The issue of how to define and determine an optimal acoustical fit to a set of anisotropic elastic constants is addressed. The optimal moduli are defined as those which minimize the mean-squared difference in the acoustical tensors between the given moduli and all possible moduli of a chosen higher material symmetry. The solution is shown to be identical to minimizing a Euclidean distance funct...

We illustrate the flow behaviour of fluids with isotropic and anisotropic microstructure (internal length, layering with bending stiffness) by means of numerical simulations of silo discharge and flow alignment in simple shear. The Cosserat theory is used to provide an internal length in the constitutive model through bending stiffness to describe isotropic microstructure and this theory is cou...

In this research, a theory has been developed to estimate the effective parameters of artificial material composed of dielectric bars placed in a periodic fashion in dielectric host medium (air) from equivalent circuit point of view and verified with HFSS simulation. The theory provides a relationship between effective permittivity and the filling factor of the constituent particle and explains...

A combined numerical and analytic approach is presented to obtain a general matrix form of constitutive relations for a bi-anisotropic material which consists of arbitrary inclusions in a host medium. This approach is based on the quasi-static Lorentz-Lorenz theory which relates the constitutive parameters of the material with the electric and magnetic dipole moments of the inclusions which can...

We report on the development and use of a highly anisotropic magnetic metamaterial for near-field imaging. The material consists of an array of Swiss Roll structures, resonant near 21.3 MHz, with a peak value of relative permeability ~35. At this peak, the material transfers an input magnetic field pattern to the output face without loss of intensity and with a spatial resolution equal to the r...

A simple heuristic algorithm, which determines the set of closed surfaces of the cubic tensor polynomial, is proposed. The algorithm is based on the requirement of positive Gaussian curvature (Stoker’s Theorem) for closed surfaces, excluding domains of tensor values, which do not provide closed surface solutions, and focus the search in the remaining domains. The identification of the closed su...

Weconstruct a nonlinear finite volume (FV) scheme for diffusion equationon star-shapedpolygonalmeshes andprove that the scheme ismonotone, i.e., it preserves positivity of analytical solutions for strongly anisotropic and heterogeneous full tensor coefficients. Our scheme has only cell-centered unknowns, and it treats material discontinuities rigorously and offers an explicit expression for the...

Polycrystalline material microstructure is simulated by Johnson-Mehl model. Finite element analysis is implemented on unit volumes of Johnson-Mehl grain structures, which are aggregates of anisotropic grains orientated by a uniform-random distribution. Monte Carlo techniques are utilized in obtaining the statistical properties of elastic moduli of the ensemble from finite element solutions. The...

A method to obtain three-dimensional data of real-world objects by integrating their material properties is presented. The material properties are defined by capturing the Reflectance Fields of the real-world objects. It is shown, unlike conventional reconstruction methods, the method is able to use the reflectance information to recover surface depth for objects having a nonLambertian surface ...

An analytical method for band structure calculations of photonic crystal fibers with liquid crystal infiltrations is presented. The scalar eigenvalue equation is extended to treat both isotropic and anisotropic materials by introducing a coefficient to describe the index contrast between the extraordinary and ordinary refractive index of the liquid crystal. The simple model provides a fast insi...