A perturbation-boundary integral equation method for transient dynamics of nonlinear elastic materials

This study presents a formulation for solving the transient dynamics of nonlinear elastic materials. By using a perturbation expansion to linearize the basic equations and applying the Laplace transform to the subsequent perturbation equations, the boundary value problem of the transformed equations is further reduced to various boundary integral equations. After discretization of the integral equations, these are solved numerically, completing the solution in the Laplace transform space. Performing a numerical inversion of the Laplace transform yields the solution of the problem in the time domain.