Anisotropic finite hyper-elastoplasticity of geomaterials with Drucker-Prager/Cap type constitutive model formulation
Abstract
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.
- Authors:
-
[2];
[1]
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Univ. of Colorado, Boulder, CO (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE; US Department of the Navy, Office of Naval Research (ONR)
- OSTI Identifier:
- 1489977
- Alternate Identifier(s):
- OSTI ID: 1636868
- Report Number(s):
- LA-UR-18-25635
Journal ID: ISSN 0749-6419
- Grant/Contract Number:
- 89233218CNA000001; N00014-17-1-2704; AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- International Journal of Plasticity
- Additional Journal Information:
- Journal Volume: 123; Journal ID: ISSN 0749-6419
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING
Citation Formats
Bennett, K. C., Regueiro, R. A., and Luscher, D. J. Anisotropic finite hyper-elastoplasticity of geomaterials with Drucker-Prager/Cap type constitutive model formulation. United States: N. p., 2018.
Web. doi:10.1016/j.ijplas.2018.11.010.
Bennett, K. C., Regueiro, R. A., & Luscher, D. J. Anisotropic finite hyper-elastoplasticity of geomaterials with Drucker-Prager/Cap type constitutive model formulation. United States. https://doi.org/10.1016/j.ijplas.2018.11.010
Bennett, K. C., Regueiro, R. A., and Luscher, D. J. Tue .
"Anisotropic finite hyper-elastoplasticity of geomaterials with Drucker-Prager/Cap type constitutive model formulation". United States. https://doi.org/10.1016/j.ijplas.2018.11.010. https://www.osti.gov/servlets/purl/1489977.
@article{osti_1489977,
title = {Anisotropic finite hyper-elastoplasticity of geomaterials with Drucker-Prager/Cap type constitutive model formulation},
author = {Bennett, K. C. and Regueiro, R. A. and Luscher, D. J.},
abstractNote = {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.},
doi = {10.1016/j.ijplas.2018.11.010},
journal = {International Journal of Plasticity},
number = ,
volume = 123,
place = {United States},
year = {Tue Dec 04 00:00:00 EST 2018},
month = {Tue Dec 04 00:00:00 EST 2018}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 15 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Bounding Surface Plasticity. III: Application to Anisotropic Cohesive Soils
journal, November 1986
- Anandarajah, A.; Dafalias, Yannis F.
- Journal of Engineering Mechanics, Vol. 112, Issue 12
Reservoir stress path and induced seismic anisotropy: results from linking coupled fluid-flow/geomechanical simulation with seismic modelling
journal, November 2016
- Angus, D. A.; Fisher, Q. J.; Segura, J. M.
- Petroleum Science, Vol. 13, Issue 4
A new thermodynamical framework for finite strain multiplicative elastoplasticity coupled to anisotropic damage
journal, July 2015
- Balieu, R.; Kringos, N.
- International Journal of Plasticity, Vol. 70
Dilatancy, compaction, and failure mode in Solnhofen limestone
journal, August 2000
- Baud, Patrick; Schubnel, Alexandre; Wong, Teng-fong
- Journal of Geophysical Research: Solid Earth, Vol. 105, Issue B8
Instrumented nanoindentation and 3D mechanistic modeling of a shale at multiple scales
journal, January 2015
- Bennett, Kane C.; Berla, Lucas A.; Nix, William D.
- Acta Geotechnica, Vol. 10, Issue 1
Hyper-elastoplastic/damage modeling of rock with application to porous limestone
journal, June 2018
- Bennett, K. C.; Borja, R. I.
- International Journal of Solids and Structures, Vol. 143
A micromechanical framework and modified self-consistent homogenization scheme for the thermoelasticity of porous bonded-particle assemblies
journal, May 2018
- Bennett, K. C.; Luscher, D. J.; Buechler, M. A.
- International Journal of Solids and Structures, Vol. 139-140
Finite strain elastoplasticity considering the Eshelby stress for materials undergoing plastic volume change
journal, February 2016
- Bennett, K. C.; Regueiro, R. A.; Borja, R. I.
