Introduction to Coupled Theories in Solid Mechanics

Abstract Introduction to coupled theories in solid mechanics is concerned with the formulation of some coupled theories of solid mechanics which form the basis for a wide range of engineering applications. These theories require a knowledge of the foundational balance laws of mechanics, thermodynamics, and electrodynamics of continua, together with a knowledge of the structure and properties of the materials which are provided by particular constitutive models for the so-called “smart-materials”, and the materials used in the many applications that involve thermo-, poro-, electro- and/or magneto-mechanical coupling. This book reviews the basic kinematics, balance laws, thermodynamics and constitutive equations for the large deformation theories of elasticity, viscoelasticity, thermoelasticity, poroelasticity, electroelasticity, and magnetoelasticity. The governing partial differential equations are formulated, and suitable boundary conditions are discussed. For specificity, attention is directed towards formulating coupled theories for elastomeric materials. The large deformation coupled theories discussed in this book have been numerically implemented in the open-source finite element program FEniCS, and representative simulations which illustrate key coupled behaviors for each theory are presented.