Modeling of dynamically loaded open-cell metallic foams

Heterogeneous cellular materials such as metallic and polymeric open-celled foams are preferable in many engineering applications requiring mitigation of energy during sudden impact loading. This brief communication presents an approach for modeling dynamically loaded open-cell metallic foams. It is implicitly assumed that there exists a length scale separation where the microstructural dimensions are much smaller than the macroscopic dimensions. In this context, a macroscopic point translates into a microscopic array of identical unit cells sharing the same macroscopic fields. Dictated by a model for the metallic cell wall constitutive behavior, the effective unit cell response is then obtained from a structural micromechanical model which enforces the principle of minimum action on a representative 3D unit cell. The effective macroscopic response at every node in the FEM mesh (equilibrium, stresses, stress tangents) is then provided by the unit cell microscopic model. The present theory allows one to define a constitutive formulation for lightweight, open-celled foams based on clear and quantifiable parameters such as microstructural topology and ligament properties while capturing the effects of dynamic loading via viscous dissipation at ligament level and microinertia at unit cell level. History of deformation is considered at ligament level while axial and bending deformation are considered at unit cell level. As observed experimentally, the resulting macroscopic FEM simulations clearly demonstrate how the material undergoes heterogeneous deformation during cellular structure collapse.