Abstract
A new nonlocal plasticity model, which is based on the integral-type nonlocal model and the cubic representative volumetric element (RVE), is proposed to simulate shear band localization in geotechnical materials such as soils and rocks. An algorithm is developed to solve the resulting nonlinear system of equations. In this algorithm, the nonlocal averaging of plastic strain over the RVE is evaluated using C0 elements instead of using C1 elements to solve the second-order gradient of plastic strains. To obtain the average plastic strain, a set of special elements, called the nonlocal elements, are constructed to approximate the RVE. The updating of average stresses of the local element is based on the nonlocal plastic strain of the corresponding nonlocal elements. Numerical examples show that mesh-independent results can be achieved using the proposed model and the algorithm, and the thickness of the shear band is insensitive to the mesh refinement.
Article PDF
Similar content being viewed by others
References
V. Tvergarrd, A. Needleman, K.K. Lo, Finite element analysis of localization in plasticity. In: J. T. Oden, G.F. Carey, eds., Finite Elements-Special problems in Solid Mechanics, Vol. 5 Prentice Hall, Englewood Cliffs, NJ, 1983: 94-157.
M. Ortiz, Y. Leroy, A. Needleman, A finite element method for localized failure analysis, Computer Methods in Applied Mechanics and Engineering, 1987, 61(2): 189–214.
H.E. Read, G.A. Hegemier, Strain softening of rock, soil and concrete-a review article, Mechanics and Materials, 1984, 27(3): 271–294.
J.P. Bardet, A comprehensive review of strain localization in elastoplastic soils, Computers and Geotechnics, 1990, 10(3): 163–188.
A. Needleman, Computational modeling of material failure, Applied Mechanics Review, 1994, 47(6): S34–S42.
Y. Tomita, Simulation of plastic instabilities in solid mechanics, Applied Mechanics Reviews, 1994, 47(6): 171–205.
R. de Borst, Some recent issues in computational failure mechanics, International Journal for Numerical Methods in Engineering, 2001, 52(1-2): 63–95.
R. de Borst, L.J. Sluys, H.B. Mös, et al., Fundamental issues in finite element analyses of localization of deformation, Engineering Computations, 1993, 10(2): 99–121.
A. Needleman, M. Ortiz, Effect of boundaries and interfaces on shear-band localization, International Journal of Solids and Structures, 1991, 28(7): 859–877.
R.I. Borja, R.A. Regueiro, Strain localization in frictional materials exhibiting displacement jumps, Computer Methods in Applied Mechanics and Engineering, 2001, 190(20-21): 2555–2580.
D. Schaeffer, Instability and ill-posedness in the deformation of granular materials, International Journal of Numerical and Analytical Methods in Geomechanics, 1990, 14(4): 253–278.
I. Vardoulakis, J. Sulem, Bifurcation Analysis in Geomechanics, London: Blackie Academic and Professional (Chapman & Hall), 1995.
R.A. Toupin, Elastic materials with couple-stresses, Archive for Rational Mechanics and Analysis, 1962, 11(1): 385–414.
R.D. Mindlin, Micro-structure in linear elasticity, Archive for Rational Mechanics and Analysis, 1964, 16(1): 51–78.
E.C. Aifantis, Gradient deformation models at nano, micro, and macro scales, Journal of Engineering Materials and Technology, 1999, 121(2): 189–202.
E.C. Aifantis, On the role of gradients in the localization of deformation and fracture, International Journal of Engineering Science, 1992, 30(10): 1279–1299.
H.B. Mös, E.C. Aifantis, A variational principle for gradient plasticity, International Journal of Solids and Structures, 1991, 28(7): 845–857.
A.C. Eringen, Vistas of nonlocal continuum physics, International Journal of Engineering Science, 1992, 30(10), 1551–1565.
A.C. Eringen, Theory of nonlocal plasticity, International Journal of Engineering Science, 1983, 21(7), 741–751.
Z.P. Bažant, F.B. Lin, Nonlocal smeared cracking model for concrete fracture, Journal of Structural Engineering, 1988, 114(11), 2493–2510.
Z.P. Bažant, Imbricate continuum and its variational derivation, Journal of Engineering Mechanics, 1984, 110(12), 1693–1712.
Z.P. Bažant, T.P. Chang, Nonlocal finite element analysis of strain softening solids, Journal of Engineering Mechanics, 1987, 113(1), 89–105.
Z.P. Bažant, M. Jirásek, Nonlocal integral formulations of plasticity and damage: Survey and progress, Journal of Engineering Mechanics, 2002, 128(11), 1119–1149.
R. de Borst, H.B. Mös, Gradient-dependent plasticity: Formulation and algorithm aspects, International Journal for Numerical Methods in Engineering, 1992, 35, 521–539.
R. de Borst, J. Pamin, Some novel developments in finite element procedures for gradient-dependent plasticity, International Journal for Numerical Methods in Engineering, 1996, 39(14), 2477–2505.
M. Jirasek, Z.P. Bažant, Inelastic Analysis of Structures, London and New York: Wiley & Sons, 2002.
R.H.J. Peerlings, M.G.D. Geers, R. de Borst, et al., A critical comparison of nonlocal and gradient-enhanced softening continua, International Journal of Solids and Structures, 2001, 38, 7723–7746.
I. Vardoulakis, The 2nd gradient flow theory of plasticity, In: F. Darve, I. Vardoulakis, eds., Degradations and Instabilities in Geomaterials, Chapter 5, CISM, DIGA-sponsored Course, Springer, 2004.
J.C. Simo, T.J.R. Hughes, Computational Inelasticity, New York: Springer-Verlag, 1998.
W. Han, B.D. Reddy, Plasticity: Mathematical Theory and Numerical Analysis, London: Springer, 1999.
S. Ramaswamy, N. Aravas, Finite element implementation of gradient plasticity models Part I: Gradient-dependent yield functions, Computer Methods in Applied Mechanics and Engineering, 1998, 163(1-4): 11–32.
S. Ramaswamy, N. Aravas, Finite element implementation of gradient plasticity models Part II: Gradient-dependent evolution equations, Computer Methods in Applied Mechanics and Engineering, 1998, 163(1-4): 33–35.
S. Wu, X. Wang, Comparison of boundary conditions of gradient elasticity and gradient plasticity, In: Inaugural International Conference of the Engineering Mechanics Institute, University of Minnesota, Minneapolis, Minnesota, 2008, May 18-21.
W.C. Rheinboldt, Methods for Solving Systems of Nonlinear Equations, Philadelphia: Society for Industrial and Applied Mathematics, 1998.
D.R.J. Owen, E. Hinton, Finite Elements in Plasticity: Theory and Practice, Swansea, U.K.: Pineridge Press Limited, 1980.
S. Wu, X. Wang, Mesh Dependence and Nonlocal Regularization of One-Dimensional Strain Softening Plasticity, Journal of Engineering Mechanics, 2010, 136(11), 1354–1365.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wu, S., Wang, X. Numerical simulation of shear band localization in geotechnical materials based on a nonlocal plasticity model. J. Mod. Transport. 19, 186–198 (2011). https://doi.org/10.1007/BF03325758
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03325758