Accurate finite-element modeling of wave propagation in composite and functionally graded materials

For the first time, we have obtained accurate numerical solutions for wave propagation in inhomogeneous materials under impact loading. We have extended the earlier developed numerical approach for elastodynamics problems in homogeneous materials to inhomogeneous materials. The approach includes the two-stage time-integration technique with the quantification and the filtering of spurious oscillations, the special design of non-uniform meshes as well as includes the standard finite elements and the elements with reduced dispersion. Similar to wave propagation in homogeneous materials in the 1-D case, we have obtained very accurate results for composite and functionally graded materials using the linear elements with lumped mass matrix and the explicit central difference method. We have also shown that specific non-uniform meshes yield much more accurate results compared to uniform meshes. We have also shown the efficiency of the finite elements with reduced dispersion compared with the standard finite elements.