement Conditions in ROCK MECHANICS AND ROCK ENGINEERING
  • 2007. Variational Extended Finite Element Model for Cohesive Cracks: Influence of Integration and Interface Law in IUTAM SYMPOSIUM ON DISCRETIZATION METHODS FOR EVOLVING DISCONTINUITIES
  • 1997. Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries in MODERN SOFTWARE TOOLS FOR SCIENTIFIC COMPUTING
  • 2017-05. Numerical evaluation of the phase-field model for brittle fracture with emphasis on the length scale in COMPUTATIONAL MECHANICS
  • 2013-06. A nonlocal continuum damage mechanics approach to simulation of creep fracture in ice sheets in COMPUTATIONAL MECHANICS
  • 2018-12. Hydro-mechanical Modeling of Tunnel Excavation in Anisotropic Shale with Coupled Damage-Plasticity and Micro-dilatant Regularization in ROCK MECHANICS AND ROCK ENGINEERING
  • 2016-12. An overview of the modelling of fracture by gradient damage models in MECCANICA
  • 1998. Approximation of Free-Discontinuity Problems in NONE
  • 2001-08. A cohesive model of fatigue crack growth in INTERNATIONAL JOURNAL OF FRACTURE
  • 2008-04. The Variational Approach to Fracture in JOURNAL OF ELASTICITY
  • 2015-05. Phase-field modeling of ductile fracture in COMPUTATIONAL MECHANICS
  • 1990-01. An analysis of decohesion along an imperfect interface in INTERNATIONAL JOURNAL OF FRACTURE
  • 2016-06. On advantages of the Kelvin mapping in finite element implementations of deformation processes in ENVIRONMENTAL EARTH SCIENCES
  • 2016-11. Application of mixed finite elements to spatially non-local model of inelastic deformations in GEM - INTERNATIONAL JOURNAL ON GEOMATHEMATICS
  • 2012-09. OpenGeoSys: an open-source initiative for numerical simulation of thermo-hydro-mechanical/chemical (THM/C) processes in porous media in ENVIRONMENTAL EARTH SCIENCES
  • 2012. Continuum Damage Mechanics, A Continuum Mechanics Approach to the Analysis of Damage and Fracture in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s13137-019-0126-6

    DOI

    http://dx.doi.org/10.1007/s13137-019-0126-6

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1111834630


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0801", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Artificial Intelligence and Image Processing", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/08", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Information and Computing Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Helmholtz Centre for Environmental Research", 
              "id": "https://www.grid.ac/institutes/grid.7492.8", 
              "name": [
                "Department of Environmental Informatics, Helmholtz Centre for Environmental Research \u2013 UFZ, Leipzig, Germany"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Yoshioka", 
            "givenName": "Keita", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Helmholtz Centre for Environmental Research", 
              "id": "https://www.grid.ac/institutes/grid.7492.8", 
              "name": [
                "Department of Environmental Informatics, Helmholtz Centre for Environmental Research \u2013 UFZ, Leipzig, Germany"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Parisio", 
            "givenName": "Francesco", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Helmholtz Centre for Environmental Research", 
              "id": "https://www.grid.ac/institutes/grid.7492.8", 
              "name": [
                "Department of Environmental Informatics, Helmholtz Centre for Environmental Research \u2013 UFZ, Leipzig, Germany"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Naumov", 
            "givenName": "Dmitri", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "TU Dresden", 
              "id": "https://www.grid.ac/institutes/grid.4488.0", 
              "name": [
                "Department of Environmental Informatics, Helmholtz Centre for Environmental Research \u2013 UFZ, Leipzig, Germany", 
                "Applied Environmental Systems Analysis, Technische Universit\u00e4t Dresden, Dresden, Germany"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Lu", 
            "givenName": "Renchao", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "TU Dresden", 
              "id": "https://www.grid.ac/institutes/grid.4488.0", 
              "name": [
                "Department of Environmental Informatics, Helmholtz Centre for Environmental Research \u2013 UFZ, Leipzig, Germany", 
                "Applied Environmental Systems Analysis, Technische Universit\u00e4t Dresden, Dresden, Germany"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Kolditz", 
            "givenName": "Olaf", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Freiberg University Of Mining And Technology", 
              "id": "https://www.grid.ac/institutes/grid.6862.a", 
              "name": [
                "Department of Environmental Informatics, Helmholtz Centre for Environmental Research \u2013 UFZ, Leipzig, Germany", 
                "Chair of Soil Mechanics and Foundation Engineering, Geotechnical Institute, Technische Universit\u00e4t Bergakademie Freiberg, Freiberg, Germany"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Nagel", 
            "givenName": "Thomas", 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1016/j.cma.2012.08.017", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000289100"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.cma.2012.01.008", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000582395"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.cma.2013.12.005", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001040102"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.cma.2015.03.005", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003057521"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/cpa.3160430805", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003556712"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/cpa.3160430805", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003556712"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0022-5096(99)00028-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003626373"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00603-003-0015-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004364346", 
              "https://doi.org/10.1007/s00603-003-0015-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.cma.2016.02.037", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004538470"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.cma.2016.02.037", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004538470"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.cma.2016.02.037", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004538470"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0022-5096(98)00034-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004753260"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.mechmat.2013.12.005", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004951748"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/nag.563", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005339072"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ijplas.2014.08.001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005371420"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11012-016-0538-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005662823", 
              "https://doi.org/10.1007/s11012-016-0538-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11012-016-0538-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005662823", 
              "https://doi.org/10.1007/s11012-016-0538-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1177/1056789510386852", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005959680"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1177/1056789510386852", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005959680"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-94-007-2666-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007267745", 
              "https://doi.org/10.1007/978-94-007-2666-6"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-94-007-2666-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007267745", 
