A state space formalism and perturbation method for generalized thermoelasticity of anisotropic bodies

A state space formalism for generalized anisotropic thermoelasticity accounting for thermomechanical coupling and thermal relaxation is developed, which includes the classical thermoelasticity as a special case. By properly grouping the field variables using matrix notations, the basic equations of thermoelasticity are formulated into a state equation and an output equation in terms of the state vector. To obtain the solution for a specific problem it suffices to solve the state equation under the prescribed conditions. For weak thermomechanical coupling an asymptotic solution can be obtained by using the method of perturbation with multiple scales. Propagation of plane harmonic thermoelastic waves in an anisotropic medium is studied within the context.