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We examine how disordering joint position influences the linear elastic behavior of lattice materials via numerical simulations in two-dimensional beam networks. Three distinct initial crystalline geometries are selected as representative…
An optimization method for the design of multi-lattice structures satisfying local buckling constraints is proposed in this paper. First, the concept of free material optimization is introduced to find an optimal elastic tensor distribution…
We propose a framework for unified analysis of mixed methods for elasticity with weakly symmetric stress. Based on a commuting diagram in the weakly symmetric elasticity complex and extending a previous stability result, stable mixed…
Elastomers are viscoelastic materials and their properties significantly depend on the loading rate. The actual stress experienced by these materials is the sum of equilibrium and dissipative (inelastic) terms. At very low loading rates we…
Deformations of heavy elastic cylinders with their axis in the direction of earth's gravity field are investigated. The specimens, made of polyacrylamide hydrogels, are attached from their top circular cross section to a rigid plate. An…
The experimental observations of many interaction-driven electronic phases in moir\'e superlattices have stimulated intense theoretical and experimental efforts to understand and engineer these correlated physics. Strain is a powerful tool…
Owing to additive manufacturing techniques, a structure at millimeter length scale (macroscale) can be produced by using a lattice substructure at micrometer length scale (microscale). Such a system is called a metamaterial at the…
We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing a statistically homogeneous set of multimodal spherical inclusions modeling the morphology of heterogeneous solid propellants (HSP).…
In this work, a novel hierarchical mechanical metamaterial is proposed that is composed of re-entrant truss-lattice elements. It is shown that this system can deform very differently and can exhibit a versatile extent of the auxetic…
Dynamic heterogeneity is now recognised as a central aspect of structural relaxation in disordered materials with slow dynamics, and was the focus of intense research in the last decade. Here we describe how initial, indirect observations…
Criticality has been proposed as a mechanism for the emergence of complexity, life, and computation, as it exhibits a balance between robustness and adaptability. In classic models of complex systems where structure and dynamics are…
In this paper we consider the stability issue for the inverse problem of determining an unknown inclusion contained in an elastic body by all the pairs of measurements of displacement and traction taken at the boundary of the body. Both the…
Motivated by an application involving additively manufactured bioresorbable polymer scaffolds supporting bone tissue regeneration, we investigate the impact of uncertain geometry perturbations on the effective mechanical properties of…
In this paper we propose two guiding principles that suggest a number of conjectures (some now proved) about various forms of rigidity for moduli spaces arising in algebraic geometry. Such conjectures have group-theoretic, topological and…
We consider a periodic lattice structure in $d=2$ or $3$ dimensions with unit cell comprising $Z$ thin elastic members emanating from a similarly situated central node. A general theoretical approach provides an algebraic formula for the…
Multi-material lightweight designs, e.g. the combination of aluminum with fiber-reinforced composites, are a key feature for the development of innovative and resource-efficient products. The connection properties of such bi-material…
Elastomeric mechanical metamaterials exhibit unconventional behaviour, emerging from their microstructures often deforming in a highly nonlinear and unstable manner. Such microstructural pattern transformations lead to non-local behaviour…
Tensegrity structures have been extensively studied over the last years due to their potential applications in modern engineering like metamaterials, deployable structures, planetary lander modules, etc. Many of the form-finding methods…
Photoelasticity is employed to investigate the stress state near stiff rectangular and rhombohedral inclusions embedded in a 'soft' elastic plate. Results show that the singular stress field predicted by the linear elastic solution for the…
In this paper we present a geometrical framework to study the uniformity of a composite material by means of double groupoid theory. The notions of vertical and horizontal uniformity are introduced, as well as other weaker ones that allows…