Viscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model

Abstract

Abstract. Employing the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions for elastoplastic materials with incomplete damage affecting both the elastic tensor and the plastic yield surface, in a softening framework and in small strain assumptions.

Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples

“…The discussion of the role of the constitutive assumptions on the emerging macroscopic behaviours shows that damage and plastic localisations may interact to produce cohesive-like cracks. This result has been confirmed through rigorous asymptotic analysis in [29,30,32], showing the convergence of a special case of the model presented in [4] to a cohesive sharp crack model. References [28] and [37] recently proposed an alternative interesting phase-field model of cohesive fracture without introducing plastic effects.…”

Globally stable quasistatic evolution for strain gradient plasticity coupled with damage

“…This is an improvement with respect to the elastoplastic-damage models in [8] and [9]: the strong damage regularizations therein (respectively W 1,γ , γ > n, and H m , m > n 2 ) permitted us to work with a continuous field α (see also e.g. [23], with H m regularization), and therefore to use Reshetnyak's Theorem for the plastic dissipation.…”

“…The proof exploits also tools from the theory of capacity. As in [8] and in [9] the plastic dissipation corresponding to an evolution of α and p in a time interval [s, t] is the H-variation of p with respect to α on [s, t], namely…”

“…We show an analogous convergence of the quasistatic evolutions for the present model to evolutions for the coupled elastoplastic damage model proposed in [8], which corresponds to the perfect plasticity for heterogeneous materials studied in [33] when the damage is constant in time. However, we have to consider a stronger (gradient) damage regularization for the Gurtin-Anand model with damage, since in [8] (and [9]) the space continuity of α is needed. An important difference with respect to the analysis in [16] relies on the fact that we cannot still characterize the global stability in the limit model by the equilibrium conditions for the Cauchy stress and the plastic constraint (cf.…”

“…material's degradation, on the other hand the dislocation density affects the damage growth. The coupling between plasticity and damage is also investigated for instance in [2] and in [8], [9], by models that do not include plastic strain derivatives. The inclusion of such terms in the formulation permits to describe size effects.…”