Related papers: Material Optimization for Nonlinearly Elastic Plan…
We are concerned with a variant of the isoperimetric problem, which in our setting arises in a geometrically nonlinear two-well problem in elasticity. More precisely, we investigate the optimal scaling of the energy of an elastic inclusion…
We study the elastic properties of soft solids containing air bubbles. Contrary to standard porous materials, the softness of the matrix allows for a coupling of the matrix elasticity to surface tension forces brought in by the bubbles.…
We derive the effective energy density of thin membranes of liquid crystal elastomers as the Gamma-limit of a widely used bulk model. These membranes can display fine-scale features both due to wrinkling that one expects in thin elastic…
We construct the closed form solution of an elastic beam with axial load using Lie symmetry method. A beam with spatially varying physical properties such as mass and second moment of inertia is considered. The governing fourth order…
Biological soft tissues exhibit elastic properties which can be dramatically different from rubber-type materials (elastomers). To gain a better understanding of the role of constitutive relationships in determining material responses under…
Via solution of appropriate variational problem it is shown that light beams with Gaussian spatial profile and sufficiently short duration provide maximal destruction of global coherence under nonlinear self-modulation.
In this paper, the distributed resource allocation problem on strongly connected and weight-balanced digraphs is investigated, where the decisions of each agent are restricted to satisfy the coupled network resource constraints and…
The ability to design the scattering properties of electromagnetic structures is of fundamental interest in optical science and engineering. While there has been great practical success applying local optimization methods to electromagnetic…
This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…
We introduce the concept of magnetoelastic metamaterials with electromagnetic properties depending on elastic deformation. We predict a strong nonlinear and bistable response of such metamaterials caused by their structural reshaping in…
The equilibrium distribution function determines macroscopic observables in statistical physics. While conventional methods correct equilibrium distributions in weakly nonlinear or near-integrable systems, they fail in strongly nonlinear…
We discuss a topology optimization problem for an elastoplastic medium. The distribution of material in a region is optimized with respect to a given target functional taking into account compliance. The incremental elastoplastic problem…
Results are presented for finding the optimal orientation of an anisotropic elastic material. The problem is formulated as minimizing the strain energy subject to rotation of the material axes, under a state of uniform stress. It is shown…
The gravitational clustering of collisionless particles in an expanding universe is modelled using some simple physical ideas. I show that it is possible to understand the nonlinear clustering in terms of three well defined regimes: (1)…
A law previously found for shear moduli of crystalline materials is developed and extended to all elastic moduli in solids and structures. Shear moduli were previously shown to depend only on specific volume. The bulk moduli of many…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…
Using dimensionally reduced models for the numerical simulation of thin objects is highly attractive as this reduces the computational work substantially. The case of narrow thin elastic bands is considered and a convergent finite element…
We consider a plate made from an isotropic but brittle elastic material, which is used to span a rigid aperture, across which a small pressure difference is applied. The problem we address is to find the structure which uses the least…
Due to the non-linearity of Hertzian contacts, the speed of sound $c$ in granular matter is expected to increase with pressure as $P^{1/6}$. A static layer of grains under gravity is thus stratified so that bulk waves are refracted toward…
Here we introduce the concept of "optimal particles" for strong interactions with electromagnetic fields. We assume that a particle occupies a given electrically small volume in space and study the required optimal relations between the…