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Integrity conditions for elastic-plastic damaged solids subjected to cyclic loading. (English) Zbl 1055.74005

Summary: We examine integrity conditions for elastic-plastic, isotropically damaged solids with isotropic and kinematic strain hardening subjected to cyclic loading. It is assumed that the damage process is coupled with plastic deformation. The shakedown conditions are assumed to be satisfied. We derive a new sufficient condition for shakedown accounting for a mixed isotropic and kinematic hardening. The problem of evaluating limit yield-condition arguments is reduced to a minmax problem. In the case of plain strain, the problem is equivalent to a hyperbolic equation. We propose a method for computing the purely elastic damaged response of the solid to a prescribed loading. The limit yield condition with specified arguments makes it possible to obtain upper and lower estimates on local actual limit values of the damage parameter admitted by the yield condition for a given loading. The estimates lead to necessary and sufficient conditions of integrity. The method is illustrated by an example.

MSC:

74A45 Theories of fracture and damage
74R20 Anelastic fracture and damage
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
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