Anisotropic finite hyper-elastoplasticity of geomaterials with Drucker-Prager/Cap type constitutive model formulation

Bennett, K. C.; Regueiro, R. A.; Luscher, D. J.

doi:10.1016/j.ijplas.2018.11.010

Title: Anisotropic finite hyper-elastoplasticity of geomaterials with Drucker-Prager/Cap type constitutive model formulation

Journal Article · Tue Dec 04 00:00:00 UTC 2018 · International Journal of Plasticity

DOI: https://doi.org/10.1016/j.ijplas.2018.11.010 · OSTI ID:1489977

Bennett, K. C. ^[1];

^[2];

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. of Colorado, Boulder, CO (United States)

The formulation of large strain anisotropic hyper-elastoplasticity of geomaterials is examined. Attention is given to the role of structure tensors (also called fabric tensors), especially in context of the Eshelby-Mandel stress and large inelastic volume changes attributable to porosity. Both (hyper-)elastic and inelastic orthotropic symmetry, reducing to the particular case of transverse isotropy, are considered. Specific material assumptions and constitutive choices are identified for the development of a novel Anisotropic Drucker-Prager/Cap (ADPC) model formulated within the intermediate configuration consistent with multiplicative split of the deformation gradient. The model is calibrated to existing experimental measurements, including high pressure large strain triaxial compression of lithographic (Solnhofen) limestone and triaxial compression measurements on Tournemire shale assessing elastoplastic anisotropy. Manifest implications of constitutive theory are investigated, including consequences of recognizing (or not) the Eshelby-Mandel stress as energy conjugate to the plastic velocity gradient and including (or not) contribution from the skew-symmetric parts of the Mandel stress to the plastic anisotropy. Numerical simple shear experiments and large deformation simulated indentation experiments are provided in order to investigate model predictions and demonstrate the overall robustness in finite element modeling.

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Research Organization:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: US Department of the Navy, Office of Naval Research (ONR); USDOE

Grant/Contract Number:: 89233218CNA000001; AC52-06NA25396

OSTI ID:: 1489977

Report Number(s):: LA-UR--18-25635

Journal Information:: International Journal of Plasticity, Journal Name: International Journal of Plasticity Vol. 123; ISSN 0749-6419

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (79)

