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This paper is concerned with the asymptotic analysis of a sequence of variational models of brittle damage in the context of linearized elasticity in the two-dimensional discrete setting. We consider a discrete version of Francfort and…
In this paper we study the homogenization effects on the model of elastic plate in the bending regime, under the assumption that the energy density (material) oscillates in the direction of thickness. We study two different cases. First, we…
A homogenization result is given for a material having brittle inclusions arranged in a periodic structure. According to the relation between the softness parameter and the size of the microstructure, three different limit models are…
We study the $\Gamma$-convergence of a class of elastica-type energies defined on immersed planar curves and depending on a small positive parameter $\epsilon$. As $\epsilon\to 0^+$, sequences with equibounded energy develop concentration…
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…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
Starting from three-dimensional nonlinear elasticity under the restriction of incompressibility, we derive reduced models to capture the behavior of strings in response to external forces. Our $\Gamma$-convergence analysis of the…
In this work, we study the effective behavior of a two-dimensional variational model within finite crystal plasticity for high-contrast bilayered composites. Precisely, we consider materials arranged into periodically alternating thin…
We analyse the $\Gamma$-convergence of general non-local convolution type functionals with varying densities depending on the space variable and on the symmetrized gradient. The limit is a local free-discontinuity functional, where the bulk…
Modeling of frictional contacts is crucial for investigating mechanical performances of composite materials under varying service environments. The paper considers a linear elasticity system with strongly heterogeneous coefficients and…
We study stochastic homogenisation of free-discontinuity surface functionals defined on piecewise rigid functions which arise in the study of fracture in brittle materials. In particular, under standard assumptions on the density, we show…
We derive a homogenized mechanical model of a masonry-type structure constituted by a periodic assemblage of blocks with interposed mortar joints. The energy functionals in the model under investigation consist in (i) a linear elastic…
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…
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…
We study the $\Gamma$-convergence of damage to fracture energy functionals in the presence of low-order nonlinear potentials that allows us to model physical phenomena such as fluid-driven fracturing, plastic slip, and the satisfaction of…
We study the effective behavior of random, heterogeneous, anisotropic, second order phase transitions energies that arise in the study of pattern formations in physical-chemical systems. Specifically, we study the asymptotic behavior, as…
We consider a family of three-dimensional stiffened plates whose dimensions are scaled through different powers of a small parameter $\varepsilon$. The plate and the stiffener are assumed to be linearly elastic, isotropic, and homogeneous.…
We study the homogenization of a class of non-local functionals featuring a rapidly oscillating periodic weight. By means of two-scale convergence, we explicitly evaluate the {\Gamma}-limit for constant target functions, revealing how the…
In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, $\mathbb{R}^k$. We prove the $\Gamma$-convergence of elastic energies for configurations of a converging…
This paper investigates the homogenization, dimension reduction, and linearization of a composite plate subjected to external loading within the framework of non-linear elasticity problem. The total elastic energy of the problem is of order…