- International Journal of Plasticity, Vol. 77
Applications of tensor functions to the formulation of yield criteria for anisotropic materials
journal, January 1988
- Betten, Josef
- International Journal of Plasticity, Vol. 4, Issue 1
A Simple Derivation of Representations for Non-Polynomial Constitutive Equations in Some Cases of Anisotropy
journal, January 1979
- Boehler, Jean-Paul
- ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 59, Issue 4
A simple orthotropic, transversely isotropic hyperelastic constitutive equation for large strain computations
journal, August 1998
- Bonet, J.; Burton, A. J.
- Computer Methods in Applied Mechanics and Engineering, Vol. 162, Issue 1-4
Critical state plasticity. Part VI: Meso-scale finite element simulation of strain localization in discrete granular materials
journal, July 2006
- Borja, Ronaldo I.; Andrade, José E.
- Computer Methods in Applied Mechanics and Engineering, Vol. 195, Issue 37-40
Pore geometry as a control on rock strength
journal, January 2017
- Bubeck, A.; Walker, R. J.; Healy, D.
- Earth and Planetary Science Letters, Vol. 457
Modeling large strain anisotropic elasto-plasticity with logarithmic strain and stress measures
journal, June 2011
- Caminero, Miguel Ángel; Montáns, Francisco Javier; Bathe, Klaus-Jürgen
- Computers & Structures, Vol. 89, Issue 11-12
A new anisotropic failure criterion for transversely isotropic solids
journal, January 1998
- Cazacu, O.; Cristescu, N. D.; Shao, J. F.
- Mechanics of Cohesive-frictional Materials, Vol. 3, Issue 1
Stress and fabric in granular material
journal, January 2013
- Chang, Ching S.; Liu, Yang
- Theoretical and Applied Mechanics Letters, Vol. 3, Issue 2
Coupled phase-field and plasticity modeling of geological materials: From brittle fracture to ductile flow
journal, March 2018
- Choo, Jinhyun; Sun, WaiChing
- Computer Methods in Applied Mechanics and Engineering, Vol. 330
A nonlinear anisotropic elastic–inelastic constitutive model for polycrystalline ceramics and minerals with application to boron carbide
journal, July 2015
- Clayton, J. D.; Tonge, A. L.
- International Journal of Solids and Structures, Vol. 64-65
Eshelby's stress tensors in finite elastoplasticity
journal, March 2000
- Cleja-Tigoiu, S.; Maugin, G. A.
- Acta Mechanica, Vol. 139, Issue 1-4
Thermodynamics with Internal State Variables
journal, July 1967
- Coleman, Bernard D.; Gurtin, Morton E.
- The Journal of Chemical Physics, Vol. 47, Issue 2
The thermodynamics of elastic materials with heat conduction and viscosity
journal, December 1963
- Coleman, Bernard D.; Noll, Walter
- Archive for Rational Mechanics and Analysis, Vol. 13, Issue 1
Plastic spin: necessity or redundancy?
journal, December 1998
- Dafalias, Yannis F.
- International Journal of Plasticity, Vol. 14, Issue 9
Finite elastic-plastic deformations: Beyond the plastic spin
journal, January 2011
- Dafalias, Yannis
- Theoretical and Applied Mechanics, Vol. 38, Issue 4
Undrained Multidirectional Direct Simple Shear Behavior of Cohesive Soil
journal, February 1996
- DeGroot, Don J.; Ladd, Charles C.; Germaine, John T.
- Journal of Geotechnical Engineering, Vol. 122, Issue 2
A modified regula falsi method for computing the root of an equation
journal, June 1971
- Dowell, M.; Jarratt, P.
- BIT, Vol. 11, Issue 2
Soil mechanics and plastic analysis or limit design
journal, January 1952
- Drucker, D. C.; Prager, W.
- Quarterly of Applied Mathematics, Vol. 10, Issue 2
Volume changes during the deformation of rocks at high pressures
journal, March 1972
- Edmond, J. M.; Paterson, M. S.
