Non-local dispersive model for wave propagation in heterogeneous media: multi-dimensional case

Three non-dispersive models in multi-dimensions have been developed. The rst model consists of a leading-order homogenized equation of motion subjected to the secularity constraints imposing uniform validity of asymptotic expansions. The second, non-local model, contains a fourth-order spatial derivative and thus requires C1 continuous nite element formulation. The third model, which is limited to the constant mass density and a macroscopically orthotropic heterogeneous medium, requires C0 continuity only and its nite element formulation is almost identical to the classical local approach with the exception of the mass matrix. The modi ed mass matrix consists of the classical mass matrix (lumped or consistent) perturbed with a sti ness matrix whose constitutive matrix depends on the unit cell solution. Numerical results are presented to validate the present formulations