Propagation of elastic waves in microporous materials employing an energetically-equivalent non-classical continuum

The elastodynamic response of engineered porous materials depends on their microstructural features. The presence of internal structure, here accounted for by an implicit non-local/non-classical continuum, gives rise to a dynamic response due to an additional degree of freedom, different from the linear elastic behaviour of Cauchy continuum. In this work, a two-scale modelling is applied, based on the energetic equivalence between a lattice at the microscale and a non-classical continuum at the macroscale. This model can represent the material non-linearity, due to porosity, through additional state of strain and stress (autoforces) instead of altering the system stiffness as in classical internal variable models. The response of a microporous plate described with the equivalent model to a monochromatic wave is compared to the original fine texture. The results prove the effectiveness of the approach in describing the wave response and also observing dispersion in wave propagation.