Exponential map Algorithm for Stress Updates in Anisotropic Multiplicative Elastoplasticity for Single Crystals Miehe, C. International Journal for Numerical Methods in Engineering, Vol. 39, Issue 19 https://doi.org/10.1002/(SICI)1097-0207(19961015)39:19<3367::AID-NME4>3.0.CO;2-7	journal	October 1996
A new anisotropic failure criterion for transversely isotropic solids Cazacu, O.; Cristescu, N. D.; Shao, J. F. Mechanics of Cohesive-frictional Materials, Vol. 3, Issue 1 https://doi.org/10.1002/(SICI)1099-1484(199801)3:1<89::AID-CFM41>3.0.CO;2-2	journal	January 1998
Thermoplasticity and strain localization in transversely isotropic materials based on anisotropic critical state plasticity: THERMOPLASTICITY AND STRAIN LOCALIZATION Semnani, Shabnam J.; White, Joshua A.; Borja, Ronaldo I. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 40, Issue 18 https://doi.org/10.1002/nag.2536	journal	May 2016
A thermomechanical anisotropic continuum model for geological materials with multiple joint sets: A thermomechanical anisotropic continuum model for geological materials with multiple joint sets Vorobiev, O. Yu.; Rubin, M. B. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 42, Issue 12 https://doi.org/10.1002/nag.2795	journal	May 2018
A robust algorithm for configurational-force-driven brittle crack propagation with R-adaptive mesh alignment Miehe, C.; Gürses, E. International Journal for Numerical Methods in Engineering, Vol. 72, Issue 2 https://doi.org/10.1002/nme.1999	journal	January 2007
A nonlocal multiscale discrete-continuum model for predicting mechanical behavior of granular materials: A NONLOCAL MULTISCALE DISCRETE-CONTINUUM MODEL FOR GRANULAR MATERIALS Liu, Yang; Sun, WaiChing; Yuan, Zifeng International Journal for Numerical Methods in Engineering, Vol. 106, Issue 2 https://doi.org/10.1002/nme.5139	journal	November 2015
Field-gradient partitioning for fracture and frictional contact in the material point method: Field-gradient partitioning for fracture and frictional contact in the material point method Homel, Michael A.; Herbold, Eric B. International Journal for Numerical Methods in Engineering, Vol. 109, Issue 7 https://doi.org/10.1002/nme.5317	journal	August 2016
Generalized radial-return mapping algorithm for anisotropic von Mises plasticity framed in material eigenspace: Generalized radial-return mapping algorithm Versino, Daniele; Bennett, Kane C. International Journal for Numerical Methods in Engineering, Vol. 116, Issue 3 https://doi.org/10.1002/nme.5921	journal	August 2018
A Simple Derivation of Representations for Non-Polynomial Constitutive Equations in Some Cases of Anisotropy Boehler, Jean-Paul ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 59, Issue 4 https://doi.org/10.1002/zamm.19790590403	journal	January 1979
The elastic energy-momentum tensor Eshelby, J. D. Journal of Elasticity, Vol. 5, Issue 3-4 https://doi.org/10.1007/BF00126994	journal	November 1975
A new representation theorem for isotropic functions: An answer to Professor G. F. Smith's criticism of my papers on representations for isotropic functions: Part 1. Scalar-valued isotropic functions Wang, C. -C. Archive for Rational Mechanics and Analysis, Vol. 36, Issue 3 https://doi.org/10.1007/BF00272241	journal	January 1970
Eshelby's stress tensors in finite elastoplasticity Cleja-Tigoiu, S.; Maugin, G. A. Acta Mechanica, Vol. 139, Issue 1-4 https://doi.org/10.1007/BF01170191	journal	March 2000
A maximum-dissipation principle in generalized plasticity Lubliner, J. Acta Mechanica, Vol. 52, Issue 3-4 https://doi.org/10.1007/BF01179618	journal	September 1984
The thermodynamics of elastic materials with heat conduction and viscosity Coleman, Bernard D.; Noll, Walter Archive for Rational Mechanics and Analysis, Vol. 13, Issue 1 https://doi.org/10.1007/BF01262690	journal	December 1963
