Towards Field Driven Design of Cellular Materials for Energy Absorption: Modeling and Simulation of Variable-thickness Schwarz-P TPMS Structures

The design, modeling and optimization of cellular materials for energy absorption remains one of the more challenging sub-domains within architected cellular and meta-materials for mechanical behavior. The work in this field is primarily of an empirical and experimental nature, with little use of modeling and simulation to drive design. Further, most of the work involves constant thickness cellular structures when there is ample evidence in nature and engineered foams that there are advantages to heterogeneity in thickness of the walls and struts that make up cellular structures. This gap can be attributed to the modeling challenges associated with accurately representing the large deformations and contact seen in cellular materials subjected to very large compressive strains. This in turn makes it difficult to implement non-empirical design, such as design emerging from a physics-based simulation. This work addresses this gap by proposing, developing, implementing and validating a continuum shell based finite element model that enables the simulation of the behavior of variable thickness Schwarz-P TPMS cellular structures. Four different fields: two rational (linear gradient and failure band) and two stochastic, are implemented and studied, with all showing improvements over the uniform thickness baseline. In so doing, the modeling approach for field driven design of variable thickness TPMS structures for energy absorption is demonstrated and validated for the first time.