On the numerical implementation of a finite strain anisotropie damage model based upon the logarithmic rate
Keywords:
Anisotropie damage, Logarithmic strain and rate, Numerical implementationAbstract
We present a fini te strain anisotropie damage madel and show its numerical implementation. Theframework ofXIAO, BRUHNS & MEYERS [XIA 00} is adopted; i.e. strain and stress measures are, respective/y, the logarithmic strain and its work-conjugate stress. Also, a combination of the additive decomposition of the stretching and the multiplicative decomposition of the deformation gradient is used, and the logarithmic rate is usedforall rate constitutive law s. Ta madel the change in mate rial symmetry induced by damage, the damage parameter is regarded as an evolving structural tensor. On the irreversible thermodynamics side, it is treated as an internat state variable. Gurson 's flow potential is used as a micromechanical basis.
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[ANA 86] ANAND L., << Moderate deformations in extension-torsion of incompressible isotropie
elastic materials », Journal of the Mechanics and Physics of Solids, voL 34, n° 3, 1986,
p. 293-304.
[BOE 87] BOEHLER J. P.,<< Representation for isotropie and anisotropie non-polynomial tensor
functions », BOEHLER J. P., Ed., Applications ofTensor Functions in Solid Mechanics,
n° 292 CISM Courses and Lectures, Springer-Verlag, 1987, p. 31-53.
[BRU 99] BRUHNS O. T .. XIAO H., MEYERS A.,<< Self-consistent Eulerian rate type elastoplasticity
models based upon the logarithmic stress rate >>, International Journal of Plasticity,
vol. 15, n° 5, 1999, p. 479-520.
[BUD 76] BUDIANSKY B., O'CONNEL R. 1., << Elastic moduli of a cracked solid >>,International
Journal of Solids and Structures, vol. 12, 1976, p. 81-97.
[COL 63] COLEMAN B. D., NOLL W.,<< The thermodynamics of elastic materials with heat
conduction and viscosity >>, Archive for Rational Mechanics and Analysis, vol. 13, 1963,
p. 167-178.
[COR 79] CORDEBOIS J. P., SIDOROFF F., <>, BOEHLER
J. P., Ed., Mechanical Behavior of Anisotropie Sol ids, n° 295 CNRS, Martinus Nijhoff
Publishers, 1979, p. 761-774.
[DOY 56] DOYLE T. C., ERICKSEN 1. L., Nonlinear Elasticity, W 4 Advances in Applied
Mechanics, Academie Press, New York, 1956.
[GUR 77] GURSON A. L., << Continuum theory of ductile rupture by void nucleation and
growth: Part 1 - Yield criteria and flow rules for porous ductile media >>, Journal of Engineering
Materials and Technology, vol. 99, 1977, p. 2-15.
[HIL 65] HILL R., << A self-consistent mechanics of composite materials >>, Journal of the
Mechanics and Physics of Solids, vol. 13, 1965, p. 213-222.
[HIL 78] HILL R., << Aspects of invariance in solid mechanics >>, YIH C.-S., Ed., Advances
in Applied Mechanics, vol. 18, p. 1-75, Academie Press, New York, 1978.
[JU 90] Ju J. W., << Isotropie and anisotropie damage variables in continuum damage mechanics
», Journal of Engineering Mechanics, vol. 116, n° 12, 1990, p. 2764-2770.
[KAC 58] KACHANOV L. M.,<< On the time to failure under creep conditions», lsw. AN SSSR.
Otd Techn. Nauk, vol. 8, 1958, p. 26-31, Zitat aus Jansson & Stigh (1985).
[KOJ 87] KoJJé M., BATHE K.-J., << The effective-stress-function algorithm for thermoelasto-
plasticity and creep >>, International Journal of Numerical Methods in Engineering,
vol. 24, 1987, p. 1509-1532.
[KRA 89] KRAJCINOVIC D., « Damage Mechanics >>, Mechanics of Mate rials, vol. 8, 1989,
p. 117-197.
