相关论文: Near optimal pentamodes as a tool for guiding stre…
The paper establishes exact lower bound on the effective elastic energy of two-dimensional, three-material composite subjected to the homogeneous, anisotropic stress. It is assumed that the materials are mixed with given volume fractions…
The set $GU_f$ of possible effective elastic tensors of composites built from two materials with positive definite elasticity tensors $\BC_1$ and $\BC_2=\Gd\BC_0$ comprising the set $U=\{\BC_1,\Gd\BC_0\}$ and mixed in proportions $f$ and…
The set $GU_f$ of possible effective elastic tensors of composites built from two materials with elasticity tensors $\BC_1>0$ and $\BC_2=0$ comprising the set $U=\{\BC_1,\BC_2\}$ and mixed in proportions $f$ and $1-f$ is partly…
In this paper we investigate numerically an instance of the problem of G-closure for two-dimensional periodic metamaterials. Specifically, we consider composites with isotropic homogenized elasticity tensor, obtained as a mixture of two…
A family of mixed finite elements is proposed for solving the first order system of linear elasticity equations in any space dimension, where the stress field is approximated by symmetric finite element tensors. This family of elements has…
The paper establishes tight lower bound for effective conductivity tensor $K_*$ of two-dimensional three-phase conducting anisotropic composites and defines optimal microstructures. It is assumed that three materials are mixed with fixed…
To derive bounds on the strain and stress response of a two-component composite material with viscoelastic phases, we revisit the so-called analytic method (Bergman 1978), which allows one to approximate the complex effective tensor,…
For the planar Navier--Lam\'e equation in mixed form with symmetric stress tensors, we prove the uniform quasi-optimal convergence of an adaptive method based on the hybridized mixed finite element proposed in [Gong, Wu, and Xu:…
Pentamode metamaterials are a type of extremal designer metamaterials which are able to demonstrate high rigidity in one direction and extremely high compliance in other directions. Pentamodes can, therefore, be considered as building…
The paper outlines novel variational technique for finding microstructures of optimal multimaterial composites, bounds of composites properties, and multimaterial optimal designs. The translation method that is used for the exact…
Electromagnetic materials with a uniaxial effective permittivity tensor, characterized by its transverse ($\epsilon_\perp$) and axial ($\epsilon_\parallel$) components, play a central role in the design of advanced photonic and…
Almost four decades ago, Bergman and Milton independently showed that the isotropic effective electric permittivity of a two-phase composite material with a given volume fraction is constrained to lie within lens-shaped regions in the…
This paper presents a synthesis approach in a density-based topology optimization setting to design large deformation compliant mechanisms for inducing desired strains in biological tissues. The modelling is based on geometrical…
The Poisson problem consists in finding an immersed surface $\Sigma\subset\mathbb{R}^m$ minimising Germain's elastic energy (known as Willmore energy in geometry) with prescribed boundary, boundary Gauss map and area which constitutes a…
We investigate the structure and mechanical behavior of assemblies of frictionless, nearly rigid equal-sized beads, in the quasistatic limit, by numerical simulation. Three different loading paths are explored: triaxial compression,…
Two finite element approximations of the Oldroyd-B model for dilute polymeric fluids are considered, in bounded 2- and 3-dimensional domains, under no flow boundary conditions. The pressure and the symmetric conformation tensor are…
We describe a new type of three material microstructures which we call wheel assemblages, that correspond to extremal conductivity and extremal bulk modulus for a composite made of two materials and an ideal material. The exact lower bounds…
This work comprises a detailed theoretical and computational study of the boundary value problem for transversely isotropic linear elastic bodies. General conditions for well-posedness are derived in terms of the material parameters. The…
We present a novel approach to understand geometric-incompatibility-induced rigidity in under-constrained materials, including sub-isostatic 2D spring networks and 2D and 3D vertex models for dense biological tissues. We show that in all…
In this paper we report a new promising idea on the design and manufacturing of ply composite structures, tailored to exhibit maximum stiffness under given weight constraints and loading conditions. It is based on the idea behind an…