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Related papers: Perfect plasticity versus damage: an unstable inte…

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In this work, we introduce a degenerating PDE system with a time-depending domain for complete damage processes under time-varying Dirichlet boundary conditions. The evolution of the system is described by a doubly nonlinear differential…

Analysis of PDEs · Mathematics 2015-02-20 Christian Heinemann , Christiane Kraus

This work presents a new modeling approach to macroscopic, polycrystalline elasto-plasticity starting from first principles and a few well-defined structural assumptions, incorporating the mildly rate-dependent (viscous) nature of plastic…

Materials Science · Physics 2015-12-21 Filip Rindler

We present a quasi-static elasticity model that accounts for damage evolution based on the ideas of Kachanov 1958 and and Rabotnov 1968. We analyze the resulting strongly nonlinear system of differential equations in view of well-posedness.…

Analysis of PDEs · Mathematics 2022-02-15 Simon Grützner , Adrian Muntean

We consider atomistic systems consisting of interacting particles arranged in atomic lattices whose quasi-static evolution is driven by time-dependent boundary conditions. The interaction of the particles is modeled by classical interaction…

Analysis of PDEs · Mathematics 2022-11-01 Rufat Badal , Manuel Friedrich , Joscha Seutter

In this paper we construct, by means of a variational formulation, the solutions of a problem of elastodynamics which includes the effect of damage for the elastic material. The result is a wave equation with time dependent operators which…

Analysis of PDEs · Mathematics 2020-09-21 Adriana Garroni , Christopher J. Larsen , David Sarrocco

We provide an adaptive finite element approximation for a model of quasi-static crack growth in dimension two. The discrete setting consists of integral functionals that are defined on continuous, piecewise affine functions, where the…

Analysis of PDEs · Mathematics 2025-03-25 Vito Crismale , Manuel Friedrich , Joscha Seutter

The main steps of the proof of the existence result for the quasi-static evolution of cracks in brittle materials, obtained in [7] in the vector case and for a general quasiconvex elastic energy, are presented here under the simplifying…

Analysis of PDEs · Mathematics 2016-09-07 Gianni Dal Maso , Gilles A. Francfort , Rodica Toader

We consider the quasi-static evolution of a brittle layer on a stiff substrate; adhesion between layers is assumed to be elastic. Employing a phase-field approach we obtain the quasi-static evolution as the limit of time-discrete evolutions…

Analysis of PDEs · Mathematics 2019-10-28 Matteo Negri

A heterogeneous quasi-brittle granular material can withstand certain levels of internal damage before global failure. This robustness depends not just on the bond strengths but also on the topology and redundancy of the bonded contact…

Soft Condensed Matter · Physics 2018-09-06 Antoinette Tordesillas , Sanath Kahagalage , Charl Ras , Michał Nitka , Jacek Tejchman

We use numerical simulations to study the dynamics of dense assemblies of self-propelled particles in the limit of extremely large, but finite, persistence times. In this limit, the system evolves intermittently between mechanical…

Soft Condensed Matter · Physics 2023-06-09 Yann-Edwin Keta , Rituparno Mandal , Peter Sollich , Robert L. Jack , Ludovic Berthier

We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the…

Analysis of PDEs · Mathematics 2007-05-23 Gianni Dal Maso , Antonio DeSimone , Maria Giovanna Mora , Massimiliano Morini

A non-equilibrium theory of isothermal and diffusionless evolution of incoherent interfaces within a plastically deforming solid is developed. The irreversible dynamics of the interface are driven by its normal motion, incoherency (slip and…

Materials Science · Physics 2015-06-03 Anurag Gupta , David Steigmann

We prove a linearization result for quasistatic fracture evolution in nonlinear elasticity. As the stiffness of the material tends to infinity, we show that rescaled displacement fields and their associated crack sets converge to a solution…

Analysis of PDEs · Mathematics 2024-11-21 Manuel Friedrich , Pascal Steinke , Kerrek Stinson

In this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the…

Analysis of PDEs · Mathematics 2018-02-13 Vito Crismale , Giuliano Lazzaroni , Gianluca Orlando

In this paper, a strain-gradient plasticity model is derived from a mesoscopic model for straight parallel edge dislocations in an infinite cylindrical crystal. The main difference to existing work is that in this work the well-separateness…

Analysis of PDEs · Mathematics 2019-05-01 Janusz Ginster

We consider the quasi-static evolution of the thermo-plasticity model in which the evolution equation law for the inelastic strain is given by the Prandtl-Reuss flow rule. The thermal part of the Cauchy stress tensor is not linearised in…

Analysis of PDEs · Mathematics 2016-12-07 Leszek Bartczak , Sebastian Owczarek

This paper deals with the quasistatic crack growth of a homogeneous elastic brittle thin film. It is shown that the quasistatic evolution of a three-dimensional cylinder converges, as its thickness tends to zero, to a two-dimensional…

Analysis of PDEs · Mathematics 2007-05-23 Jean-Francois Babadjian

We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is…

Analysis of PDEs · Mathematics 2007-05-23 Gianni Dal Maso , Antonio DeSimone , Maria Giovanna Mora , Massimiliano Morini

We address a three-dimensional model capable of describing coupled damage and plastic effects in solids at finite strains. Formulated within the variational setting of {\it generalized standard materials}, the constitutive model results…

Analysis of PDEs · Mathematics 2020-12-30 David Melching , Michael Neunteufel , Joachim Schöberl , Ulisse Stefanelli

The starting point for this work is a static macroscopic model for a high-contrast layered material in single-slip finite crystal plasticity, identified in [Christowiak & Kreisbeck, Calc. Var. PDE (2017)] as a homogenization limit via…

Analysis of PDEs · Mathematics 2021-08-03 Elisa Davoli , Carolin Kreisbeck