A modified regula falsi method for computing the root of an equation Dowell, M.; Jarratt, P. BIT, Vol. 11, Issue 2 https://doi.org/10.1007/BF01934364	journal	June 1971
A constitutive model for orthotropic elasto-plasticity at large strains Itskov, M.; Aksel, N. Archive of Applied Mechanics, Vol. 74, Issue 1-2 https://doi.org/10.1007/s00419-004-0339-4	journal	October 2004
Coupled Axisymmetric Thermo-Poro-Mechanical Finite Element Analysis of Energy Foundation Centrifuge Experiments in Partially Saturated Silt Wang, W.; Regueiro, R. A.; McCartney, J. S. Geotechnical and Geological Engineering, Vol. 33, Issue 2 https://doi.org/10.1007/s10706-014-9801-4	journal	July 2014
Instrumented nanoindentation and 3D mechanistic modeling of a shale at multiple scales Bennett, Kane C.; Berla, Lucas A.; Nix, William D. Acta Geotechnica, Vol. 10, Issue 1 https://doi.org/10.1007/s11440-014-0363-7	journal	January 2015
Stress-induced anisotropy in granular materials: fabric, stiffness, and permeability Kuhn, Matthew R.; Sun, WaiChing; Wang, Qi Acta Geotechnica, Vol. 10, Issue 4 https://doi.org/10.1007/s11440-015-0397-5	journal	June 2015
Reservoir stress path and induced seismic anisotropy: results from linking coupled fluid-flow/geomechanical simulation with seismic modelling Angus, D. A.; Fisher, Q. J.; Segura, J. M. Petroleum Science, Vol. 13, Issue 4 https://doi.org/10.1007/s12182-016-0126-1	journal	November 2016
Anisotropic finite plasticity based on structural tensors—different strategies and application to forming simulations Reese, S.; Pietryga, M. P.; Vladimirov, I. N. International Journal of Material Forming, Vol. 2, Issue S1 https://doi.org/10.1007/s12289-009-0530-9	journal	August 2009
Nonlinear tensor functions of several tensor arguments Lokhin, V. V.; Sedov, L. I. Journal of Applied Mathematics and Mechanics, Vol. 27, Issue 3 https://doi.org/10.1016/0021-8928(63)90149-7	journal	January 1963
A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition: Part I. Continuum formulation Simo, J. C. Computer Methods in Applied Mechanics and Engineering, Vol. 66, Issue 2 https://doi.org/10.1016/0045-7825(88)90076-X	journal	February 1988
Volume changes during the deformation of rocks at high pressures Edmond, J. M.; Paterson, M. S. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Vol. 9, Issue 2 https://doi.org/10.1016/0148-9062(72)90019-8	journal	March 1972
On the effects of plastic rotation in the finite deformation of anisotropic elastoplastic materials Loret, B. Mechanics of Materials, Vol. 2, Issue 4 https://doi.org/10.1016/0167-6636(83)90021-2	journal	December 1983
An alternative model for anisotropic elasticity based on fabric tensors Zysset, P. K.; Curnier, A. Mechanics of Materials, Vol. 21, Issue 4 https://doi.org/10.1016/0167-6636(95)00018-6	journal	November 1995
Applications of tensor functions to the formulation of yield criteria for anisotropic materials Betten, Josef International Journal of Plasticity, Vol. 4, Issue 1 https://doi.org/10.1016/0749-6419(88)90003-4	journal	January 1988
Eshelby stress in elastoplasticity and ductile fracture Maugin, Gérard A. International Journal of Plasticity, Vol. 10, Issue 4 https://doi.org/10.1016/0749-6419(94)90040-X	journal	January 1994
On the modelling of anisotropic elastic and inelastic material behaviour at large deformation Svendsen, Bob International Journal of Solids and Structures, Vol. 38, Issue 52 https://doi.org/10.1016/S0020-7683(01)00140-8	journal	December 2001
A constitutive frame of elastoplasticity at large strains based on the notion of a plastic metric Miehe, Christian International Journal of Solids and Structures, Vol. 35, Issue 30 https://doi.org/10.1016/S0020-7683(97)00175-3	journal	October 1998
Definition of a general implicit orthotropic yield criterion Oller, Sergio; Car, Eduardo; Lubliner, Jacob Computer Methods in Applied Mechanics and Engineering, Vol. 192, Issue 7-8 https://doi.org/10.1016/S0045-7825(02)00605-9	journal	February 2003
