Abstract
AbstractWe introduce a model for elastoplasticity at finite strains coupled with damage. The internal energy of the deformed elastoplastic body depends on the deformation, the plastic strain, and the unidirectional isotropic damage. The main novelty is a dissipation distance allowing the description of coupled dissipative behavior of damage and plastic strain. Moving from time‐discretization, we prove the existence of energetic solutions to the quasistatic evolution problem.
Highlights
Failure in ductile materials, such as metals or polymers, proceeds from the initiation of micro-defects, followed by their diffuse growth accompanied by large irreversible deformations, up to the formation of localized macroscopic cracks
We introduce a model for elastoplasticity at finite strains coupled with damage
The internal energy of the deformed elastoplastic body depends on the deformation, the plastic strain, and the unidirectional isotropic damage
Summary
Failure in ductile materials, such as metals or polymers, proceeds from the initiation of micro-defects, followed by their diffuse growth accompanied by large irreversible deformations, up to the formation of localized macroscopic cracks. We consider rate-independent evolution of the energy coupled with a dissipation distance between internal states given by (P , z, P, ẑ) = ∫Ω D(P (x), z(x), P(x), ẑ(x)) dx The latter depends on the joint behavior of plastic strain and damage. To prove this result we apply a standard time-discretization scheme introduced by MIELKE and co-workers.[38,41] This scheme has shown to be very successful in order to achieve existence of energetic solution to rate-independent systems It is versatile, as it has been employed in many different settings, like in problems of nonlinear plasticity (e.g., [34,39]), damage,[40,50,51] cracks growth
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