              "https://doi.org/10.1007/978-94-007-2666-6"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ijrmms.2005.05.014", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008329359"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2514/6.2001-1486", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009523480"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s12665-016-5429-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009747178", 
              "https://doi.org/10.1007/s12665-016-5429-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s12665-016-5429-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009747178", 
              "https://doi.org/10.1007/s12665-016-5429-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/nme.2012", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012121584"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/nme.1130", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012739863"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.engfracmech.2010.08.009", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014003700"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ijsolstr.2015.08.003", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014138872"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ijrmms.2016.04.017", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014333905"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jmps.2016.07.019", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016900966"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0013-7944(01)00060-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016908625"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/nme.1761", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017483012"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1010839522926", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017817952", 
              "https://doi.org/10.1023/a:1010839522926"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.cma.2015.06.009", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021035151"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevlett.87.045501", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021036418"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevlett.87.045501", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021036418"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0013-7944(01)00128-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021037770"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/(sici)1097-0207(19961015)39:19<3391::aid-nme7>3.0.co;2-d", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021336236"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0020-7683(00)00196-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021504002"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10659-007-9107-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021868146", 
              "https://doi.org/10.1007/s10659-007-9107-3"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/nag.732", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022434119"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s12665-012-1546-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022580431", 
              "https://doi.org/10.1007/s12665-012-1546-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jocs.2015.11.007", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023064831"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.engfracmech.2006.08.025", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023160367"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00466-012-0778-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024481036", 
              "https://doi.org/10.1007/s00466-012-0778-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0022-5096(90)90001-k", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024491619"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0022-5096(90)90001-k", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024491619"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4612-1986-6_8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027383930", 
              "https://doi.org/10.1007/978-1-4612-1986-6_8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4612-1986-6_8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027383930", 
              "https://doi.org/10.1007/978-1-4612-1986-6_8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.engfracmech.2015.06.015", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027701537"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00466-015-1151-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028664845", 
              "https://doi.org/10.1007/s00466-015-1151-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4020-6530-9_17", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029354478", 
              "https://doi.org/10.1007/978-1-4020-6530-9_17"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4020-6530-9_17", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029354478", 
              "https://doi.org/10.1007/978-1-4020-6530-9_17"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jmps.2009.04.011", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030287053"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jmps.2015.04.006", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031785796"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00018611", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031896098", 
              "https://doi.org/10.1007/bf00018611"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00018611", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031896098", 
              "https://doi.org/10.1007/bf00018611"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.engfracmech.2015.05.023", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034182944"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0097344", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034415225", 
              "https://doi.org/10.1007/bfb0097344"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0097344", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034415225", 
              "https://doi.org/10.1007/bfb0097344"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.actbio.2013.05.009", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034506235"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ijrmms.2016.07.020", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034515153"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/1097-0207(20010210)50:4<993::aid-nme164>3.0.co;2-m", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035168127"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0045-7825(99)00324-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035192194"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jrmge.2014.06.001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036461761"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1146/annurev-fluid-010814-014736", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039381363"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/0965-0393/17/4/043001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041449465"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/0965-0393/17/4/043001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041449465"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/nme.2861", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043208080"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/nme.2861", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043208080"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.cma.2016.05.015", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044747022"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ijsolstr.2014.12.004", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045198676"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/(sici)1097-0207(19990910)46:1<131::aid-nme726>3.0.co;2-j", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