On the spatial formulation of anisotropic multiplicative elasto-plasticity Menzel, A.; Steinmann, P. Computer Methods in Applied Mechanics and Engineering, Vol. 192, Issue 31-32 https://doi.org/10.1016/S0045-7825(03)00353-0	journal	August 2003
A simple orthotropic, transversely isotropic hyperelastic constitutive equation for large strain computations Bonet, J.; Burton, A. J. Computer Methods in Applied Mechanics and Engineering, Vol. 162, Issue 1-4 https://doi.org/10.1016/S0045-7825(97)00339-3	journal	August 1998
Plastic spin: necessity or redundancy? Dafalias, Yannis F. International Journal of Plasticity, Vol. 14, Issue 9 https://doi.org/10.1016/S0749-6419(98)00036-9	journal	December 1998
Laboratory investigation of the mechanical behaviour of Tournemire shale Niandou, H.; Shao, J. F.; Henry, J. P. International Journal of Rock Mechanics and Mining Sciences, Vol. 34, Issue 1 https://doi.org/10.1016/S1365-1609(97)80029-9	journal	January 1997
Analysis of layered wooden shells using an orthotropic elasto-plastic model for multi-axial loading of clear spruce wood Mackenzie-Helnwein, Peter; Müllner, Herbert W.; Eberhardsteiner, Josef Computer Methods in Applied Mechanics and Engineering, Vol. 194, Issue 21-24 https://doi.org/10.1016/j.cma.2004.07.051	journal	June 2005
Critical state plasticity. Part VI: Meso-scale finite element simulation of strain localization in discrete granular materials Borja, Ronaldo I.; Andrade, José E. Computer Methods in Applied Mechanics and Engineering, Vol. 195, Issue 37-40 https://doi.org/10.1016/j.cma.2005.08.020	journal	July 2006
Implicit dynamic three-dimensional finite element analysis of an inelastic biphasic mixture at finite strain Regueiro, R. A.; Ebrahimi, D. Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 29-32 https://doi.org/10.1016/j.cma.2010.03.003	journal	June 2010
A semi-implicit discrete-continuum coupling method for porous media based on the effective stress principle at finite strain Wang, Kun; Sun, WaiChing Computer Methods in Applied Mechanics and Engineering, Vol. 304 https://doi.org/10.1016/j.cma.2016.02.020	journal	June 2016
Coupled phase-field and plasticity modeling of geological materials: From brittle fracture to ductile flow Choo, Jinhyun; Sun, WaiChing Computer Methods in Applied Mechanics and Engineering, Vol. 330 https://doi.org/10.1016/j.cma.2017.10.009	journal	March 2018
A multiscale multi-permeability poroplasticity model linked by recursive homogenizations and deep learning Wang, Kun; Sun, WaiChing Computer Methods in Applied Mechanics and Engineering, Vol. 334 https://doi.org/10.1016/j.cma.2018.01.036	journal	June 2018
Application of the concept of evolving structure tensors to the modeling of initial and induced anisotropy at large deformation Svendsen, B.; Levkovitch, V.; Wang, J. Computers & Structures, Vol. 84, Issue 17-18 https://doi.org/10.1016/j.compstruc.2006.01.037	journal	June 2006
Modeling large strain anisotropic elasto-plasticity with logarithmic strain and stress measures Caminero, Miguel Ángel; Montáns, Francisco Javier; Bathe, Klaus-Jürgen Computers & Structures, Vol. 89, Issue 11-12 https://doi.org/10.1016/j.compstruc.2011.02.011	journal	June 2011
Pore geometry as a control on rock strength Bubeck, A.; Walker, R. J.; Healy, D. Earth and Planetary Science Letters, Vol. 457 https://doi.org/10.1016/j.epsl.2016.09.050	journal	January 2017
A formulation of anisotropic continuum elastoplasticity at finite strains. Part I: Modelling Sansour, C.; Karsaj, I.; Soric, J. International Journal of Plasticity, Vol. 22, Issue 12 https://doi.org/10.1016/j.ijplas.2006.04.002	journal	December 2006
A micromechanics-based elastoplastic damage model for granular materials at low confining pressure Zhu, Q. Z.; Shao, J. F.; Mainguy, M. International Journal of Plasticity, Vol. 26, Issue 4 https://doi.org/10.1016/j.ijplas.2009.09.006	journal	April 2010
