A multi-field approach to modeling the dynamic response of cellular materials

A multi-field approach is developed for simulating the continuum-scale mechanical response of cellular materials. This approach departs from traditional methods used to model cellular materials, which focus almost exclusively on the mechanical response of the cellular solid, while essentially ignoring the fluids permeating these material systems. In the present work, conservation equations are derived in multi-field form, producing a coupled set of governing equations with source terms depending on gradients in the cellular solid stress, but also on gradients in the permeating fluid pressure and momentum exchange resulting from relative motion between the cellular solid and permeating fluid fields. The multi-field equations of motion are implemented in a standard finite-volume computational test bed and used to study the dynamic response of cellular material systems. The influence of various permeating fluids, along with the effects of aperture size, loading rate, and boundary conditions, also are examined. By incorporating an advanced constitutive model for cellular solids into a multi-field response formulation, a promising new approach for simulating the finite-strain dynamic response of cellular materials is offered. Results demonstrate that the permeating fluid can play a major role in the general response of cellular material systems, contributing to the overall load-carrying capacity of the materials and affecting rate dependence and signal propagation speeds. Furthermore, the results point to the usefulness of the multi-field formulation and provide evidence to suggest that any modeling approach developed for cellular materials gives a proper accounting of the pressure evolution and flow behavior of the fluids present in these material systems.