zbMATH — the first resource for mathematics

A coupled theory of damage mechanics and finite strain elasto-plasticity. II: Damage and finite strain plasticity. (English) Zbl 0728.73039
Summary: A constitutive model is formulated her for anisotropic continuum damage mechanics using finite strain plasticity. The formulation is given in spatial coordinates (Eulerian reference frame) and incorporates both isotropic and kinematic hardening. The von Mises yield criterion is modified to include the effects of damage through the use of the hypothesis of elastic energy equivalence. A modified elasto-plastic stiffness tensor that includes the effects of damage is derived within the framework of the proposed model. Numerical implementation of the proposed model includes the finite element formulation where an Updated Lagrangian description is used. The basic example of finite simple shear is solved. The problem of crack initiation is also solved for a thin elasto-plastic plate with a center crack that is subjected to inplane tension. This problem is solved in the companion paper using the coupled theory of elasticity with damage [part I, see the foregoing entry (Zbl 0728.73038)].

74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74C20 Large-strain, rate-dependent theories of plasticity
74R99 Fracture and damage
74S05 Finite element methods applied to problems in solid mechanics
74A20 Theory of constitutive functions in solid mechanics
74C99 Plastic materials, materials of stress-rate and internal-variable type
74E10 Anisotropy in solid mechanics
Full Text: DOI
[1] Lee, E.H.; Mallet, R.L.; Wertheimer, T.B., Stress analysis for anisotropic hardening in finite-deformation plasticity, Trans. ASME, J. appl. mech., 50, 554-560, (1983) · Zbl 0524.73046
[2] Defalias, Y.F., Corotational rates for kinematic hardening at large plastic deformations, Trans. ASME J appl. mech., 50, 561-565, (1983) · Zbl 0524.73047
[3] Onat, E.T., Shear flow of kinematically hardening rigid-plastic materials, (), 311-324
[4] Onat, E.T., Representation of inelastic behaviour in the presence of anisotropy and of finite deformations, (), 231-264
[5] Dafalias, Y.F., A missing link in the macroscopic constitutive formulation of large plastic deformations, (), 135-151
[6] Loret, B., On the effects of plastic rotation in the deformation of anisotropic elastoplastic materials, Mech. mater., 2, 287-304, (1983)
[7] Mandel, J., Relations de comportement des milieux elastiques-plastiques et elastiques-viscoplasticuqes, notion de repere directeur, (), 387-400
[8] Mandel, J., Director vectors and constitutive equations for plastic and viscoplastic media, (), 135-143
[9] Onat, E.T.; Leckie, F.A., Representation of mechanical behaviour in the presence of changing internal structure, J. appl. mech., 55, 1-10, (1988)
[10] Murakami, S.; Ohmo, N., A continuum theory of creep and creep damage, (), 422-444
[11] Leckie, F.A.; Onat, E.T., Tensorial nature of damage measuring internal variables, (), 140-155
[12] Fardshisheh, F.; Onat, E.T., Representation of elastoplastic behaviour by means of state variables, (), 89-115 · Zbl 0273.73025
[13] Geary, J.A.; Onat, E.T., Representation of nonlinear hereditary mechanical behaviour, Oak ridge national laboratory report, ORNL-TM-4525, (1974)
[14] Chaboche, J.L., Le concept de constrainte effective applique a l’elasticite et a la viscoplasticite en presence d’un endommagemment anisotrope, (), 738-759, (in French).
