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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…
The homogenization results obtained by Bacca et al. (Homogenization of heterogeneous Cauchy-elastic materials leads to Mindlin second-gradient elasticity. Part I: Closed form expression for the effective higher-order constitutive tensor.…
The packing of elastic bodies has emerged as a paradigm for the study of macroscopic disordered systems. However, progress is hampered by the lack of controlled experiments. Here we consider a model experiment for the isotropic…
In the perspective of homogenization theory, strain-gradient elasticity is a strategy to describe the overall behaviour of materials with coarse mesostructure. In this approach, the effect of the mesostructure is described by the use of…
Passive elastic elements can contribute to stability, energetic efficiency, and impact absorption in both biological and robotic systems. They also add dynamical complexity which makes them more challenging to model and control. The impact…
This paper extends the Hu-Zhang element for linear elasticity to curved domains, preserving strong symmetry and H(div)-conformity. The non-polynomial structure of the curved Hu-Zhang element makes it difficult to analyze the stability,…
We study the homogenisation of geometrically nonlinear elastic composites with high contrast. The composites we analyse consist of a perforated matrix material, which we call the "stiff" material, and a "soft" material that fills the pores.…
A simple model of inelastic hard-rods subject to a one-dimensional array of identical wells is introduced. The energy loss due to inelastic collisions is balanced by the work supplied by an external stochastic heat-bath. We explore the…
Disordered solids exhibit unusual properties of their vibrational states and thermal conductivities. Recent progresses have well established the concept of "elastic heterogeneity", i.e., disordered materials show spatially inhomogeneous…
Interest in the elastic properties of regular lattices constructed from domain walls has recently been motivated by cosmological applications as solid dark energy. This work investigates the particularly simple examples of triangular,…
In this paper we present a fully-coupled, two-scale homogenization method for dynamic loading in the spirit of FE$^2$ methods. The framework considers the balance of linear momentum including inertia at the microscale to capture possible…
This study investigates the impact of sliders -- constraints acting on elastic rods allowing for a transverse displacement jump while maintaining axial and rotational displacement continuity -- on the dynamics of a periodic elastic grid,…
The subject of mechanical metamaterials has been gaining significant attention, however, their widespread application is still halted. Such materials are usually considered as stand-alone, vis-\`a-vis all characteristic length scales being…
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…
Mechanical and elastic properties of materials are among the most fundamental quantities for many engineering and industrial applications. Here, we present a formulation that is efficient and accurate for calculating the elastic and bending…
In this chapter we describe a selection of mathematical techniques and results that suggest interesting links between the theory of gratings and the theory of homogenization, including a brief introduction to the latter. By no means do we…
Soft composite solids are made of inclusions dispersed within soft matrices. They are ubiquitous in nature and form the basis of many biological tissues. In the field of materials science, synthetic soft composites are promising candidates…
We show that artificial magnetism of periodic dielectric or metal/dielectric structures has limitations and is subject to at least two "uncertainty principles". First, the stronger the magnetic response (the deviation of the effective…
We present a formulation for high-order generalized periodicity conditions in the context of a high-order electromechanical theory including flexoelectricity, strain gradient elasticity and gradient dielectricity, with the goal of studying…
We consider a linearly thermoelastic composite medium,which consists of a homogeneous matrix containing a statistically inhomogeneous random set of inclusions, when the concentration of the inclusions is a function of the coordinates…