Strain localization and strain propagation in collapsible solid foams

During compression of brittle or ductile solid foams deformation is, on the scale of the cellular microstructure, characterized by local collapse of cells and the development of strain localization bands ('crushing bands' or 'collapse bands'). On the macroscopic scale, one may either observe the formation and expansion of a macroscopic collapse band which accommodates the imposed compressive strain, or more diffuse accumulation of damage with macroscopically homogeneous deformation. We use a compressive strain gradient plasticity framework to study the nucleation and spreading of collapse bands in solid foams with regular and disordered microstructures. It is demonstrated that foams with ordered microstructure may exhibit a macroscopically inhomogeneous deformation mode which is characterized by a yield point followed by nucleation and spreading of a single collapse band. With increasing disorder we find a transition to macroscopically homogeneous deformation behavior characterized by apparently monotonic hardening and the diffuse nucleation of multiple, non-spreading bands.