[15] Pecherski, R.B., Discussion of sufficient condition of plastic flow localization, (), 767-779
[16] Paulun, J.E.; Pecherski, R.B., Study of corotational rates for kinematic hardening in finite deformation plasticity, Arch. mech., 37, 6, 661-677, (1985) · Zbl 0593.73040
[17] Atluri, S.N., On constitutive relations at finite strain: hypoelasticity and elasto-plasticity with isotropic or kinematic hardening, Comput. meth. appl. mech. engng, 43, 137-171, (1984) · Zbl 0571.73001
[18] Johnson, G.C.; Bammann, D.J., A discussion of stress rates in finite deformation problems, Int. J. solids struct., 2, 8, 725-737, (1984) · Zbl 0546.73031
[19] Fressengeas, C.; Molinari, A., Representations de comportement plastique anisotrope aux grandes deformations, Arch. mech., 36, (1984) · Zbl 0568.73046
[20] Moss, W.C., On instabilities in large deformation simple shear loading, Comput. meth. appl. mech. engng, 46, 329-338, (1984) · Zbl 0549.73027
[21] Simo, J.C.; Pister, K.S., Remarks on rate constitutive equations for finite deformation problems: computational implications, Comput. meth. appl. mech. engng, 46, 201-215, (1984) · Zbl 0525.73042
[22] Voyiadjis, G.Z., Experimental determination of the material parameters of elasto-plastic work-hardening metal alloys, Mater. sci. engng J., 62, 1, 99-107, (1984)
[23] Voyiadjis, G.J.; Kiousis, P.D., Stress rate and the Lagrangian formulation of the finite-strain plasticity for a von Mises kinematic hardening model, Int. J. solids struct., 23, 1, 95-109, (1987) · Zbl 0601.73047
[24] (), 111
[25] Murakami, S., Mechanical modelling of material damage, J. appl. mech., 55, 280-286, (1988)
[26] Voyiadjis, G.Z.; Kattan, P.I., Eulerian constitutive model for finite strain plasticity with anisotropic hardening, Mech. mater. int. J., 7, 4, 279-293, (1989)
[27] Sidoroff, F., Description of anisotropic damage application to elasticity, (), 237-244
[28] Lee, H.; Peng, K.; Wang, J., An anisotropic damage criterion for deformation instability and its applications to forming limit analysis of metal plates, Eng. fract. mech., 21, 1031-1054, (1985)
[29] Nemat-Nasser, S., Decomposition of strain measures and their rates in finite deformation elasto-plasticity, Int. J. solids struct., 15, 155-166, (1979) · Zbl 0391.73033
[30] Lee, E.H., Some comments on elasto-plastic analysis, Int. J. solids struct., 17, 859-872, (1981) · Zbl 0474.73034
[31] Asaro, R.J., Micromechanics of crystals and polycrystals, Adv. appl. mech., 23, 1-115, (1983)
[32] Ziegler, H., A modification of Prager’s hardening rule, Q. appl. math., 17, 55-65, (1959) · Zbl 0086.18704
[33] Dienes, J.K., On the analysis of rotation and stress rate in deforming bodies, Acta mech., 32, 217-232, (1979) · Zbl 0414.73005
[34] Guo, Zhong-Heng, Time derivatives of tensor fields in nonlinear continuum mechanics, Arch. mech. stos., 1, 15, 131-163, (1963) · Zbl 0116.15604
[35] Zhong-Heng, Guo; Dubey, R.H., Spins in a deforming continuum, S.M. archives, 9, 53-61, (1984) · Zbl 0546.73002
[36] Yano, K., The theory of Lie derivatives and its applications, (1957), North-Holland Amsterdam · Zbl 0077.15802
[37] Kattan, P.I.; Voyiadjis, G.Z., A coupled theory of damage mechanics and finite strain elasto-plasticity. —I. damage and elastic deformations, Int. J. engng sci., 28, 5, 421-435, (1990) · Zbl 0728.73038
[38] Kienkiewicz, O.C., The finite element method, (1977), McGraw-Hill New York
[39] Zienkiewicz, O.C.; Morgan, K., Finite elements and approximation, (1983), Wiley New York · Zbl 0582.65068
[40] Chow, C.L.; Wang, J., A finite element analysis of continuum damage mechanics for ductile fracture, Int. J. fract., 38, 83-102, (1988)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.