One-Dimensional Numerical Framework for Shock Compaction of Cellular Foams

Abstract

A one-dimensional (1D) finite-volume implementation, based on the second-order Godunov method for predicting dynamic response of foams that exhibit irreversible compaction, is presented. Cellular foams, with an upward concave stress-strain relationship associated with densification of the material resulting from collapse of the cell structure, have the possibility of a strong discontinuity with shock-type characteristics. An approximate solution to the local Riemann problem is developed considering all possible wave structure(s) in the material based on the quasi-static response of the material. The prediction of dynamic compaction response of the foam subjected to solid impact is shown to compare favorably with experimental results. For an applied blast pressure loading, attenuation of transmitted stress wave in the foam is shown to be a result of the energy dissipation provided by compaction of the foam.