Modeling Dynamic Gradual and Rate Dependent Closing and Opening of Pores in Porous Materials

Abstract

Most models for dynamic deformation of porous materials assume that under compressive loading, pore closure is instantaneous. Such an approach is sometimes known as the snowplough model.  But pore closing, as well as pore opening, is a relatively slow mechanical process that involves fracture, plastic flow and material motion on the mesoscale. As a result, a shock loaded porous material may become overstressed relative to its quasistatic pore closing/opening curves. It is then plausible to assume that when overstressed, the material state point would fall back onto the quasistatic curve (in the pressure-porosity plane) at a rate that is an increasing function of the amount of overstress. In this way the pore opening and closing processes become rate dependent. Here we develop and describe such a rate dependent pore opening/closing model. The model includes: 1) an equation of state for porous materials based on Herrmann’s assumptions; 2) the quasistatic opening/closing curves; 3) rate functions for overstress relaxation; and 4) strength reduction of the porous material. We implemented our model in a hydrocode, and we show examples of some uniaxial strain (planar impact) runs.