Ricerc@Sapienza

The macroscopic behavior of materials with anisotropic microstructure described as micropolar continua is investigated in the present work. Micropolar continua are characterized by a higher number of kinematical and dynamical descriptors than classical continua and related stress and strain measures, namely the micro-rotation gradient (curvature) and the relative rotation with their work conjugated counterparts, the micro-couple, and the skew-symmetric part of the stress, respectively.

In this work, material symmetries in homogenized composites are analyzed. Composite materials are described as materials made of rigid particles and elastic interfaces. Rigid particles of arbitrary hexagonal shape are considered and their geometry described by a limited set of parameters. The purpose of this study is to analyze different geometrical configurations of the assemblies corresponding to various material symmetries such as orthotetragonal, auxetic and chiral.

We consider an anisotropic hyperbolic equation with memory term: ?t2u(x,t)=?i,j=1n?i(aij(x)?ju)+?0t?|?|?2b?(x,t,?)?x?u(x,?)d?+R(x,t)f(x) for $x \in \Omega$ and $t\in (0, T)$ , which is a simplified model equation for viscoelasticity. The main result is a both-sided Lipschitz stability estimate for an inverse source problem of determining a spatial varying factor $f(x)$ of the force term $R(x, t)\,f(x)$ .