045872079"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.cma.2004.07.025", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046318626"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ijplas.2016.04.011", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047146680"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/pamm.201610212", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047150993"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ijsolstr.2012.04.036", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047577539"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0008-8846(76)90007-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047591196"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0008-8846(76)90007-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047591196"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ijsolstr.2016.03.026", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1048269793"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.engfracmech.2005.07.012", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050266937"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.engfracmech.2005.07.012", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050266937"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.compstruc.2016.11.010", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050790878"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0013-7944(01)00083-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050797744"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/cnm.799", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051896755"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/cnm.799", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051896755"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s13137-016-0083-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052033876", 
              "https://doi.org/10.1007/s13137-016-0083-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s13137-016-0083-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052033876", 
              "https://doi.org/10.1007/s13137-016-0083-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.cma.2015.09.010", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052141761"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/nme.941", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052329990"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0045-7825(99)00213-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052839841"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1029/jz071i016p03939", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052977168"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jmps.2010.02.010", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053233824"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00466-017-1373-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1054055771", 
              "https://doi.org/10.1007/s00466-017-1373-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00466-017-1373-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1054055771", 
              "https://doi.org/10.1007/s00466-017-1373-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1061/(asce)0733-9399(1991)117:5(1070)", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1057582088"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1061/(asce)0733-9399(2002)128:11(1119)", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1057584007"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1063/1.1712886", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1057780619"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevlett.112.014301", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060762380"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevlett.112.014301", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060762380"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1115/1.1526599", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062071612"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2118/110845-pa", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1068947345"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2118/116470-pa", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1068947945"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ijrmms.2017.01.016", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1083762795"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/2016jb013572", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1084006467"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.cma.2017.03.039", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1084066593"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.commatsci.2017.06.010", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1090990485"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jmps.2017.09.006", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1091544306"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2118/20409-ms", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1096935222"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2118/159154-ms", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1097021625"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.21012/fc9.263", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1099082960"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00603-018-1569-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1106343578", 
              "https://doi.org/10.1007/s00603-018-1569-z"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ijsolstr.2018.12.019", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1110836445"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ijsolstr.2018.12.019", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1110836445"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ijsolstr.2018.12.019", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1110836445"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ijsolstr.2018.12.019", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1110836445"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2019-12", 
        "datePublishedReg": "2019-12-01", 
        "description": "The numerical treatment of propagating fractures as embedded discontinuities is a challenging task for which an analyst has to select a suitable numerical method from a range of options. Since their inception in the mid-80s, smeared approaches for fracture simulation such as non-local damage, gradient damage or more lately phase-field modelling have steadily gained popularity. One of the appeals of a smeared implicit fracture representation, the ability to handle complex topologies with unknown crack paths in relatively coarse meshes as well as multiple-crack interaction and multiphysics, is a fundamental requirement for the numerical simulation of hydraulic fracturing in complex situations which is technically more difficult to achieve with many other methods. However, in hydraulic fracturing simulations, not only the prediction of the fracture path but also the computation of fracture width and propagation pressure (frac pressure) is crucial for reliable and meaningful applications of the simulation tool; how to determine some of these quantities in smeared representations is not immediately obvious. In this study, two of the most popular smeared approaches of recent, namely non-local damage and phase-field models, and an approach in which the solution space is locally enriched to capture a strong discontinuity combined with a cohesive-zone model are verified against fundamental hydraulic fracture propagation problems in the toughness-dominated regime. The individual theoretical foundations of each approach are discussed and differences in the treatment of physical and numerical properties of the methods when applied to the same physical problems are highlighted through examples.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s13137-019-0126-6", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isFundedItemOf": [
          {
            "id": "sg:grant.6384573", 
