Wave Propagation in Microstructured Solids

Abstract

A general model of bodies with vectorial microstructures is introduced, which includes many particular models such as scalar and affine microstructures, Cosserat continua, and liquid crystals. Assuming the existence of a strain energy function, the field equations are obtained via a variational principle as Euler-Lagrange equations of an energetic functional. Dissipative forces are also introduced. Equilibrium and stability problems are briefly discussed. Within the framework of singular surfaces theory, nonlinear acceleration and shock waves are studied and proper propagation conditions for nondissipative materials are given. The influence of dissipation is briefly discussed.