The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models

By K. Pham, Jean-Jacques Marigo, C. Maurini. 2011

195 citations recorded by the source corpus.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/af6db04371c94b4c530446dcb9ebd6007e4fd569

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Comparison of Phase-Field Models of Fracture Coupled with Plasticity (2018, background): “Such material bifurcation, associated to the choice of an “intermediate” bar length, is very well investigated and explained in [19].”
On the choice of parameters in the phase field method for simulating crack initiation with experimental validation (2016, background): “Analyses leading to similar relationships can also be found in [19,5, 7,31].”
From the onset of damage to rupture: construction of responses with damage localization for a general class of gradient damage models (2013, methodology): “The goal of the present paper is to extend the results of Benallal and Marigo (2007) and to complete those of Pham et al. (2011a) for a large class of elastic-softening material.”
Phase-field modeling of anisotropic brittle fracture including several damage mechanisms (2018, unknown): “The issue of true stability and non-uniqueness of solutions for the evolution problem are obviously still present in this framework and we refer to [48] for more details on the matter.”
Crack nucleation in variational phase-field models of brittle fracture (2018, unknown): “Comparison between numerical simulations with the AT 1 and AT 2 models and damaged and undamaged boundary conditions on the notch edges with experiments in steel from Strandberg (2002) (left), and Duraluminium (middle) and PMMA (right) from Seweryn (1994) .”
An overview of the modelling of fracture by gradient damage models (2016, unknown): “After some calculations which are not reproduced here (see [9] or [42]), the infimum of the Rayleigh ratio (41) is given by”
Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples (2017, unknown): “As will be shown in the next section, since # ′(0) > 0 , see [60] , all these choices will imply an initial purely elastic stage in the response, noted as ( E ).”