Comparison of Phase-Field Models of Fracture Coupled with Plasticity

Abstract

In the last few years several authors have proposed different phasefield models aimed at describing ductile fracture phenomena. Most of these models fall within the class of variational approaches to fracture proposed by Francfort and Marigo [13]. For the case of brittle materials, the key concept due to Griffith consists in viewing crack growth as the result of a competition between bulk elastic energy and surface energy. For ductile materials, however, an additional contribution to the energy dissipation is present and is related to plastic deformations. Of crucial importance for the performance of the modeling approaches is the way the coupling is realized between plasticity and phase field evolution. Our aim is a critical revision of the main constitutive choices underlying the available models and a comparative study of the resulting predictive capabilities.

Damage model for plastic materials at finite strains

“…In the current work, we prove the existence of an energetic solution to models of incomplete damage coupled with gradient plasticity at finite strains, under structural assumptions that comply with contemporary engineering models . More specifically, we consider an elastoplastic body subjected to a deformation .…”

“…[29] Later on, ALESSI et al [2][3][4] developed its non-local extension by including gradients of a damage variable into the stored energy, in the spirit of variational models for regularized brittle fracture and gradient damage developed in the mathematical, e.g., [9,10,24,40] and engineering, e.g., [22,33,44,45] literature. Such enrichment introduces an additional length scale into the energy functional to characterize the regions to which damage localizes; see also [1] for an overview and comparison of available formulations. Very recently, this class of models has been extended to a finite-strain regime independently by AMBATI et al, [5] BORDEN et al, [8] and MIEHE et al [35] The last formulation involves additional regularization with gradients of plastic strains to control the localization of permanent strains, too.…”

“…In the current work, we prove the existence of an energetic solution to models of incomplete damage coupled with gradient plasticity at finite strains, under structural assumptions that comply with contemporary engineering models. [1] More specifically, we consider an elastoplastic body Ω ⊂ ℝ subjected to a deformation ∶ Ω → ℝ . In nonlinear plasticity it is commonly assumed that the deformation gradient ∇ complies for the multiplicative decomposition ∇ = where ∶ Ω → ℝ × and ∶ Ω → ( ) stand for the elastic and plastic strains.…”

Phase-field approximation for a class of cohesive fracture energies with an activation threshold

“…In Theorem 4.2 we may assume also J u k Ω, by [31,Remark 6.3], in turn using [36]. At this stage, [36,Lemma 5.2] gives that for any p > 1 the n−1 dimensional simplexes in the decomposition of J u may be taken pairwise disjoint and such that also J u ∩Π j ∩Π i = ∅ for any two different hyperplanes Π i , Π j (if p ∈ (1,2] it is enough to employ the capacitary argument in [30,Remark 3.5]). Moreover, we notice that our function (f p )…”

Fatigue Effects in Elastic Materials with Variational Damage Models: A Vanishing Viscosity Approach

“…When the stress level is high enough to induce plastic deformations, the material is usually subjected to a so-called low-cycle fatigue regime; instead, high-cycle fatigue occurs if the stress is below the yield stress such that the strains are primarily elastic. Models where fatigue effects are induced by the cumulation of plastic deformations have been recently studied in [3,4,2,1] and [9,11,12].…”