Simulation of elastic wave propagation using cellular automata and peridynamics, and comparison with experiments

• Peridynamic and Cellular Automata 2D-elastodynamic responses are evaluated.
• Each method is subjected to a normal load on a half-plane (Lamb’s Problem).
• Cellular Automata and Peridynamics reproduce the shape and location of the pressure, shear and Rayleigh wave very well.
• Neither method is able to follow experimental results.

Peridynamics is a non-local continuum mechanics formulation that can handle spatial discontinuities as the governing equations are integro-differential equations which do not involve gradients such as strains and deformation rates. This paper employs bond-based peridynamics. Cellular Automata is a local computational method which, in its rectangular variant on interior domains, is mathematically equivalent to the central difference finite difference method. However, cellular automata does not require the derivation of the governing partial differential equations and provides for common boundary conditions based on physical reasoning. Both methodologies are used to solve a half-space subjected to a normal load, known as Lamb’s Problem. The results are compared with theoretical solution from classical elasticity and experimental results. This paper is used to validate our implementation of these methods.