Wave propagation in finite element and mass-spring-dashpot lattice models

Abstract

Numerical efficiency comparisons of a four-node finite element model (FEM), a mass-spring lattice model (MSLM), and a mass-spring-dashpot lattice model (MSDLM) are investigated. Specifically, the error in the ultrasonic phase speed with variations in Poisson's ratio and angle of incidence is evaluated in each model of an isotropic elastic solid. With regard to phase speed, materials with constant N grid spaces per P-wavelength having Poisson's ratios between 0.0 and 0.25 are modeled more accurately with the MSLM. Materials with Poisson's ratios between 0.35 and 0.5 and N grid spaces per P-wavelength are more accurately modeled with the FEM. Materials whose Poisson's ratio is between 0.25 and 0.35 are modeled equally accurately. With regard to phase speed, viscoelastic materials modeled with FEM and MSDLM show good agreement with known analytical solutions. The computational expense of all three models is also examined. The number of floating point operations (FLOPS) needed to achieve a specified phase speed accuracy is calculated for each different model. While the FEM and MSLM have nearly the same computation cost, the MSDLM is 5 times more costly than either the FEM or MSLM.