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

Abstract

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.

Lamb's problem on random mass density fields with fractal and Hurst effects

“…The ideal homogeneous, material modelled is CR-39 as it is used by Dally in an experimental study [6]. A study comparing the experimental results with the results from CA and a non-local numerical method for homogeneous mass density fields can be found in [27]. Nishawala et al [27] also includes a convergence study.…”

“…A study comparing the experimental results with the results from CA and a non-local numerical method for homogeneous mass density fields can be found in [27]. Nishawala et al [27] also includes a convergence study. CR-39 has an Young's modulus of 3.85 GPa (559 ksi), Poisson ratio of 1/3 and homogeneous mass density 1300 kg m −3 .…”

Anti-plane shear Lamb's problem on random mass density fields with fractal and Hurst effects

“…The classical in-plane Lamb's problem was studied both theoretically and experimentally [1,2]. The in-plane Lamb's problem on random mass density fields with fractal and Hurst effects was studied numerically in [9,10,11], where both pressure (P) and Rayleigh (R) waves were considered. The present study concentrates on the shear wave analysis.…”

Solving partial differential equations in computational mechanics via nonlocal numerical approaches

“…The known discrete methods, which make use of nonlocality are: nonlocal finite difference (FD) method, nonlocal finite element (FE) method, cellular automata, e.g. when applying a secondary von Neumann neighborhood, and the methods based on the micropolar and Cosserat theories …”