Damage model for plastic materials at finite strains

Abstract

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. 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.

A finite-strain model for incomplete damage in elastoplastic materials

“…As shown in [44], as the time step size τ tends to zero, incremental solutions converge to trajectories fulfilling the energy balance for all time, as well as a so-called global stability condition. These two properties qualify such time continuous trajectories as energetic solutions [50,53] of the quasistatic evolution problem.…”

“…In the quasistatic setting, the problem can be regularized by augmenting the energy by second-length-scale terms featuring gradients of the internal variables. This would guarantee strong compactness of the internal states P and z and would allow to show existence of suitable weak solutions, see [44]. In order to move in this direction, one has to replace X and ξ by…”

“…A first existence result for the coupled quasistatic evolution for finite elastoplasticity and damage has been recently obtained in [44]. The aim of this paper is to elucidate the mechanical basis of such model and present a suite of numerical simulations.…”

“…The material constitutive model is then obtained from the balance of conservative and dissipative forces as ∂ (F ,P ,z) W (F , P , z) + ∂ ( Ḟ , Ṗ , ż) R(P , z, Ṗ , ż) 0, see Subsection 1.5. This balance embodies the variational structure of the model, which in turn yields thermodynamical consistency, see Subsection 1.4, and allows for a comprehensive mathematical treatment [44]. The potentials R z and R p are positively 1-homogeneous in the rate variables, so that the constitutive model is of rate-independent type [50], as it is often assumed in damage and plasticity.…”

A lower semicontinuity result for linearised elasto-plasticity coupled with damage in $W^{1,γ}$, $γ>1$

“…In the quasi-static setting we mention [18,20,22] for the case of perfect plasticity and [19] for a strain-gradient plasticity model; the case of hardening for plasticity is treated in [13,46,48], while in [47] the possible presence of damage healing is taken into account. We additionally refer to [37] for the study of finite-strain plasticity with damage, to [27] for perfect plasticity in viscoelastic solids in the dynamical setting, and to [45] for thermo-viscoplasticity.…”