            "type": "MonetaryGrant"
          }
        ], 
        "isPartOf": [
          {
            "id": "sg:journal.1136832", 
            "issn": [
              "1869-2672", 
              "1869-2680"
            ], 
            "name": "GEM - International Journal on Geomathematics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "1", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "10"
          }
        ], 
        "name": "Comparative verification of discrete and smeared numerical approaches for the simulation of hydraulic fracturing", 
        "pagination": "13", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "33d20c2ec1f2a913d6202ff4013c2ad74677c83bc639a71e615cde4dad3b3b1f"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s13137-019-0126-6"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1111834630"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s13137-019-0126-6", 
          "https://app.dimensions.ai/details/publication/pub.1111834630"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T08:59", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000327_0000000327/records_114961_00000000.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1007%2Fs13137-019-0126-6"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s13137-019-0126-6'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s13137-019-0126-6'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s13137-019-0126-6'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s13137-019-0126-6'


     

    This table displays all metadata directly associated to this object as RDF triples.

    395 TRIPLES      21 PREDICATES      120 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s13137-019-0126-6 schema:about anzsrc-for:08
    2 anzsrc-for:0801
    3 schema:author N7c795e0667904610a3653da2423cd26d
    4 schema:citation sg:pub.10.1007/978-1-4020-6530-9_17
    5 sg:pub.10.1007/978-1-4612-1986-6_8
    6 sg:pub.10.1007/978-94-007-2666-6
    7 sg:pub.10.1007/bf00018611
    8 sg:pub.10.1007/bfb0097344
    9 sg:pub.10.1007/s00466-012-0778-7
    10 sg:pub.10.1007/s00466-015-1151-4
    11 sg:pub.10.1007/s00466-017-1373-8
    12 sg:pub.10.1007/s00603-003-0015-y
    13 sg:pub.10.1007/s00603-018-1569-z
    14 sg:pub.10.1007/s10659-007-9107-3
    15 sg:pub.10.1007/s11012-016-0538-4
    16 sg:pub.10.1007/s12665-012-1546-x
    17 sg:pub.10.1007/s12665-016-5429-4
    18 sg:pub.10.1007/s13137-016-0083-2
    19 sg:pub.10.1023/a:1010839522926
    20 https://doi.org/10.1002/(sici)1097-0207(19961015)39:19<3391::aid-nme7>3.0.co;2-d
    21 https://doi.org/10.1002/(sici)1097-0207(19990910)46:1<131::aid-nme726>3.0.co;2-j
    22 https://doi.org/10.1002/1097-0207(20010210)50:4<993::aid-nme164>3.0.co;2-m
    23 https://doi.org/10.1002/2016jb013572
    24 https://doi.org/10.1002/cnm.799
    25 https://doi.org/10.1002/cpa.3160430805
    26 https://doi.org/10.1002/nag.563
    27 https://doi.org/10.1002/nag.732
    28 https://doi.org/10.1002/nme.1130
    29 https://doi.org/10.1002/nme.1761
    30 https://doi.org/10.1002/nme.2012
    31 https://doi.org/10.1002/nme.2861
    32 https://doi.org/10.1002/nme.941
    33 https://doi.org/10.1002/pamm.201610212
    34 https://doi.org/10.1016/0008-8846(76)90007-7
    35 https://doi.org/10.1016/0022-5096(90)90001-k
    36 https://doi.org/10.1016/j.actbio.2013.05.009
    37 https://doi.org/10.1016/j.cma.2004.07.025
    38 https://doi.org/10.1016/j.cma.2012.01.008
    39 https://doi.org/10.1016/j.cma.2012.08.017
    40 https://doi.org/10.1016/j.cma.2013.12.005
    41 https://doi.org/10.1016/j.cma.2015.03.005
    42 https://doi.org/10.1016/j.cma.2015.06.009
    43 https://doi.org/10.1016/j.cma.2015.09.010
    44 https://doi.org/10.1016/j.cma.2016.02.037
    45 https://doi.org/10.1016/j.cma.2016.05.015
    46 https://doi.org/10.1016/j.cma.2017.03.039
    47 https://doi.org/10.1016/j.commatsci.2017.06.010
    48 https://doi.org/10.1016/j.compstruc.2016.11.010
    49 https://doi.org/10.1016/j.engfracmech.2005.07.012
    50 https://doi.org/10.1016/j.engfracmech.2006.08.025
    51 https://doi.org/10.1016/j.engfracmech.2010.08.009
    52 https://doi.org/10.1016/j.engfracmech.2015.05.023
    53 https://doi.org/10.1016/j.engfracmech.2015.06.015
    54 https://doi.org/10.1016/j.ijplas.2014.08.001
    55 https://doi.org/10.1016/j.ijplas.2016.04.011
    56 https://doi.org/10.1016/j.ijrmms.2005.05.014
    57 https://doi.org/10.1016/j.ijrmms.2016.04.017
    58 https://doi.org/10.1016/j.ijrmms.2016.07.020
    59 https://doi.org/10.1016/j.ijrmms.2017.01.016
    60 https://doi.org/10.1016/j.ijsolstr.2012.04.036
    61 https://doi.org/10.1016/j.ijsolstr.2014.12.004
    62 https://doi.org/10.1016/j.ijsolstr.2015.08.003
    63 https://doi.org/10.1016/j.ijsolstr.2016.03.026
    64 https://doi.org/10.1016/j.ijsolstr.2018.12.019
    65 https://doi.org/10.1016/j.jmps.2009.04.011
    66 https://doi.org/10.1016/j.jmps.2010.02.010
    67 https://doi.org/10.1016/j.jmps.2015.04.006
    68 https://doi.org/10.1016/j.jmps.2016.07.019
    69 https://doi.org/10.1016/j.jmps.2017.09.006
    70 https://doi.org/10.1016/j.jocs.2015.11.007
    71 https://doi.org/10.1016/j.jrmge.2014.06.001
    72 https://doi.org/10.1016/j.mechmat.2013.12.005
    73 https://doi.org/10.1016/s0013-7944(01)00060-1
    74 https://doi.org/10.1016/s0013-7944(01)00083-2
    75 https://doi.org/10.1016/s0013-7944(01)00128-x
    76 https://doi.org/10.1016/s0020-7683(00)00196-7
    77 https://doi.org/10.1016/s0022-5096(98)00034-9
    78 https://doi.org/10.1016/s0022-5096(99)00028-9
    79 https://doi.org/10.1016/s0045-7825(99)00213-3
    80 https://doi.org/10.1016/s0045-7825(99)00324-2
    81 https://doi.org/10.1029/jz071i016p03939
    82 https://doi.org/10.1061/(asce)0733-9399(1991)117:5(1070)
    83 https://doi.org/10.1061/(asce)0733-9399(2002)128:11(1119)
    84 https://doi.org/10.1063/1.1712886
    85 https://doi.org/10.1088/0965-0393/17/4/043001
    86 https://doi.org/10.1103/physrevlett.112.014301
    87 https://doi.org/10.1103/physrevlett.87.045501
    88 https://doi.org/10.1115/1.1526599
    89 https://doi.org/10.1146/annurev-fluid-010814-014736
    90 https://doi.org/10.1177/1056789510386852
    91 https://doi.org/10.21012/fc9.263
    92 https://doi.org/10.2118/110845-pa
    93 https://doi.org/10.2118/116470-pa
    94 https://doi.org/10.2118/159154-ms
    95 https://doi.org/10.2118/20409-ms
    96 https://doi.org/10.2514/6.2001-1486
    97 schema:datePublished 2019-12
    98 schema:datePublishedReg 2019-12-01
    99 schema:description The numerical treatment of propagating fractures as embedded discontinuities is a challenging task for which an analyst has to select a suitable numerical method from a range of options. Since their inception in the mid-80s, smeared approaches for fracture simulation such as non-local damage, gradient damage or more lately phase-field modelling have steadily gained popularity. One of the appeals of a smeared implicit fracture representation, the ability to handle complex topologies with unknown crack paths in relatively coarse meshes as well as multiple-crack interaction and multiphysics, is a fundamental requirement for the numerical simulation of hydraulic fracturing in complex situations which is technically more difficult to achieve with many other methods. However, in hydraulic fracturing simulations, not only the prediction of the fracture path but also the computation of fracture width and propagation pressure (frac pressure) is crucial for reliable and meaningful applications of the simulation tool; how to determine some of these quantities in smeared representations is not immediately obvious. In this study, two of the most popular smeared approaches of recent, namely non-local damage and phase-field models, and an approach in which the solution space is locally enriched to capture a strong discontinuity combined with a cohesive-zone model are verified against fundamental hydraulic fracture propagation problems in the toughness-dominated regime. The individual theoretical foundations of each approach are discussed and differences in the treatment of physical and numerical properties of the methods when applied to the same physical problems are highlighted through examples.
