Engineering Transactions, 44, 3-4, pp. 445-469, 1996

On Regularization of Plastic Flow Localization in a Soil Material

M. Lengnick
Universität Hannover, Hannover

T. Łodygowski
Poznań University of Technology, Poznań

P. Perzyna
Institute of Fundamental Technological Research, Warszawa

E. Stein
Universität Hannover, Hannover

Density-dependent critical state line (Cam-Clay type) model is regularized by viscoplastic formulation to assure the mathematical well-posedness of the initial Cauchy problem. In computations this reduces the so-called Primary Mesh Dependence which is defined in the paper. Several numerical examples of two-dimensional plane strain pillar problem confirm the validity of the proposed formulation and its usefulness in numerical calculations.

Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


ABAQUS. Manuals for v. 4.9, Reports, Hibbitt, Karlsson and Sorensen, Inc., 1990.

T. ADACHI and F. OKA, Constitutive equations for normally consolidated clay based on elasto-viscoplasticity, Solids and Foundations, 22, 4, 57-70, 1982.

T. ADACHI, F. OKA and M. MIMURA, Mathematical structure of an overstress elasto-viscoplastic model for clay, Solids and Foundations, 27, 4, 31-42, 1987.

A. BENALLAL, Ill-posedness and localisation in solid structures, [in:] Proc. Third Intern. Conference on Computational Plasticity, Fundamentals and Applications, R.J. OWEN, E. OÑATE and E. HINTON [Eds.], Barcelona, April 6-10, 1992, pp. 483-508, 1992.

R. DE BORST, Fundamental issues in finite element analyses of localization of deformation, Engng. Comp., 10, 99-121, 1993.

A. DRESCHER, Experimental verification of a body with density hardening [in Polish], Engng. Trans., 3, 351-387, 1972.

M.K. DUSZEK and P. PERZYNA, Adiabatic shear band localization in elastic-plastic single crystals, Int. J. Solids Struc., 30, 61-89, 1993.

M.K. DUSZEK-PERZYNA, M. LENGNICK, T. ŁODYGOWSKI, P. PERZYNA and E. STEIN, Thermodynamic theory of elasto-viscoplasticity of geological materials and localization phenomena in dynamic loading processes [in preparation].

G. ENGELN-MÜLLGES and F. REUTER, Formelsammlung zur Numerischen Mathematik mit Standard-FORTRAN 77-Programmen, BI Wissenschaftsverlag, 1988.

M.E. GURTIN, An introduction to continuum mechanics, Academic Press, 1981.

R. HILL, Acceleration waves in solids, J. Mech. Phys. Solids, 10, 1-16, 1962.

T. HUGHES, Numerical implementation of constitutive modeIs: rate-independent deviatoric plasticity, pp. 29-57, Martinus Nijhoff, Boston 1984.

T.J.R. HUGHES, T. KATO and J.E. MARSDEN, Well-posed quasi-linear second­order hyperbolic systems with applications to nonlinear elastodynamics and general relativity, Arch. Rat. Mech. Anal., 63, 273-294, 1977.

T. KATO, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Rational Mech. Anal., 58, 181-205, 1975.

K. KIBLER, M. LENGNICK and T. ŁODYGOWSKI, Selected aspects of the well-posedness of the localized plastic flow processes, CA MES [submitted for publication].

E.H. LEE, Elastic-plastic deformations at finite strains, J. Appl. Mech., 36, 1969.

S. LEROUEIL, M. KOBBAJ, F. TAVENAS and R. BOUCHARD, Stress-strain-strain rate relation for the compressibility of sensitive natural clays, Geotechnique, 35, 159-180, 1985.

T. ŁODYGOWSKI, Mesh-independent beam elements for strain localization, Meth. in Civil Engng., 3, 3, 9-24, 1993.

T. ŁODYG0WSKI, Theoretical and numerical aspects of plastic strain localization, Wyd. Rozprawy Politechniki Poznańskiej, Nr 312, 1996.

T. ŁODYGOWSKI, On avoiding of spurious mesh sensitivity in numerical analysis of plastic strain localization, CAMES, 2, 3, 231-248, 1995.