- International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Vol. 9, Issue 2
The Force on an Elastic Singularity
journal, November 1951
- Eshelby, J. D.
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 244, Issue 877
Micromechanics-based multimechanism bounding surface model for sands
journal, March 2017
- Fang, H. L.; Zheng, H.; Zheng, J.
- International Journal of Plasticity, Vol. 90
A non-coaxial critical-state model for sand accounting for fabric anisotropy and fabric evolution
journal, February 2017
- Gao, Zhiwei; Zhao, Jidong
- International Journal of Solids and Structures, Vol. 106-107
Deformation of Rocks under High Confining Pressures: I. Experiments at Room Temperature
journal, July 1936
- Griggs, David T.
- The Journal of Geology, Vol. 44, Issue 5
A Variational Principle of Maximum Plastic work in Classical Plasticity
journal, January 1948
- Hill, R.
- The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 1, Issue 1
Strength differential effect in age hardened aluminum alloys
journal, December 2017
- Holmen, Jens Kristian; Frodal, Bjørn Håkon; Hopperstad, Odd Sture
- International Journal of Plasticity, Vol. 99
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
journal, August 2016
- Homel, Michael A.; Herbold, Eric B.
- International Journal for Numerical Methods in Engineering, Vol. 109, Issue 7
A constitutive model for orthotropic elasto-plasticity at large strains
journal, October 2004
- Itskov, M.; Aksel, N.
- Archive of Applied Mechanics, Vol. 74, Issue 1-2
Identification of material parameters for Drucker–Prager plasticity model for FRP confined circular concrete columns
journal, February 2012
- Jiang, Jia-Fei; Wu, Yu-Fei
- International Journal of Solids and Structures, Vol. 49, Issue 3-4
Anisotropic three-dimensional behavior of a normally consolidated clay
journal, October 1993
- Kirkgard, M. M.; Lade, P. V.
- Canadian Geotechnical Journal, Vol. 30, Issue 5
Stress-induced anisotropy in granular materials: fabric, stiffness, and permeability
journal, June 2015
- Kuhn, Matthew R.; Sun, WaiChing; Wang, Qi
- Acta Geotechnica, Vol. 10, Issue 4
A constitutive model of frozen saline sandy soil based on energy dissipation theory
journal, March 2016
- Lai, Yuanming; Liao, Mengke; Hu, Kai
- International Journal of Plasticity, Vol. 78
Elastic-Plastic Deformation at Finite Strains
journal, March 1969
- Lee, E. H.
- Journal of Applied Mechanics, Vol. 36, Issue 1
Anisotropic Critical State Theory: Role of Fabric
journal, March 2012
- Li, Xiang Song; Dafalias, Yannis F.
- Journal of Engineering Mechanics, Vol. 138, Issue 3
Numerical investigation of granular material behaviour under rotational shear
journal, May 2010
- Li, X.; Yu, H. -S.
- Géotechnique, Vol. 60, Issue 5
A nonlocal multiscale discrete-continuum model for predicting mechanical behavior of granular materials: A NONLOCAL MULTISCALE DISCRETE-CONTINUUM MODEL FOR GRANULAR MATERIALS
journal, November 2015
- Liu, Yang; Sun, WaiChing; Yuan, Zifeng
- International Journal for Numerical Methods in Engineering, Vol. 106, Issue 2
Nonlinear tensor functions of several tensor arguments
journal, January 1963
- Lokhin, V. V.; Sedov, L. I.
- Journal of Applied Mathematics and Mechanics, Vol. 27, Issue 3
On the effects of plastic rotation in the finite deformation of anisotropic elastoplastic materials
journal, December 1983
- Loret, B.
- Mechanics of Materials, Vol. 2, Issue 4
Anisotropic yield function based on stress invariants for BCC and FCC metals and its extension to ductile fracture criterion
journal, February 2018
- Lou, Yanshan; Yoon, Jeong Whan
- International Journal of Plasticity, Vol. 101
A maximum-dissipation principle in generalized plasticity
journal, September 1984
- Lubliner, J.
