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We analyze the $\Gamma$-convergence of sequences of free-discontinuity functionals arising in the modeling of linear elastic solids with surface discontinuities, including phenomena as fracture, damage, or material voids. We prove…

Analysis of PDEs · Mathematics 2020-10-15 Manuel Friedrich , Matteo Perugini , Francesco Solombrino

We investigate the emergence of isotropic linear elasticity in amorphous and polycrystalline solids, via extensive numerical simulations. We show that the elastic properties are correlated over a finite length scale $\xi_E$, so that the…

Soft Condensed Matter · Physics 2021-05-19 Shivam Mahajan , Joyjit Chattoraj , Massimo Pica Ciamarra

We consider a heterogeneous elastic structure which is stratified in some direction. We derive the limit problem under the assumption that the Lam\'e coefficients and their inverses weakly* converge to Radon measures. Our method applies…

Analysis of PDEs · Mathematics 2016-03-03 Michel Bellieud , Shane Cooper

In this paper an asymptotic homogenization method for the analysis of composite materials with periodic microstructure in presence of thermodiffusion is described. Appropriate down-scaling relations correlating the microscopic fields to the…

Mathematical Physics · Physics 2015-12-31 A. Bacigalupo , L. Morini , A. Piccolroaz

We perform via $\Gamma$-convergence a 2d-1d dimension reduction analysis of a single-slip elastoplastic body in large deformations. Rigid plastic and elastoplastic regimes are considered. In particular, we show that limit deformations can…

Analysis of PDEs · Mathematics 2023-09-13 Dominik Engl , Stefan Krömer , Martin Kružík

This paper is an extension of the result by Christowiak and Kreisbeck (2017), which addresses the Gamma-convergence approach to a homogenization problem for composite materials consisting of two distinct types of parallel layers. In…

Analysis of PDEs · Mathematics 2025-02-11 Akira Ishikawa , Karel Svadlenka

Using the notion of Gamma-convergence, we discuss the limiting behavior of the 3d nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales…

Analysis of PDEs · Mathematics 2008-11-17 Marta Lewicka , Maria Giovanna Mora , Mohammad Reza Pakzad

Discrete fine-scale models, in the form of either particle or lattice models, have been formulated successfully to simulate the behavior of quasi-brittle materials whose mechanical behavior is inherently connected to fracture processes…

Materials Science · Physics 2016-02-17 Roozbeh Rezakhani , Gianluca Cusatis

We carry out the homogenization of a fluid-structure interaction problem consisting in the periodic inclusions of a viscous fluid in an elastic body. We get a macrostructure model where the body behaves as a viscoelastic material with a…

Analysis of PDEs · Mathematics 2024-05-20 Juan Casado-Díaz

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

We develop the theory of anomalous elasticity in two-dimensional flexible materials with orthorhombic crystal symmetry. Remarkably, in the universal region, where characteristic length scales are larger than the rather small Ginzburg scale…

Mesoscale and Nanoscale Physics · Physics 2022-03-14 I. S. Burmistrov , V. Yu. Kachorovskii , M. J. Klug , J. Schmalian

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

The main result of this work is a homogenization theorem via variational convergence for elastic materials with stiff checkerboard-type heterogeneities under the assumptions of physical growth and non-self-interpenetration. While the…

Analysis of PDEs · Mathematics 2023-03-29 Wolf-Patrick Düll , Dominik Engl , Carolin Kreisbeck

The presence of prestrain can have a tremendous effect on the mechanical behavior of slender structures. Prestrained elastic plates show spontaneous bending in equilibrium -- a property that makes such objects relevant for the fabrication…

Analysis of PDEs · Mathematics 2023-01-18 Klaus Böhnlein , Stefan Neukamm , David Padilla-Garza , Oliver Sander

In this work we consider the elasticity problem for two domains separated by a heterogeneous layer. The layer has an $\varepsilon-$periodic structure, $\varepsilon\ll1$, including a multiple micro-contact between the structural components.…

Analysis of PDEs · Mathematics 2015-11-25 Georges Griso , Anastasia Migunova , Julia Orlik

The inclusion of rigid elements into elastic composites may lead to superior mechanical properties for the equivalent elastic continuum, such as, for instance, extreme auxeticity. To allow full exploitation of these properties, a tool for…

Classical Physics · Physics 2025-01-16 Luca Viviani , Davide Bigoni , Andrea Piccolroaz

In this paper we extend the asymptotic analysis in [LLOO], performed on a structure consisting of two linearly elastic bodies connected by a thin soft nonlinear Kelvin-Voigt viscoelastic adhesive layer, to the case in which the total mass…

Analysis of PDEs · Mathematics 2019-12-13 Elena Bonetti , Giovanna Bonfanti , Christian Licht , Riccarda Rossi

This paper is devoted to study of the limiting behaviour of an elastic material with periodically distributed rigid inclusions of size {\epsilon}, as the small parameter {\epsilon} goes to zero. We address here the case with inclusions of…

Analysis of PDEs · Mathematics 2024-10-29 Lazarus Signing

This paper investigates the effects of plasticity on the effective fracture toughness. A layered material is considered as a modelling system. An elastic-plastic phase-field model and a surfing boundary condition are used to study how the…

Computational Engineering, Finance, and Science · Computer Science 2020-10-15 Stella Brach

The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the…

Disordered Systems and Neural Networks · Physics 2020-09-29 Jishnu N. Nampoothiri , Yinqiao Wang , Kabir Ramola , Jie Zhang , Subhro Bhattacharjee , Bulbul Chakraborty