    100 schema:genre research_article
    101 schema:inLanguage en
    102 schema:isAccessibleForFree false
    103 schema:isPartOf N74435d0cd37d449cb897bc8df36472d4
    104 Nc9c76d495c804d45b5eff9f7476fa7fc
    105 sg:journal.1136832
    106 schema:name Comparative verification of discrete and smeared numerical approaches for the simulation of hydraulic fracturing
    107 schema:pagination 13
    108 schema:productId N7881aa23c477479f9312b60fcaea6553
    109 Na45245a6ae594bac9cd8042c0d20529a
    110 Nb03a189826bf4d128cbe2fcb8c0caedf
    111 schema:sameAs https://app.dimensions.ai/details/publication/pub.1111834630
    112 https://doi.org/10.1007/s13137-019-0126-6
    113 schema:sdDatePublished 2019-04-11T08:59
    114 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    115 schema:sdPublisher N969c8eb9cf35466aaa0d7ebe83261509
    116 schema:url https://link.springer.com/10.1007%2Fs13137-019-0126-6
    117 sgo:license sg:explorer/license/
    118 sgo:sdDataset articles
    119 rdf:type schema:ScholarlyArticle
    120 N0abd4d4d94334eae990172d2e3cdf6aa schema:affiliation https://www.grid.ac/institutes/grid.7492.8
    121 schema:familyName Yoshioka
    122 schema:givenName Keita
    123 rdf:type schema:Person
    124 N0b1f1b5c703a425c8d0d01c9e94e8d8f schema:affiliation https://www.grid.ac/institutes/grid.7492.8
    125 schema:familyName Parisio
    126 schema:givenName Francesco
    127 rdf:type schema:Person
    128 N5d1efb3fa99c49a79407c0ecfd2dccb6 schema:affiliation https://www.grid.ac/institutes/grid.7492.8
    129 schema:familyName Naumov
    130 schema:givenName Dmitri
    131 rdf:type schema:Person
    132 N701c5f4efc6d48778d4b6e614922659a schema:affiliation https://www.grid.ac/institutes/grid.6862.a
    133 schema:familyName Nagel
    134 schema:givenName Thomas
    135 rdf:type schema:Person
    136 N7133c08b33cc4748a55b584e474d585a rdf:first Nd3ef1758da4a403c82d181b9fc97c367
    137 rdf:rest Nc4410841eb7e4675bdd43d5c7c4f6dae
    138 N74435d0cd37d449cb897bc8df36472d4 schema:volumeNumber 10
    139 rdf:type schema:PublicationVolume
    140 N7881aa23c477479f9312b60fcaea6553 schema:name doi
    141 schema:value 10.1007/s13137-019-0126-6
    142 rdf:type schema:PropertyValue
    143 N7c795e0667904610a3653da2423cd26d rdf:first N0abd4d4d94334eae990172d2e3cdf6aa
    144 rdf:rest Nf8e4ad70382449eab190dd0f5384ab84
    145 N969c8eb9cf35466aaa0d7ebe83261509 schema:name Springer Nature - SN SciGraph project
    146 rdf:type schema:Organization
    147 Na45245a6ae594bac9cd8042c0d20529a schema:name dimensions_id
    148 schema:value pub.1111834630
    149 rdf:type schema:PropertyValue
    150 Nac7f2c1740404b408347654e78b0e4f9 schema:affiliation https://www.grid.ac/institutes/grid.4488.0
    151 schema:familyName Lu
    152 schema:givenName Renchao
    153 rdf:type schema:Person
    154 Nae682400d7694dbeb8848d1b66af44ae rdf:first N5d1efb3fa99c49a79407c0ecfd2dccb6
    155 rdf:rest Neda0a1aeb5eb4155bc2d1d2c44a12f7e
    156 Nb03a189826bf4d128cbe2fcb8c0caedf schema:name readcube_id
    157 schema:value 33d20c2ec1f2a913d6202ff4013c2ad74677c83bc639a71e615cde4dad3b3b1f
    158 rdf:type schema:PropertyValue
    159 Nc4410841eb7e4675bdd43d5c7c4f6dae rdf:first N701c5f4efc6d48778d4b6e614922659a
    160 rdf:rest rdf:nil
    161 Nc9c76d495c804d45b5eff9f7476fa7fc schema:issueNumber 1
    162 rdf:type schema:PublicationIssue
    163 Nd3ef1758da4a403c82d181b9fc97c367 schema:affiliation https://www.grid.ac/institutes/grid.4488.0
    164 schema:familyName Kolditz
    165 schema:givenName Olaf
    166 rdf:type schema:Person
    167 Neda0a1aeb5eb4155bc2d1d2c44a12f7e rdf:first Nac7f2c1740404b408347654e78b0e4f9
    168 rdf:rest N7133c08b33cc4748a55b584e474d585a
    169 Nf8e4ad70382449eab190dd0f5384ab84 rdf:first N0b1f1b5c703a425c8d0d01c9e94e8d8f
    170 rdf:rest Nae682400d7694dbeb8848d1b66af44ae
    171 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
    172 schema:name Information and Computing Sciences
    173 rdf:type schema:DefinedTerm
    174 anzsrc-for:0801 schema:inDefinedTermSet anzsrc-for:
    175 schema:name Artificial Intelligence and Image Processing
    176 rdf:type schema:DefinedTerm
    177 sg:grant.6384573 http://pending.schema.org/fundedItem sg:pub.10.1007/s13137-019-0126-6
    178 rdf:type schema:MonetaryGrant
    179 sg:journal.1136832 schema:issn 1869-2672
    180 1869-2680
    181 schema:name GEM - International Journal on Geomathematics
    182 rdf:type schema:Periodical
    183 sg:pub.10.1007/978-1-4020-6530-9_17 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029354478
    184 https://doi.org/10.1007/978-1-4020-6530-9_17
    185 rdf:type schema:CreativeWork
    186 sg:pub.10.1007/978-1-4612-1986-6_8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027383930
    187 https://doi.org/10.1007/978-1-4612-1986-6_8
    188 rdf:type schema:CreativeWork
    189 sg:pub.10.1007/978-94-007-2666-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007267745
    190 https://doi.org/10.1007/978-94-007-2666-6
    191 rdf:type schema:CreativeWork
    192 sg:pub.10.1007/bf00018611 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031896098
