MICROCONTINUUM FIELD THEORIES. - Volume 1, Foundations and solids (Relié)

Microcontinuum Field Theories constitutes an extension of classical field the- ories-of elastic solids, viscous fluids, electromagnetism, and the like-to microscopic length and time scales. Material bodies are viewed as collections of a large number of deformable particles, (subcontinua), suitable for modeling blood, porous media, polymers, liquid crystals, slurries, and composite materials. This volume is concerned with the fundamentals and the dynamics of microcontinua. It presents a thorough discussion of the kinematics of microcontinua, strain, stress tensors, balance laws, thermodynamics, and constitutive equations for solids and fluids subject to electromagnetic fields and mechanical loads. The discussion includes boundary- and initial-value problems and presents variational and uniqueness theorems. Solutions are given for many applied problems involving micropolar, microstretch, and micromorphic bodies, and electromagnetic solids.