B. LORET, An introduction to classical theory of elastoplasticity, [in:] Geomaterials: constitutive equations and modelling, F. DARVE (Ed.], pp. 149-186, Elsevier Applied Science, London and New York 1990.

J. MANDEL, Conditions de stabilité et postulat de Drucker, [in:] Rheology and Soil Mechanics, J. KRAVTCHENKO and P.M. SIRIEYS [Eds.], pp. 58-68, Springer, Berlin 1966.

J.C. NAGTEGAAL and F.E. VELDPAUS, On the implementation of finite strain plasticity equations in a numerical model, [in:] Numerical analysis of forming processes, J.F.T. PITMAN, O.C. ZIENKIEWICZ, R.D. WOOD and J.M. ALEXANDER [Eds.], John Wiley and Sons Ltd., 1984.

A. NEEDLEMAN, Material rate dependence and mesh sensitivity in localization problems, Comp. Meth. in Appl. Mech. Engng., 67, 69-85, 1988.

A. NEEDLEMAN and M. ORTIZ, Effect of boundaries and interfaces on shear-band localization, Int. J. Solids Struc., 28, 7, 859-877, 1991.

P. PERZYNA, The constitutive equations for rate sensitive plastic materials, Quart. Appl. Math., 20, 321-332, 1963.

P. PERZYNA, Fundamental problems in viscoplasticity, [in:] Advances in Applied Mechanics, C.-S. YIH [Ed.], 9, pp. 243-377, Academic Press, 1966.

P. PERZYNA, Thermodynamic theory of viscoplasticity, [in:] Advances in Applied Mechanics, 11, pp. 313-354, Academic Press, 1971.

P. PERZYNA, Constitutive equations of dynamics plasticity, [in:] Computational Plasticity, Fundamentals and Applications, D.R.J. OWEN, E. OÑATE and E. HINTON [Eds.], Swansea, Barcelona, April 6-10, 1992, Pineridge Press, pp. 483-508, 1992.

P. PERZYNA, Analysis of the fundamental equations describing thermoplastic flow process in solid body, Arch. Mech., 43, 287-296, 1993.

S. PIETRUSZCZAK and Z. MRÓZ, Numerical analysis of elastic-plastic compression of pillars accounting for material hardening and softening, Int. J. Rock Mech. Min. Sci. Geomech., 17, 199-207, 1980.

J.R. RICE, The localization of plastic deformation, [in:] Theoretical and Applied Mechanics, W.T. KOITER [Ed.], pp. 207-220, North-Holland Publishing Company, 1976.

J.W. RUDNICKI and J.R. RICE, Conditions for the localization of deformations in pressure-sensitive dilatant materials, J. Mech. Phys. of Solids, 23, 371-394, 1975.

L.J. SLUYS, J. BLOCK and R. DE BORST, Wave propagation and localization in viscoplastic media, [in:] Int. Conf. on Comp. Plasticity, Fundamentals and Applications, COMPLAS III, Barcelona, Spain, April 4-9, 1992, E. HINTON D. OWEN, E. OÑATE [Eds.], pp. 539-550, 1992.

E. STEIN, S. OHNIMUS, B. SEIFERT and R. MAHNKEN, Adaptive Finite-Element Diskretisirungen von Flächentragwerken, Bauingenieur [in press], 1993.

F. TAVENAS and S. LEROUEIL, The behaviour of embankments on clay foundations, Canadian Geotech. J., 17, 236-260, 1980.

F. TAVENAS, S. LEROUEIL, P. LA ROCHELLE and M. ROY, Creep behaviour of an undisturbed lightly overconsolidated clay, Canadian Geotech. J., 15, 402-423, 1978.

C. TRUESDELL and W. NOLL, The nonlinear field theories, [in:] Handbuch der Physik, Band III/3, Springer, Berlin, Heidelberg, New York 1965.

D.M. WOOD, Soil behaviour and critical state soil mechanics, Technical Report, Cambridge University Press, 1990.

M. ŻYCZKOWSKI, Combined loadings in the theory of plasticity, PWN, 1981.