    193 https://doi.org/10.1007/bf00018611
    194 rdf:type schema:CreativeWork
    195 sg:pub.10.1007/bfb0097344 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034415225
    196 https://doi.org/10.1007/bfb0097344
    197 rdf:type schema:CreativeWork
    198 sg:pub.10.1007/s00466-012-0778-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024481036
    199 https://doi.org/10.1007/s00466-012-0778-7
    200 rdf:type schema:CreativeWork
    201 sg:pub.10.1007/s00466-015-1151-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028664845
    202 https://doi.org/10.1007/s00466-015-1151-4
    203 rdf:type schema:CreativeWork
    204 sg:pub.10.1007/s00466-017-1373-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054055771
    205 https://doi.org/10.1007/s00466-017-1373-8
    206 rdf:type schema:CreativeWork
    207 sg:pub.10.1007/s00603-003-0015-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1004364346
    208 https://doi.org/10.1007/s00603-003-0015-y
    209 rdf:type schema:CreativeWork
    210 sg:pub.10.1007/s00603-018-1569-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1106343578
    211 https://doi.org/10.1007/s00603-018-1569-z
    212 rdf:type schema:CreativeWork
    213 sg:pub.10.1007/s10659-007-9107-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021868146
    214 https://doi.org/10.1007/s10659-007-9107-3
    215 rdf:type schema:CreativeWork
    216 sg:pub.10.1007/s11012-016-0538-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005662823
    217 https://doi.org/10.1007/s11012-016-0538-4
    218 rdf:type schema:CreativeWork
    219 sg:pub.10.1007/s12665-012-1546-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1022580431
    220 https://doi.org/10.1007/s12665-012-1546-x
    221 rdf:type schema:CreativeWork
    222 sg:pub.10.1007/s12665-016-5429-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009747178
    223 https://doi.org/10.1007/s12665-016-5429-4
    224 rdf:type schema:CreativeWork
    225 sg:pub.10.1007/s13137-016-0083-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052033876
    226 https://doi.org/10.1007/s13137-016-0083-2
    227 rdf:type schema:CreativeWork
    228 sg:pub.10.1023/a:1010839522926 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017817952
    229 https://doi.org/10.1023/a:1010839522926
    230 rdf:type schema:CreativeWork
    231 https://doi.org/10.1002/(sici)1097-0207(19961015)39:19<3391::aid-nme7>3.0.co;2-d schema:sameAs https://app.dimensions.ai/details/publication/pub.1021336236
    232 rdf:type schema:CreativeWork
    233 https://doi.org/10.1002/(sici)1097-0207(19990910)46:1<131::aid-nme726>3.0.co;2-j schema:sameAs https://app.dimensions.ai/details/publication/pub.1045872079
    234 rdf:type schema:CreativeWork
    235 https://doi.org/10.1002/1097-0207(20010210)50:4<993::aid-nme164>3.0.co;2-m schema:sameAs https://app.dimensions.ai/details/publication/pub.1035168127
    236 rdf:type schema:CreativeWork
    237 https://doi.org/10.1002/2016jb013572 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084006467
    238 rdf:type schema:CreativeWork
    239 https://doi.org/10.1002/cnm.799 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051896755
    240 rdf:type schema:CreativeWork
    241 https://doi.org/10.1002/cpa.3160430805 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003556712
    242 rdf:type schema:CreativeWork
    243 https://doi.org/10.1002/nag.563 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005339072
    244 rdf:type schema:CreativeWork
    245 https://doi.org/10.1002/nag.732 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022434119
    246 rdf:type schema:CreativeWork
    247 https://doi.org/10.1002/nme.1130 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012739863
    248 rdf:type schema:CreativeWork
    249 https://doi.org/10.1002/nme.1761 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017483012
    250 rdf:type schema:CreativeWork
    251 https://doi.org/10.1002/nme.2012 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012121584
    252 rdf:type schema:CreativeWork
    253 https://doi.org/10.1002/nme.2861 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043208080
    254 rdf:type schema:CreativeWork
    255 https://doi.org/10.1002/nme.941 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052329990
    256 rdf:type schema:CreativeWork
    257 https://doi.org/10.1002/pamm.201610212 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047150993
    258 rdf:type schema:CreativeWork
    259 https://doi.org/10.1016/0008-8846(76)90007-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047591196
    260 rdf:type schema:CreativeWork
    261 https://doi.org/10.1016/0022-5096(90)90001-k schema:sameAs https://app.dimensions.ai/details/publication/pub.1024491619
    262 rdf:type schema:CreativeWork
    263 https://doi.org/10.1016/j.actbio.2013.05.009 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034506235
    264 rdf:type schema:CreativeWork
    265 https://doi.org/10.1016/j.cma.2004.07.025 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046318626
