ABSTRACT

CH A P T E R 18 Wave Propagation in Hyperelastic Waveguides

The study of wave propagation in solids, especially in the presence of nonlinearities, is quite challenging and it requires a robust, efficient, and extensible computational framework. A large variety of computational schemes have been developed in the past to address the various issues that arise in the numerical modeling of stress wave propagation. The standard computational workhorse in contemporary research is the finite element method, which we studied in Chapter 12, where we studied several variants of FEM. The solution of dynamic problems in solid mechanics is typically carried out by employing the FEM to discretize the spatial part of the governing equations and employing an appropriately chosen finite difference (FD) scheme for time marching [24], [161], [169]. This has been developed and refined to study a wide range of problems in linear elasticity. Problems involving non-linearities are typically solved iteratively, and often using a linearization procedure [24].