- Acta Mechanica, Vol. 52, Issue 3-4
Analysis of layered wooden shells using an orthotropic elasto-plastic model for multi-axial loading of clear spruce wood
journal, June 2005
- Mackenzie-Helnwein, Peter; Müllner, Herbert W.; Eberhardsteiner, Josef
- Computer Methods in Applied Mechanics and Engineering, Vol. 194, Issue 21-24
Eshelby stress in elastoplasticity and ductile fracture
journal, January 1994
- Maugin, Gérard A.
- International Journal of Plasticity, Vol. 10, Issue 4
On the spatial formulation of anisotropic multiplicative elasto-plasticity
journal, August 2003
- Menzel, A.; Steinmann, P.
- Computer Methods in Applied Mechanics and Engineering, Vol. 192, Issue 31-32
Exponential map Algorithm for Stress Updates in Anisotropic Multiplicative Elastoplasticity for Single Crystals
journal, October 1996
- Miehe, C.
- International Journal for Numerical Methods in Engineering, Vol. 39, Issue 19
A constitutive frame of elastoplasticity at large strains based on the notion of a plastic metric
journal, October 1998
- Miehe, Christian
- International Journal of Solids and Structures, Vol. 35, Issue 30
A robust algorithm for configurational-force-driven brittle crack propagation with R-adaptive mesh alignment
journal, January 2007
- Miehe, C.; Gürses, E.
- International Journal for Numerical Methods in Engineering, Vol. 72, Issue 2
Laboratory investigation of the mechanical behaviour of Tournemire shale
journal, January 1997
- Niandou, H.; Shao, J. F.; Henry, J. P.
- International Journal of Rock Mechanics and Mining Sciences, Vol. 34, Issue 1
Yield Function for Soil with Anisotropic Fabric
journal, January 1989
- Oda, Masanobu; Nakayama, Hideo
- Journal of Engineering Mechanics, Vol. 115, Issue 1
Definition of a general implicit orthotropic yield criterion
journal, February 2003
- Oller, Sergio; Car, Eduardo; Lubliner, Jacob
- Computer Methods in Applied Mechanics and Engineering, Vol. 192, Issue 7-8
Anisotropic finite plasticity based on structural tensors—different strategies and application to forming simulations
journal, August 2009
- Reese, S.; Pietryga, M. P.; Vladimirov, I. N.
- International Journal of Material Forming, Vol. 2, Issue S1
A Nonlocal Phenomenological Anisotropic Finite Deformation Plasticity Model Accounting for Dislocation Defects
journal, June 2002
- Regueiro, Richard A.; Bammann, Douglas J.; Marin, Esteban B.
- Journal of Engineering Materials and Technology, Vol. 124, Issue 3
Implicit dynamic three-dimensional finite element analysis of an inelastic biphasic mixture at finite strain
journal, June 2010
- Regueiro, R. A.; Ebrahimi, D.
- Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 29-32
On a formulation for anisotropic elastoplasticity at finite strains invariant with respect to the intermediate configuration
journal, November 2007
- Sansour, Carlo; Karšaj, Igor; Sorić, Jurica
- Journal of the Mechanics and Physics of Solids, Vol. 55, Issue 11
A formulation of anisotropic continuum elastoplasticity at finite strains. Part I: Modelling
journal, December 2006
- Sansour, C.; Karsaj, I.; Soric, J.
- International Journal of Plasticity, Vol. 22, Issue 12
Thermoplasticity and strain localization in transversely isotropic materials based on anisotropic critical state plasticity: THERMOPLASTICITY AND STRAIN LOCALIZATION
journal, May 2016
- Semnani, Shabnam J.; White, Joshua A.; Borja, Ronaldo I.
- International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 40, Issue 18
Approximate macroscopic yield criteria for Drucker-Prager type solids with spheroidal voids
journal, December 2017
- Shen, W. Q.; Zhang, J.; Shao, J. F.
- International Journal of Plasticity, Vol. 99
A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition: Part I. Continuum formulation
journal, February 1988
- Simo, J. C.
