Young-Measure Quasi-Static Damage Evolution

Fiaschi, Alice; Knees, Dorothee; Stefanelli, Ulisse

doi:10.1007/s00205-011-0474-3

Cited by 18 publications

(25 citation statements)

References 34 publications

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“…Henceforth, C denotes a suitable constant depending only on γ 1 , γ 2 , r, and on the functions α 0 , e 0 , and w. We immediately deduce that 16) and, from the fact that t → p k (t) is constant on the intervals [t…”

Section: Approximate Solutions Let Us Fix a Sequence Of Subdivisions (Tmentioning

confidence: 93%

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Globally stable quasistatic evolution for a coupled elastoplastic–damage model

Crismale

2016

ESAIM: COCV

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Abstract. We show the existence of globally stable quasistatic evolutions for a rateindependent material model with elastoplasticity and incomplete damage, in small strain assumptions. The main feature of our model is that the scalar internal variable which describes the damage affects both the elastic tensor and the plastic yield surface. It is also possible to require that the history of plastic strain up to the current state influences the future evolution of damage.

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Section: Approximate Solutions Let Us Fix a Sequence Of Subdivisions (Tmentioning

confidence: 93%

“…Models for elastic materials where the bulk energy depends on a scalar damage variable were considered for instance in [18,30,28,4,38,16,37,21,22] (without plasticity). In contrast, in the elastoplastic setting of e.g.…”

Section: Introductionmentioning

confidence: 99%

Globally stable quasistatic evolution for a coupled elastoplastic–damage model

Crismale

2016

ESAIM: COCV

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“…For the analysis of general models for partial, isotropic damage with a rate-independent damage evolution we refer to the works, e.g. [MR06, TM10, Tho13,FKS10] and to the monography [MR15] for an overview on rate-independent processes. The viscous, rate-dependent counterpart is studied e.g.…”

Section: Wwwgamm-mitteilungenorgmentioning

confidence: 99%

Phase‐Field Fracture at Finite Strains Based on Modified Invariants: A Note on its Analysis and Simulations

2018

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Key words Phase-field model for fracture, Ambrosio-Tortorelli, viscous evolution, finite strains, modified invariants MSC (2010) 35K85,74B20,74B20,74R10,74R20We present recent results on the mathematical analysis of phase-field model for anisotropic fracture at finite strains. It is based on a modification of the Ambrosio-Tortorelli model, formulated for polyconvex energy densities in terms of the modified invariants of the right Cauchy-Green strain tensor and augmented by a viscous dissipation for the phase-field variable. A suitable notion of solution is introduced and used for the simulation of a conchoidal fracture in a brittle specimen.

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“…They choose a z-mixture of a linearly elastic strong and weak material with two different elasticity tensors. A non-gradient model for incomplete damage in the framework of Young measures is considered in [19].…”

Section: Introductionmentioning

confidence: 99%

Modeling and analysis of a phase field system for damage and phase separation processes in solids

Kraus

Bonetti

Heinemann

et al. 2015

Journal of Differential Equations

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In this work, we analytically investigate a multi-component system for describing phase separation and damage processes in solids. The model consists of a parabolic diffusion equation of fourth order for the concentration coupled with an elliptic system with material dependent coefficients for the strain tensor and a doubly nonlinear differential inclusion for the damage function. The main aim of this paper is to show existence of weak solutions for the introduced model, where, in contrast to existing damage models in the literature, different elastic properties of damaged and undamaged material are regarded. To prove existence of weak solutions for the introduced model, we start with an approximation system. Then, by passing to the limit, existence results of weak solutions for the proposed model are obtained via suitable variational techniques.

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Young-Measure Quasi-Static Damage Evolution

Cited by 18 publications

References 34 publications

Globally stable quasistatic evolution for a coupled elastoplastic–damage model

Globally stable quasistatic evolution for a coupled elastoplastic–damage model

Phase‐Field Fracture at Finite Strains Based on Modified Invariants: A Note on its Analysis and Simulations

Modeling and analysis of a phase field system for damage and phase separation processes in solids

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