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

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The paper studies the asymptotic analysis of a model coupling elastoplasticity and damage depending on three parameters -- governing viscosity, plastic hardening, and convergence rate of plastic strain and displacement to equilibrium -- as…

Analysis of PDEs · Mathematics 2022-04-12 Vito Crismale , Giuliano Lazzaroni , Riccarda Rossi

We consider load controlled quasistatic evolution. Well posedness results for the nonlocal continuum model related to peridynamics are established. We show local existence and uniqueness of quasistatic evolution for load paths originating…

Analysis of PDEs · Mathematics 2023-01-04 Debdeep Bhattacharya , Robert P. Lipton

Fracture involves interaction across large and small length scales. With the application of enough stress or strain to a brittle material, atomistic scale bonds will break, leading to fracture of the macroscopic specimen. From the…

Soft Condensed Matter · Physics 2022-02-04 Debdeep Bhattacharya , Patrick Diehl , Robert P. Lipton

We provide a rigorous justification of the classical linearization approach in plasticity. By taking the small-deformations limit, we prove via \Gamma-convergence for rate-independent processes that energetic solutions of the quasi-static…

Analysis of PDEs · Mathematics 2011-11-07 Alexander Mielke , Ulisse Stefanelli

We study a model for the deformation of a visco-elasto-plastic material that is nearly incompressible. It originates from geophysics, is given in the Eulerian description and combines a Kelvin-Voigt rheology in the spherical part with a…

Analysis of PDEs · Mathematics 2025-12-22 Thomas Eiter

We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo. The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute…

Analysis of PDEs · Mathematics 2007-05-23 Gianni Dal Maso , Rodica Toader

The paper is devoted to the study of quasi-static brittle crack evolution. We work under the following assumptions: a linear elastic body, with or without initial cracks inside, evolves in a quasi-static manner under an imposed path of…

Analysis of PDEs · Mathematics 2007-05-23 Marius Buliga

This study addresses ductile fracture of single grains in metals by modeling of the formation and propagation of transgranular cracks. A proposed model integrates gradient extended hardening, phase-field modeling for fracture, and crystal…

Numerical Analysis · Mathematics 2024-11-01 Kim Louisa Auth , Jim Brouzoulis , Magnus Ekh

Using numerical simulations, we study the failure of an amorphous solid under quasi-static expansion starting from a homogeneous high-density state. During the volume expansion, we demonstrate the existence of instabilities manifesting via…

Soft Condensed Matter · Physics 2023-03-10 Umang A. Dattani , Smarajit Karmakar , Pinaki Chaudhuri

In this paper we prove a two-dimensional existence result for a variational model of crack growth for brittle materials in the realm of linearized elasticity. Starting with a time-discretized version of the evolution driven by a prescribed…

Analysis of PDEs · Mathematics 2018-07-10 Manuel Friedrich , Francesco Solombrino

In this work we introduce a new system of partial differential equations as a simplified model for the evolution of reversible martensitic transformations under thermal cycling in low hysteresis alloys. The model is developed in the context…

Analysis of PDEs · Mathematics 2018-11-20 Francesco Della Porta

This paper is devoted to the study of a hemivariational inequality modeling the quasistatic bilateral frictional contact between a viscoelastic body and a rigid foundation. The damage effect is built into the model through a parabolic…

Numerical Analysis · Mathematics 2019-12-18 Weimin Han , Michal Jureczka , Anna Ochal

A mechanical model is introduced for predicting the initiation and evolution of complex fracture patterns without the need for a damage variable or law. The model, a continuum variant of Newton's second law, uses integral rather than…

Analysis of PDEs · Mathematics 2016-02-02 Robert Lipton , Stewart Silling , Richard Lehoucq

A rate-independent model coupling small strain associative elasto-plasticity and damage is studied via a 'vanishing-viscosity' analysis with respect to all the variables describing the system. This extends the analysis performed for the…

Analysis of PDEs · Mathematics 2019-10-10 Vito Crismale , Riccarda Rossi

We propose a discontinuous finite element approximation for a model of quasi-static growth of brittle fractures in linearly elastic bodies formulated by Francfort and Marigo, and based on the classical Griffith's criterion. We restrict our…

Analysis of PDEs · Mathematics 2007-05-23 A. Giacomini , M. Ponsiglione

A nonlocal model of peridynamic type for dynamic brittle damage is introduced consisting of two phases, one elastic and the other inelastic. Evolution from the elastic to the inelastic phase depends on material strength. Existence and…

Analysis of PDEs · Mathematics 2024-04-02 Robert P. Lipton , Debdeep Bhattacharya

By comparing the response to external strains in metallic glasses and in Lenard-Jones glasses we find a quantitative universality of the fundamental plastic instabilities in the athermal, quasistatic limit. Microscopically these two types…

Soft Condensed Matter · Physics 2015-06-03 Ratul Dasgupta , Smarajit Karmakar , Itamar Procaccia

This work is concerned with an asymptotic analysis, in the sense of $\Gamma$-convergence, of a sequence of variational models of brittle damage in the context of linearized elasticity. The study is performed as the damaged zone concentrates…

Analysis of PDEs · Mathematics 2019-11-19 Jean-Francois Babadjian , Flaviana Iurlano , Filip Rindler

Starting from a prototypical model of elasto-plasticity in the small-strain and quasi-static setting, where the evolution of the plastic distortion is driven exclusively by the motion of discrete dislocations, this work performs a rigorous…

Analysis of PDEs · Mathematics 2025-03-26 Paolo Bonicatto , Filip Rindler

A rate-independent model for the quasistatic evolution of a magnetoelastic thin film is advanced and analyzed. Starting from the three-dimensional setting, we present an evolutionary $\Gamma$-convergence argument in order to pass to the…

Analysis of PDEs · Mathematics 2014-05-28 Martin Kružík , Ulisse Stefanelli , Chiara Zanini