Wave propagation in microstructured materials using peridynamics

Wave propagation in heterogeneous materials, such as aluminum or composite materials, is affected by singularities in the mechanical properties arising from changes in the constituent phases. Classical mechanics describes this phenomenon using local equations that are valid only in regular domains; when singularities are present, however, the partial derivatives on which these equations rely are no longer well-defined. To overcome this limitation, a nonlocal peridynamic model for a one-dimensional domain is developed, in which integral equations replace differential equations. The ability of this model to represent the insertion of a specific constituent within a matrix made of another material is investigated, and the influence of the model parameters on this behavior is systematically analyzed. The results show that the proposed model recovers the prototype microelastic material behavior when the heterogeneous medium tends toward homogeneity, both as the amount of the inserted constituent within the matrix decreases and as the material properties of the phases approach each other. Moreover, the model captures the additional reflections and wave distortions induced by the passage of the wave through the different constituents. It is also demonstrated that parameters such as the peridynamic horizon, the material disorder, and the contrast between the material properties of the components strongly affect the wave propagation characteristics.