The notion of a Hall matrix, associated with a possibly anisotropic conducting material in the presence of a small magnetic field, is introduced. Then, for any material having a microstructure we prove a general homogenization result satisfied by the Hall matrix in the framework of the Hconvergence of Murat-Tartar. Extending a result of Bergman, it is shown that the Hall matrix can be computed ...

We analyze plane strain static thermoelastic deformations of a simply supported functionally graded (FG) plate by a meshless local Petrov–Galerkin (MLPG) method. Material moduli are assumed to vary only in the thickness direction. The plate material is made of two isotropic randomly distributed constituents and the macroscopic response is also modeled as isotropic. Displacements and stresses co...

The following paper presents the results of modelling of the magnetic characteristics of isotropic (Ni–Zn ferrite) and anisotropic material (Fe40Ni38Mo4B18 amorphous alloy in as quenched state), both useful for sensor applications. For the modelling an extended Jiles–Atherton model was used. Extension of the model connects model’s parameter k, describing average energy required to break pinning...

Polymer-stabilized optically isotropic liquid crystals, including blue phases, are emerging as a strong contender for next-generation display technology because they exhibit some revolutionary features such as no need for surface alignment, submillisecond response time, isotropic dark state, and cell gap insensitivity. The basic material properties, including electric field-induced birefringenc...

We consider two-dimensional, two-phase, elastic composites consisting of a soft isotropic medium into which hard elastic inclusions have been placed, requiring that the inclusions be interconnected only at corner points. Denoting by the ratio of Young's modulus for the soft and hard phases, we show that the leading term in the asymptotic expansion as ! 0 for the eeective moduli can be calculate...

We develop a model for the reflection and transmission of plane waves by an isotropic layer sandwiched between two uniaxial crystals of arbitrary orientation. In the laboratory frame, reflection and transmission coefficients corresponding to the principal polarization directions in each crystal are given explicitly in terms of the [Formula: see text] axis and propagation directions. The solutio...

Transformation theory is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by selection of the matrix relating displacements in the two descriptions. This gauge matrix can be chosen to make the transformed density isotropic for any transformation although the stress i...

Bone adaptation algorithms that predict the relationship between bone loads and density assume that bone is effectively isotropic. The isotropic assumption cannot explain bone anisotropy and directionality, which are evident from the trabecular architecture. We have modeled the trabecular bone in the proximal femur as effectively orthotropic. Instead of determining the density distribution, we ...

Cohesive-frictional and rough powders are the subject of this study. The behavior under isotropic compression is examined for different material properties involving Coulomb friction, rolling-resistance and contact-adhesion. Under isotropic compression, the density continuously increases according to Bauers exponential law, see Ref. (Bauer 1999). However, at a certain pressure/density, the beha...

In this paper the radial deformation and the corresponding stresses in a functionally graded orthotropic hollow cylinder with the variation in thickness and density according to power law and rotating about its axis under pressure is investigated by using Seth's transition theory. The material of the cylinder is assumed to be non-homogeneous and orthotropic. This theory helps to achieve better ...