Anisotropic finite elastoplasticity with nonlinear kinematic and isotropic hardening and application to sheet metal forming Vladimirov, Ivaylo N.; Pietryga, Michael P.; Reese, Stefanie International Journal of Plasticity, Vol. 26, Issue 5 https://doi.org/10.1016/j.ijplas.2009.09.008	journal	May 2010
A new thermodynamical framework for finite strain multiplicative elastoplasticity coupled to anisotropic damage Balieu, R.; Kringos, N. International Journal of Plasticity, Vol. 70 https://doi.org/10.1016/j.ijplas.2015.03.006	journal	July 2015
Finite strain elastoplasticity considering the Eshelby stress for materials undergoing plastic volume change Bennett, K. C.; Regueiro, R. A.; Borja, R. I. International Journal of Plasticity, Vol. 77 https://doi.org/10.1016/j.ijplas.2015.10.007	journal	February 2016
A constitutive model of frozen saline sandy soil based on energy dissipation theory Lai, Yuanming; Liao, Mengke; Hu, Kai International Journal of Plasticity, Vol. 78 https://doi.org/10.1016/j.ijplas.2015.10.008	journal	March 2016
Micromechanics-based multimechanism bounding surface model for sands Fang, H. L.; Zheng, H.; Zheng, J. International Journal of Plasticity, Vol. 90 https://doi.org/10.1016/j.ijplas.2017.01.011	journal	March 2017
Strength differential effect in age hardened aluminum alloys Holmen, Jens Kristian; Frodal, Bjørn Håkon; Hopperstad, Odd Sture International Journal of Plasticity, Vol. 99 https://doi.org/10.1016/j.ijplas.2017.09.004	journal	December 2017
Approximate macroscopic yield criteria for Drucker-Prager type solids with spheroidal voids Shen, W. Q.; Zhang, J.; Shao, J. F. International Journal of Plasticity, Vol. 99 https://doi.org/10.1016/j.ijplas.2017.09.008	journal	December 2017
Anisotropic yield function based on stress invariants for BCC and FCC metals and its extension to ductile fracture criterion Lou, Yanshan; Yoon, Jeong Whan International Journal of Plasticity, Vol. 101 https://doi.org/10.1016/j.ijplas.2017.10.012	journal	February 2018
Identification of material parameters for Drucker–Prager plasticity model for FRP confined circular concrete columns Jiang, Jia-Fei; Wu, Yu-Fei International Journal of Solids and Structures, Vol. 49, Issue 3-4 https://doi.org/10.1016/j.ijsolstr.2011.10.002	journal	February 2012
A nonlinear anisotropic elastic–inelastic constitutive model for polycrystalline ceramics and minerals with application to boron carbide Clayton, J. D.; Tonge, A. L. International Journal of Solids and Structures, Vol. 64-65 https://doi.org/10.1016/j.ijsolstr.2015.03.024	journal	July 2015
A non-coaxial critical-state model for sand accounting for fabric anisotropy and fabric evolution Gao, Zhiwei; Zhao, Jidong International Journal of Solids and Structures, Vol. 106-107 https://doi.org/10.1016/j.ijsolstr.2016.11.019	journal	February 2017
A micromechanical framework and modified self-consistent homogenization scheme for the thermoelasticity of porous bonded-particle assemblies Bennett, K. C.; Luscher, D. J.; Buechler, M. A. International Journal of Solids and Structures, Vol. 139-140 https://doi.org/10.1016/j.ijsolstr.2018.02.001	journal	May 2018
Hyper-elastoplastic/damage modeling of rock with application to porous limestone Bennett, K. C.; Borja, R. I. International Journal of Solids and Structures, Vol. 143 https://doi.org/10.1016/j.ijsolstr.2018.03.011	journal	June 2018
On a formulation for anisotropic elastoplasticity at finite strains invariant with respect to the intermediate configuration Sansour, Carlo; Karšaj, Igor; Sorić, Jurica Journal of the Mechanics and Physics of Solids, Vol. 55, Issue 11 https://doi.org/10.1016/j.jmps.2007.03.013	journal	November 2007
Dilatancy, compaction, and failure mode in Solnhofen limestone Baud, Patrick; Schubnel, Alexandre; Wong, Teng-fong Journal of Geophysical Research: Solid Earth, Vol. 105, Issue B8 https://doi.org/10.1029/2000JB900133	journal	August 2000
