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We first consider an elastic thin heterogeneous cylinder of radius of order epsilon: the interior of the cylinder is occupied by a stiff material (fiber) that is surrounded by a soft material (matrix). By assuming that the elasticity tensor…
It is shown that second-order homogenization of a Cauchy-elastic dilute suspension of randomly distributed inclusions yields an equivalent second gradient (Mindlin) elastic material. This result is valid for both plane and three-dimensional…
This paper concerns the rigorous periodic homogenization for a weakly coupled electroelastic system of a nonlinear electrostatic equation with an elastic equation enriched with electrostriction. Such coupling is employed to describe…
This paper is concerned with the Boundary Element simulation of elastic domains that contain thin inclusions that have elastic material properties, which are different to the domain. With thin inclusions we mean inclusions with extreme…
In this work the linear elastic properties of materials containing spherical voids are calculated and compared using finite element simulations. The focus is on homogeneous solid materials with spherical, empty voids of equal size. The…
Rigidity is an emergent property of materials - it is not a feature of individual components that comprise the structure, but instead arises from interactions between many constituent parts. Recently, it has been recognized that…
Abstract. We present a framework for the kinematics of a material body undergoing anelastic deformation. For such processes, the material structure of the body, as reflected by the geometric structure given to the set of body points,…
We illustrate a broken Hardy inequality on discontinuous finite element spaces, blowing up with a logarithmic factor with respect to the meshes size. This is motivated by numerical analysis for the strain gradient elasticity with natural…
Amorphous solids are mechanically rigid while possessing a disordered structure similar to that of dense liquids. Recent research indicates that dynamical heterogeneity, spatio-temporal fluctuations in local dynamical behavior, might help…
This paper presents the derivation of the homogenized equations that describe the macroscopic mechanical response of elastomers filled with liquid inclusions in the setting of small quasistatic deformations. The derivation is carried out…
A dual hybrid Virtual Element scheme for plane linear elastic problems is presented and analysed. In particular, stability and convergence results have been established. The method, which is first order convergent, has been numerically…
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…
While static equilibria of flexible strings subject to various load types (gravity, hydrostatic pressure, Newtonian wind) is well understood textbook material, the combinations of the very same loads can give rise to complex spatial…
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…
Mechanical instabilities can be exploited to design innovative structures, able to change their shape in the presence of external stimuli. In this work, we derive a mathematical model of an elastic beam subjected to an axial force and…
Elastic geodesic grids (EGG) are lightweight structures that can be easily deployed to approximate designer provided free-form surfaces. In the initial configuration the grids are perfectly flat, during deployment, though, curvature is…
This paper presents a theory for the behaviour of isotropic-hardening/softening elastoplastic materials that do not have a preferred reference configuration. In spite of important differences, many ingredients of classical plasticity are…
In this article, we discuss the equality of two inner products on a vector space. Particularly, we look at some geometric properties that are given to a vector space by an inner product namely, length and angle, and we ask under what…
Embedding rigid inclusions into elastic matrix materials is a procedure of high practical relevance, for instance for the fabrication of elastic composite materials. We theoretically analyze the following situation. Rigid spherical…
Architected metamaterials like foams and lattices exhibit complex responses governed by microstructural instabilities, localization, and phase-transition-like phenomena. Their behavior is further affected by heterogeneities inherent in…