    266 rdf:type schema:CreativeWork
    267 https://doi.org/10.1016/j.cma.2012.01.008 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000582395
    268 rdf:type schema:CreativeWork
    269 https://doi.org/10.1016/j.cma.2012.08.017 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000289100
    270 rdf:type schema:CreativeWork
    271 https://doi.org/10.1016/j.cma.2013.12.005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001040102
    272 rdf:type schema:CreativeWork
    273 https://doi.org/10.1016/j.cma.2015.03.005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003057521
    274 rdf:type schema:CreativeWork
    275 https://doi.org/10.1016/j.cma.2015.06.009 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021035151
    276 rdf:type schema:CreativeWork
    277 https://doi.org/10.1016/j.cma.2015.09.010 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052141761
    278 rdf:type schema:CreativeWork
    279 https://doi.org/10.1016/j.cma.2016.02.037 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004538470
    280 rdf:type schema:CreativeWork
    281 https://doi.org/10.1016/j.cma.2016.05.015 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044747022
    282 rdf:type schema:CreativeWork
    283 https://doi.org/10.1016/j.cma.2017.03.039 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084066593
    284 rdf:type schema:CreativeWork
    285 https://doi.org/10.1016/j.commatsci.2017.06.010 schema:sameAs https://app.dimensions.ai/details/publication/pub.1090990485
    286 rdf:type schema:CreativeWork
    287 https://doi.org/10.1016/j.compstruc.2016.11.010 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050790878
    288 rdf:type schema:CreativeWork
    289 https://doi.org/10.1016/j.engfracmech.2005.07.012 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050266937
    290 rdf:type schema:CreativeWork
    291 https://doi.org/10.1016/j.engfracmech.2006.08.025 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023160367
    292 rdf:type schema:CreativeWork
    293 https://doi.org/10.1016/j.engfracmech.2010.08.009 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014003700
    294 rdf:type schema:CreativeWork
    295 https://doi.org/10.1016/j.engfracmech.2015.05.023 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034182944
    296 rdf:type schema:CreativeWork
    297 https://doi.org/10.1016/j.engfracmech.2015.06.015 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027701537
    298 rdf:type schema:CreativeWork
    299 https://doi.org/10.1016/j.ijplas.2014.08.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005371420
    300 rdf:type schema:CreativeWork
    301 https://doi.org/10.1016/j.ijplas.2016.04.011 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047146680
    302 rdf:type schema:CreativeWork
    303 https://doi.org/10.1016/j.ijrmms.2005.05.014 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008329359
    304 rdf:type schema:CreativeWork
    305 https://doi.org/10.1016/j.ijrmms.2016.04.017 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014333905
    306 rdf:type schema:CreativeWork
    307 https://doi.org/10.1016/j.ijrmms.2016.07.020 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034515153
    308 rdf:type schema:CreativeWork
    309 https://doi.org/10.1016/j.ijrmms.2017.01.016 schema:sameAs https://app.dimensions.ai/details/publication/pub.1083762795
    310 rdf:type schema:CreativeWork
    311 https://doi.org/10.1016/j.ijsolstr.2012.04.036 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047577539
    312 rdf:type schema:CreativeWork
    313 https://doi.org/10.1016/j.ijsolstr.2014.12.004 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045198676
    314 rdf:type schema:CreativeWork
    315 https://doi.org/10.1016/j.ijsolstr.2015.08.003 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014138872
    316 rdf:type schema:CreativeWork
    317 https://doi.org/10.1016/j.ijsolstr.2016.03.026 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048269793
    318 rdf:type schema:CreativeWork
    319 https://doi.org/10.1016/j.ijsolstr.2018.12.019 schema:sameAs https://app.dimensions.ai/details/publication/pub.1110836445
    320 rdf:type schema:CreativeWork
    321 https://doi.org/10.1016/j.jmps.2009.04.011 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030287053
    322 rdf:type schema:CreativeWork
    323 https://doi.org/10.1016/j.jmps.2010.02.010 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053233824
    324 rdf:type schema:CreativeWork
    325 https://doi.org/10.1016/j.jmps.2015.04.006 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031785796
    326 rdf:type schema:CreativeWork
    327 https://doi.org/10.1016/j.jmps.2016.07.019 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016900966
    328 rdf:type schema:CreativeWork
    329 https://doi.org/10.1016/j.jmps.2017.09.006 schema:sameAs https://app.dimensions.ai/details/publication/pub.1091544306
    330 rdf:type schema:CreativeWork
    331 https://doi.org/10.1016/j.jocs.2015.11.007 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023064831
