Multi-field asymptotic homogenization approach for Bloch wave propagation in periodic thermodiffusive elastic materials

Multi-field asymptotic homogenization methods are proposed to describe the behaviour of periodic Cauchy materials subject to several physical phenomena, focusing on thermodiffusion. The resulting homogenized models provide the overall constitutive tensors and overall inertial terms. Moreover, they allow one to investigate the complex band structures associated with damped Bloch waves travelling in periodic materials, avoiding the challenging computations needed by the adoption of micromechanical approaches.