[KRA 96] KRAJCINOVIC D., Damage Mechanics, Applied Mathematics and Mechanics,
North-Holland, Amsterdam, 1996.
[KRO 60] KROENER E., « Allgemeine Kontinuumstheorie der Yersetzungen und Eigenspannungen
>>, Archive for Rational Mechanics and Analysis, vol. 4, 1960, p. 273-334.
[LEE 69] LEE E. H., << Elastic-plastic deformation at finite strains >>, Journal of Applied Mechanics,
vol. 36, 1969, p. 1-6.
[LEH 89] LEHMANN T., << Sorne thermodynamical considerations on inelastic deformations
including damage processes »,Acta Mechanica, vol. 79, 1989, p. 1-24.
[LEM 90] LEMAITRE J., CHABOCHE 1.-L., Mechanics of Solid Materials, Cambridge University
Press, Cambridge, 1990.
[LEM 96] LEMAITRE J ., A Course on Damage Mechanics, Springer-Verlag, Berlin, 2 édition,
[MUR 88] MURAKAMI S.,« Mechanical Mode1ing of Materia1 Damage», Journal of Applied
Mechanics, vol. 55, 1988, p. 280-286.
[NAG 90] NAGHDI P. M., « A critical review of the state of finite plasticity », Journal of
Applied Mathematics and Physics (Z4.MP), vol. 41, 1990, p. 315-394.
[OGD 84] OGDEN R. W., Non-linear Elastic Defonnations, Ellis Horwood Limited, Chichester,
[SCH 95] SCHIECK B., STUMPF H., << The appropriate corotational rate, exact formula for
the plastic spin and constitutive mode! for finite elastoplasticity », International Journal of
Solids and Structures, vol. 32, n° 24, 1995, p. 3643-3667.
[SIM 85] SIMO J. C., TAYLOR R. L., « Consistent tangent operators for rate-independent
elastoplasticity », Computer Methods in Applied Mechanics and Engineering, vol. 48,
, p. 101-118.
[SIM 92] SIMO J. C., << Algorithms for static and dynamic multiplicative plasticity that preserve
the classical return mapping schemes of the infinitesimal theory »,Computer Methods
in Applied Mechanics and Engineering, vol. 99, 1992, p. 61-112.
[SIM 98] S!MO J. C., HUGHES T. J. R., Computationallnelasticity, vol. 7 de lnterdisciplinary
Applied Mathematics, Springer, New York, 1998.
[SOU 92] DE SOUZA NETO E., PERlé 0., OWEN D. R. J., << A Computational mode! for
ductile damage at finite strains >>, OWEN D. R. J., 0NATE E., HINTON E., Eds., Computational
Plasticity: Fundamentals and Applications, Pineridge Press, 1992, p. 1425-1441.
[TVE 82] TVERGAARD V., << Ductile fracture by cavity nucleation between larger voids »,
Journal of the Mechanics and Physics ofSolids, vol. 30, n° 4, 1982, p. 265-286.
[XIA 97] XIAO H., BRUHNS O. T., MEYERS A.,<< Logarithmic strain, logarithmic spin and
logarithmic rate», Acta Mechanica, vol. 124, 1997, p. 89-105.
[XIA 98a] XIAO H., BRUHNS O. T., MEYERS A.,<< On objective corotational rates and their
defining spin tensors >>, International Journal of Solids and Structures, vol. 35, n° 30,
, p. 4001-4014.
[XIA 98b] XIAO H., BRUHNS O. T., MEYERS A.,<< Strain rates and material spins>>, Journal
of Elasticity, vol. 52, 1998, p. 1-41.
[XIA 00] XIAO H., BRUHNS O. T., MEYERS A.,« A consistent finite elastoplasticity theory
combining additive and multiplicative decomposition of the stretching and the deformation
gradient>>, International Journal of Plasticity, vol. 16, n° 2, 2000, p. 143-177.
