Porous compaction models for lattice metamaterials

Specialized equations of state (EOS) and strength models are required for compaction of porous materials, as the relationship between hydrostatic pressure and volumetric deformation must account for both elimination of void space and compression of the solid. The commonly used compaction models available in the shock physics literature (e.g., p-alpha, p-lambda) are generally applied to simulate materials with unstructured porosity, such as granular compaction of metallic powders and geomaterials.

The applicability of current compaction models to collapse of materials with structured porosity, such as additively manufactured lattice metamaterials, is an open question. This work investigates the dynamic compaction of multiple lattice types in LLNL’s ALE3D hydrocode and evaluates the applicability of the p-alpha model. A more general compaction model is derived that does not require pressure-distension relationships to be prescribed. A procedure to fully evaluate the model from quasistatic confined compression is demonstrated and used to generate model predictions under shock conditions.