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We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
Long range order and symmetry in heterogeneous materials architected on crystal lattices lead to elastic and inelastic anisotropies and thus limit mechanical functionalities in particular crystallographic directions. Here, we present a…
Spatial heterogeneity in the elastic properties of soft random solids is investigated via a two-pronged approach. First, a nonlocal phenomenological model for the elastic free energy is examined. This features a quenched random kernel,…
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…
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…
The revolutionary advancements in metal additive manufacturing have enabled the production of alloy-based lattice structures with complex geometrical features and high resolutions. This has encouraged the development of nonlinear material…
When used in bulk applications, mechanical metamaterials set forth a multiscale problem with many orders of magnitude in scale separation between the micro and macro scales. However, mechanical metamaterials fall outside conventional…
The ability to design and fabricate materials with tailored mechanical properties, combined with immunity to damage, is a frontier of materials engineering. For example, materials which are characterized by elastic properties that depend on…
The modelling of heterogeneous and architected materials poses a significant challenge, demanding advanced homogenisation techniques. However, the complexity of this task can be considerably simplified through the application of micropolar…
Two approaches to incorporate heterogeneity in discrete models are compared. In the first, standard approach, the heterogeneity is dictated by geometrical structure of the discrete system. In the second approach, the heterogeneity is…
Using a geometric formalism of elasticity theory we develop a systematic theoretical method for controlling and manipulating the mechanical response of slender solids to external loads. We formally express global mechanical properties…
This paper proposes that elastic potentials, which may be rigorously formulated using the negative Gibbs free energy or the complementary strain energy density, should be used as the basis for the plastic part of elasto-plastic constitutive…
Heterogeneous materials exhibit anisotropy which is influenced by factors such as individual phase properties and microstructural configuration that form crucial descriptors of heterogeneity. A review of anisotropy indices proposed in the…
Critically elastic materials - those that are rigid with a single state of self-stress - can be generated from parent systems with two states of self-stress by the removal of one of many constraints. We show that the elastic moduli of the…
Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading…
An orthotropic metamaterial is composed of elements arrayed periodically in space. The element includes two cuboid structures. The first structure is the basic structure of the element, and the second structure is the transformation of the…
We shall consider some common models in linear thermo-elasticity within a common structural framework. Due to the flexibility of the structural perspective we will obtain well-posedness results for a large class of generalized models…
Contact problems with Coulomb friction in linear elasticity are notoriously difficult and their mathematical analysis is still largely incomplete. In this paper, a model problem with heterogeneous friction coefficient is considered in…
Recent progress in advanced additive manufacturing techniques has stimulated the growth of the field of mechanical metamaterials. One area particular interest in this subject is the creation of auxetic material properties through elastic…
Many biological and engineering materials have nonperiodic microstructures for which classical periodic homogenization results do not apply. Certain nonperiodic microstructures may be approximated by locally periodic microstructures for…