- Computer Methods in Applied Mechanics and Engineering, Vol. 66, Issue 2
The anisotropic tensors
journal, January 1957
- Smith, G. F.; Rivlin, R. S.
- Quarterly of Applied Mathematics, Vol. 15, Issue 3
On the modelling of anisotropic elastic and inelastic material behaviour at large deformation
journal, December 2001
- Svendsen, Bob
- International Journal of Solids and Structures, Vol. 38, Issue 52
Application of the concept of evolving structure tensors to the modeling of initial and induced anisotropy at large deformation
journal, June 2006
- Svendsen, B.; Levkovitch, V.; Wang, J.
- Computers & Structures, Vol. 84, Issue 17-18
Generalized radial-return mapping algorithm for anisotropic von Mises plasticity framed in material eigenspace: Generalized radial-return mapping algorithm
journal, August 2018
- Versino, Daniele; Bennett, Kane C.
- International Journal for Numerical Methods in Engineering, Vol. 116, Issue 3
Anisotropic finite elastoplasticity with nonlinear kinematic and isotropic hardening and application to sheet metal forming
journal, May 2010
- Vladimirov, Ivaylo N.; Pietryga, Michael P.; Reese, Stefanie
- International Journal of Plasticity, Vol. 26, Issue 5
A thermomechanical anisotropic continuum model for geological materials with multiple joint sets: A thermomechanical anisotropic continuum model for geological materials with multiple joint sets
journal, May 2018
- Vorobiev, O. Yu.; Rubin, M. B.
- International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 42, Issue 12
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
journal, January 1970
- Wang, C. -C.
- Archive for Rational Mechanics and Analysis, Vol. 36, Issue 3
Evolution of Various Fabric Tensors for Granular Media toward the Critical State
journal, October 2017
- Wang, Rui; Fu, Pengcheng; Zhang, Jian-Min
- Journal of Engineering Mechanics, Vol. 143, Issue 10
Coupled Axisymmetric Thermo-Poro-Mechanical Finite Element Analysis of Energy Foundation Centrifuge Experiments in Partially Saturated Silt
journal, July 2014
- Wang, W.; Regueiro, R. A.; McCartney, J. S.
- Geotechnical and Geological Engineering, Vol. 33, Issue 2
A semi-implicit discrete-continuum coupling method for porous media based on the effective stress principle at finite strain
journal, June 2016
- Wang, Kun; Sun, WaiChing
- Computer Methods in Applied Mechanics and Engineering, Vol. 304
A multiscale multi-permeability poroplasticity model linked by recursive homogenizations and deep learning
journal, June 2018
- Wang, Kun; Sun, WaiChing
- Computer Methods in Applied Mechanics and Engineering, Vol. 334
Theory of Representations for Tensor Functions—A Unified Invariant Approach to Constitutive Equations
journal, November 1994
- Zheng, Q. -S.
- Applied Mechanics Reviews, Vol. 47, Issue 11
A micromechanics-based elastoplastic damage model for granular materials at low confining pressure
journal, April 2010
- Zhu, Q. Z.; Shao, J. F.; Mainguy, M.
- International Journal of Plasticity, Vol. 26, Issue 4
An alternative model for anisotropic elasticity based on fabric tensors
journal, November 1995
- Zysset, P. K.; Curnier, A.
- Mechanics of Materials, Vol. 21, Issue 4
Works referencing / citing this record:
An energy approach to Modified Cam-Clay plasticity and damage modeling of cohesive soils
journal, November 2019
- Bennett, Kane C.
- Acta Geotechnica, Vol. 15, Issue 1
Generalized radial-return mapping algorithm for anisotropic von Mises plasticity framed in material eigenspace: Generalized radial-return mapping algorithm
journal, August 2018
- Versino, Daniele; Bennett, Kane C.
- International Journal for Numerical Methods in Engineering, Vol. 116, Issue 3
Boundary element analysis of transversely isotropic bi‐material halfspaces with inclined planes of isotropy and interfaces
journal, August 2019
- Xiao, Sha; Yue, Zhongqi Quentin; Xiao, Hongtian
- International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 43, Issue 17