Related papers: Optimal Elastostatic Cloaks
The prospect of rendering objects invisible has intrigued researchers for centuries. Transformation optics based invisibility cloak design is now bringing this goal from science fictions to reality and has already been demonstrated…
The development of accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions…
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…
Commonly used linear and nonlinear constitutive material models in deformation simulation contain many simplifications and only cover a tiny part of possible material behavior. In this work we propose a framework for learning customized…
A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…
This paper deals with shape optimization for elastic materials under stochastic loads. It transfers the paradigm of stochastic dominance, which allows for flexible risk aversion via comparison with benchmark random variables, from…
An effective cylindrical cloak may be conceptualized as an assembly of adjacent local neighbourhoods, each of which is made from a homogenized composite material (HCM). The HCM is required to be a certain uniaxial dielectric-magnetic…
An analytical method of electromagnetic wave interactions with a general radially anisotropic cloak is established. It is able to deal with arbitrary parameters ($\epsilon_r(r)$, $\mu_r(r)$, $\epsilon_t(r)$ and $\mu_t(r)$) of a radially…
Space folding techniques based on non-monotonic transforms lead to a new class of cylindrical isotropic acoustic cloaks with a constant negative density and a spatially varying negative bulk modulus. We consider an external cloak consisting…
The concept of scattering coefficients has played a pivotal role in a broad range of inverse scattering and imaging problems in acoustic, and electromagnetic media. In view of their promising applications in inverse problems related to…
A cylindrical wave expansion method is developed to obtain the scattering field for an ideal two-dimensional cylindrical invisibility cloak. A near-ideal model of the invisibility cloak is set up to solve the boundary problem at the inner…
The closest tensors of higher symmetry classes are derived in explicit form for a given elasticity tensor of arbitrary symmetry. The mathematical problem is to minimize the elastic length or distance between the given tensor and the closest…
The ability to control electromagnetic fields, heat currents, electric currents, and other physical phenomena by coordinate transformation methods has resulted in novel functionalities, such as cloaking, field rotations, and concentration…
We evaluate the elasticity of arrested short-ranged attractive colloids by combining an analytically solvable elastic model with a hierarchical arrest scheme into a new approach, which allows to discriminate the microscopic (primary…
Based on a coordinate transformation approach, Pendry {\it et al.} have reported electromagnetically anisotropic and inhomogeneous shells that, in theory, completely shield an interior structure of arbitrary size from electromagnetic fields…
A theory is developed for evaluation of nonlinear elastic moduli of composite materials with nonlinear inclusions dispersed in another nonlinear material (matrix). We elaborate a method aimed for determination of elastic parameters of a…
In this paper we report the numerical design and experimental validation of a pentamode cloak for scattering reduction of elliptical targets in underwater acoustics. Despite being a well-known theoretical concept, experimental validations…
A classical problem in elasticity theory involves an inhomogeneity embedded in a material of given stress and shear moduli. The inhomogeneity is a region of arbitrary shape whose stress and shear moduli differ from those of the surrounding…
An algorithm is devised for solving minimization problems with equality constraints. The algorithm uses first-order derivatives of both the objective function and the constraints. The step is computed as a sum between a steepest-descent…
We consider the problem of model selection and estimation in situations where the number of parameters diverges with the sample size. When the dimension is high, an ideal method should have the oracle property [J. Amer. Statist. Assoc. 96…