Effective Governing Equations for Viscoelastic Composites.

We derive the governing equations for the overall behaviour of linear viscoelastic composites comprising two families of elastic inclusions, subphases and/or fibres, and an incompressible Newtonian fluid interacting with the solid phases at the microscale. We assume that the distance between each of the subphases is very small in comparison to the length of the whole material (the macroscale). We can exploit this sharp scale separation and apply the asymptotic (periodic) homogenization method (AHM) which decouples spatial scales and leads to the derivation of the new homogenised model.

Effective Properties of Homogenised Nonlinear Viscoelastic Composites.

We develop a general approach for the computation of the effective properties of nonlinear viscoelastic composites. For this purpose, we employ the asymptotic homogenisation technique to decouple the equilibrium equation into a set of local problems. The theoretical framework is then specialised to the case of a strain energy density of the Saint-Venant type, with the second Piola-Kirchhoff stress tensor also featuring a memory contribution.

Asymptotic Homogenization Applied to Flexoelectric Rods.

In this manuscript, the equilibrium problem for a flexoelectric one-dimensional composite material is studied. The two-scales asymptotic homogenization method is used to derive the homogenized formulation of this problem. The manuscript offers a step-by-step methodology to derive effective coefficients and to solve local problems.

The role of malignant tissue on the thermal distribution of cancerous breast.

The present work focuses on the integration of analytical and numerical strategies to investigate the thermal distribution of cancerous breasts. Coupled stationary bioheat transfer equations are considered for the glandular and heterogeneous tumor regions, which are characterized by different thermophysical properties. The cross-section of the cancerous breast is identified by a homogeneous glandular tissue that surrounds the heterogeneous tumor tissue, which is assumed to be a two-phase periodic composite with non-overlapping circular inclusions and a square lattice distribution, wherein the constituents exhibit isotropic thermal conductivity behavior.