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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

We investigate finite-strain elastoplastic evolution in the nonassociative setting. The constitutive material model is formulated in variational terms and coupled with the quasistatic equilibrium system. We introduce measure-valued…

Analysis of PDEs · Mathematics 2025-05-08 Ulisse Stefanelli , Andreas Vikelis

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

We derive exact expressions for effective elastodynamic properties of two-phase composites in the long-wavelength (quasistatic) regime via homogenized constitutive relations that are local in space. This is accomplished by extending the…

Materials Science · Physics 2021-01-01 J. Kim , S. Torquato

We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense…

Analysis of PDEs · Mathematics 2016-04-13 Fabian Christowiak , Carolin Kreisbeck

We study the existence of quasistatic evolutions for a family of gradient damage models which take into account fatigue, that is the process of weakening in a material due to repeated applied loads. The main feature of these models is the…

Analysis of PDEs · Mathematics 2020-09-24 Roberto Alessi , Vito Crismale , Gianluca Orlando

We study a variational model for the quasistatic growth of cracks with fractional di- mension in brittle materials. We give a minimal set of properties of the collection of admissible cracks which ensure the existence of a quasistatic…

Optimization and Control · Mathematics 2016-02-29 Gianni Dal Maso , Marco Morandotti

We propose a model for quasistatic growth of cavities and cracks in two-dimensional nonlinear elasticity. Cavities and cracks are modeled as discrete and compact subsets of a planar domain, respectively, and deformations are defined only…

Analysis of PDEs · Mathematics 2025-07-22 Marco Bresciani , Manuel Friedrich

Dimension-reduction homogenization results for thin films have been obtained under hypotheses of periodicity or almost-periodicity of the energies in the directions of the mid-plane of the film. In this note we consider thin films, obtained…

Analysis of PDEs · Mathematics 2022-12-22 Irene Anello , Andrea Braides , Fabrizio Caragiulo

This work is devoted to the analysis of the interplay between internal variables and high-contrast microstructure in inelastic solids. As a concrete case-study, by means of variational techniques, we derive a macroscopic description for an…

Analysis of PDEs · Mathematics 2024-10-14 Elisa Davoli , Chiara Gavioli , Valerio Pagliari

Quasicrystals and their periodic approximants are complex phases, which have by now been observed in many metallic alloys, soft matter systems, and particle simulations. In recent experiments of thin-film perovskites on solid substrates,…

Soft Condensed Matter · Physics 2024-08-07 Nydia Roxana Varela-Rosales , Michael Engel

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

In this paper we contribute to studying the issue of quasistatic limit in the context of Griffith's theory by investigating a one-dimensional debonding model. It describes the evolution of a thin film partially glued to a rigid substrate…

Analysis of PDEs · Mathematics 2020-01-08 Filippo Riva

In this article, we discuss the stability of soft quasicrystalline phases in a coupled-mode Swift-Hohenberg model for three-component systems, where the characteristic length scales are governed by the positive-definite gradient terms.…

Soft Condensed Matter · Physics 2016-04-20 Kai Jiang , Jiajun Tong , Pingwen Zhang

We analyse a numerical scheme for a system arising from a novel description of the standard elastic--perfectly plastic response. The elastic--perfectly plastic response is described via rate-type equations that do not make use of the…

Numerical Analysis · Mathematics 2024-09-10 Pablo Alexei Gazca-Orozco , Vít Průša , Karel Tůma

This paper addresses the question of the interplay between relaxation and irreversibility through quasi-static evolutions in damage mechanics, by inquiring the following question: can the quasi-static evolution of an elastic material…

Analysis of PDEs · Mathematics 2023-06-16 Elise Bonhomme

We study the mechanics of a reversible decohesion (unzipping) of an elastic layer subjected to quasi-static end-point loading. At the micro level the system is simulated by an elastic chain of particles interacting with a rigid foundation…

Other Quantitative Biology · Quantitative Biology 2015-05-13 F. Maddalena , D. Percivale , G. Puglisi , L. Truskinovsky

The quasistatic, Prandtl-Reuss perfect plasticity at small strains is combined with a gradient, reversible (i.e. admitting healing) damage which influences both the elastic moduli and the yield stress. Existence of weak solutions of the…

Numerical Analysis · Mathematics 2015-05-06 Tomáš Roubíček , Jan Valdman

We introduce a new model of irreversible quasistatic crack growth in which the evolution of cracks is the limit of a suitably modified $\epsilon$-gradient flow of the energy functional, as the "viscosity" parameter $\epsilon$ tends to zero.

Analysis of PDEs · Mathematics 2007-05-23 Rodica Toader , Chiara Zanini

In this paper we study the derivation of nonlinear bending models for prestrained elastic plates from three-dimensional non-linear elasticity via homogenization and dimension reduction. We compare effective models obtained by either…

Analysis of PDEs · Mathematics 2025-09-11 Klaus Boehnlein , Lucas Bouck , Stefan Neukamm , David Padilla-Garza , Kai Richter