Bounding Surface Plasticity. III: Application to Anisotropic Cohesive Soils Anandarajah, A.; Dafalias, Yannis F. Journal of Engineering Mechanics, Vol. 112, Issue 12 https://doi.org/10.1061/(ASCE)0733-9399(1986)112:12(1292)	journal	November 1986
Yield Function for Soil with Anisotropic Fabric Oda, Masanobu; Nakayama, Hideo Journal of Engineering Mechanics, Vol. 115, Issue 1 https://doi.org/10.1061/(ASCE)0733-9399(1989)115:1(89)	journal	January 1989
Undrained Multidirectional Direct Simple Shear Behavior of Cohesive Soil DeGroot, Don J.; Ladd, Charles C.; Germaine, John T. Journal of Geotechnical Engineering, Vol. 122, Issue 2 https://doi.org/10.1061/(ASCE)0733-9410(1996)122:2(91)	journal	February 1996
Anisotropic Critical State Theory: Role of Fabric Li, Xiang Song; Dafalias, Yannis F. Journal of Engineering Mechanics, Vol. 138, Issue 3 https://doi.org/10.1061/(ASCE)EM.1943-7889.0000324	journal	March 2012
Evolution of Various Fabric Tensors for Granular Media toward the Critical State Wang, Rui; Fu, Pengcheng; Zhang, Jian-Min Journal of Engineering Mechanics, Vol. 143, Issue 10 https://doi.org/10.1061/(ASCE)EM.1943-7889.0001342	journal	October 2017
Thermodynamics with Internal State Variables Coleman, Bernard D.; Gurtin, Morton E. The Journal of Chemical Physics, Vol. 47, Issue 2 https://doi.org/10.1063/1.1711937	journal	July 1967
Stress and fabric in granular material Chang, Ching S.; Liu, Yang Theoretical and Applied Mechanics Letters, Vol. 3, Issue 2 https://doi.org/10.1063/2.1302102	journal	January 2013
Deformation of Rocks under High Confining Pressures: I. Experiments at Room Temperature Griggs, David T. The Journal of Geology, Vol. 44, Issue 5 https://doi.org/10.1086/624455	journal	July 1936
The anisotropic tensors Smith, G. F.; Rivlin, R. S. Quarterly of Applied Mathematics, Vol. 15, Issue 3 https://doi.org/10.1090/qam/101883	journal	January 1957
Soil mechanics and plastic analysis or limit design Drucker, D. C.; Prager, W. Quarterly of Applied Mathematics, Vol. 10, Issue 2 https://doi.org/10.1090/qam/48291	journal	January 1952
A Variational Principle of Maximum Plastic work in Classical Plasticity Hill, R. The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 1, Issue 1 https://doi.org/10.1093/qjmam/1.1.18	journal	January 1948
The Force on an Elastic Singularity Eshelby, J. D. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 244, Issue 877 https://doi.org/10.1098/rsta.1951.0016	journal	November 1951
A Nonlocal Phenomenological Anisotropic Finite Deformation Plasticity Model Accounting for Dislocation Defects Regueiro, Richard A.; Bammann, Douglas J.; Marin, Esteban B. Journal of Engineering Materials and Technology, Vol. 124, Issue 3 https://doi.org/10.1115/1.1480410	journal	June 2002
Theory of Representations for Tensor Functions—A Unified Invariant Approach to Constitutive Equations Zheng, Q. -S. Applied Mechanics Reviews, Vol. 47, Issue 11 https://doi.org/10.1115/1.3111066	journal	November 1994
Elastic-Plastic Deformation at Finite Strains Lee, E. H. Journal of Applied Mechanics, Vol. 36, Issue 1 https://doi.org/10.1115/1.3564580	journal	March 1969
Anisotropic three-dimensional behavior of a normally consolidated clay Kirkgard, M. M.; Lade, P. V. Canadian Geotechnical Journal, Vol. 30, Issue 5 https://doi.org/10.1139/t93-075	journal	October 1993
Numerical investigation of granular material behaviour under rotational shear Li, X.; Yu, H. -S. Géotechnique, Vol. 60, Issue 5 https://doi.org/10.1680/geot.2010.60.5.381	journal	May 2010
Finite elastic-plastic deformations: Beyond the plastic spin Dafalias, Yannis Theoretical and Applied Mechanics, Vol. 38, Issue 4 https://doi.org/10.2298/TAM1104321D	journal	January 2011

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