    332 rdf:type schema:CreativeWork
    333 https://doi.org/10.1016/j.jrmge.2014.06.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036461761
    334 rdf:type schema:CreativeWork
    335 https://doi.org/10.1016/j.mechmat.2013.12.005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004951748
    336 rdf:type schema:CreativeWork
    337 https://doi.org/10.1016/s0013-7944(01)00060-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016908625
    338 rdf:type schema:CreativeWork
    339 https://doi.org/10.1016/s0013-7944(01)00083-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050797744
    340 rdf:type schema:CreativeWork
    341 https://doi.org/10.1016/s0013-7944(01)00128-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1021037770
    342 rdf:type schema:CreativeWork
    343 https://doi.org/10.1016/s0020-7683(00)00196-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021504002
    344 rdf:type schema:CreativeWork
    345 https://doi.org/10.1016/s0022-5096(98)00034-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004753260
    346 rdf:type schema:CreativeWork
    347 https://doi.org/10.1016/s0022-5096(99)00028-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003626373
    348 rdf:type schema:CreativeWork
    349 https://doi.org/10.1016/s0045-7825(99)00213-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052839841
    350 rdf:type schema:CreativeWork
    351 https://doi.org/10.1016/s0045-7825(99)00324-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035192194
    352 rdf:type schema:CreativeWork
    353 https://doi.org/10.1029/jz071i016p03939 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052977168
    354 rdf:type schema:CreativeWork
    355 https://doi.org/10.1061/(asce)0733-9399(1991)117:5(1070) schema:sameAs https://app.dimensions.ai/details/publication/pub.1057582088
    356 rdf:type schema:CreativeWork
    357 https://doi.org/10.1061/(asce)0733-9399(2002)128:11(1119) schema:sameAs https://app.dimensions.ai/details/publication/pub.1057584007
    358 rdf:type schema:CreativeWork
    359 https://doi.org/10.1063/1.1712886 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057780619
    360 rdf:type schema:CreativeWork
    361 https://doi.org/10.1088/0965-0393/17/4/043001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041449465
    362 rdf:type schema:CreativeWork
    363 https://doi.org/10.1103/physrevlett.112.014301 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060762380
    364 rdf:type schema:CreativeWork
    365 https://doi.org/10.1103/physrevlett.87.045501 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021036418
    366 rdf:type schema:CreativeWork
    367 https://doi.org/10.1115/1.1526599 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062071612
    368 rdf:type schema:CreativeWork
    369 https://doi.org/10.1146/annurev-fluid-010814-014736 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039381363
    370 rdf:type schema:CreativeWork
    371 https://doi.org/10.1177/1056789510386852 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005959680
    372 rdf:type schema:CreativeWork
    373 https://doi.org/10.21012/fc9.263 schema:sameAs https://app.dimensions.ai/details/publication/pub.1099082960
    374 rdf:type schema:CreativeWork
    375 https://doi.org/10.2118/110845-pa schema:sameAs https://app.dimensions.ai/details/publication/pub.1068947345
    376 rdf:type schema:CreativeWork
    377 https://doi.org/10.2118/116470-pa schema:sameAs https://app.dimensions.ai/details/publication/pub.1068947945
    378 rdf:type schema:CreativeWork
    379 https://doi.org/10.2118/159154-ms schema:sameAs https://app.dimensions.ai/details/publication/pub.1097021625
    380 rdf:type schema:CreativeWork
    381 https://doi.org/10.2118/20409-ms schema:sameAs https://app.dimensions.ai/details/publication/pub.1096935222
    382 rdf:type schema:CreativeWork
    383 https://doi.org/10.2514/6.2001-1486 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009523480
    384 rdf:type schema:CreativeWork
    385 https://www.grid.ac/institutes/grid.4488.0 schema:alternateName TU Dresden
    386 schema:name Applied Environmental Systems Analysis, Technische Universität Dresden, Dresden, Germany
    387 Department of Environmental Informatics, Helmholtz Centre for Environmental Research – UFZ, Leipzig, Germany
    388 rdf:type schema:Organization
    389 https://www.grid.ac/institutes/grid.6862.a schema:alternateName Freiberg University Of Mining And Technology
    390 schema:name Chair of Soil Mechanics and Foundation Engineering, Geotechnical Institute, Technische Universität Bergakademie Freiberg, Freiberg, Germany
    391 Department of Environmental Informatics, Helmholtz Centre for Environmental Research – UFZ, Leipzig, Germany
    392 rdf:type schema:Organization
    393 https://www.grid.ac/institutes/grid.7492.8 schema:alternateName Helmholtz Centre for Environmental Research
    394 schema:name Department of Environmental Informatics, Helmholtz Centre for Environmental Research – UFZ, Leipzig, Germany
    395 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...