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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)].

MSC:
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
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