Impact induced compression and decompression waves in porous meta-materials modeled using a continuum theory of phase transitions

Abstract

Porous meta-materials with both regular and random microstructure are of intense research interest today due to their interesting dynamical properties, including but not limited to, their acoustic band structure, shock absorption properties, and fracture toughness. Some of these materials can exist in a rarefied or densified state depending on the state of stress, and recover their original configuration after a cycle of loading and unloading. Often, they exhibit a hysteretic stress–strain response under quasistatic uniaxial compression. As such, many aspects of their mechanical behavior can be captured using a continuum theory of phase transitions. In this work, the dynamical behavior of such materials is explored. It is shown that the impact problem for these materials can result in propagating shocks, phase boundaries, and fans. The impact problems admit multiple solutions for the same set of initial and boundary conditions leading to non-uniqueness. This non-uniqueness can be remedied using a nucleation criterion and kinetic laws, as is known from the continuum theory of phase transitions. The fan solutions which arise in decompressive impact problems have not received much attention in the literature and may be regarded as a novel contribution of this work. The analysis presented here may have applications in the dynamic behavior of a broad class of porous materials including architected truss-like metastructures and random fiber networks.