On the compressive strength of brittle lattice metamaterials

Abstract

Lightweight architected materials made of a brittle parent solid have great potential for use in environments where extreme conditions occur due to their excellent strength-to-weight ratio and temperature resistance. In this study we combine experimental and modeling efforts to correlate the strength of three-dimensional lattice metamaterials to topological and microstructural characteristics, as well as the mechanical behavior of the base material. Three regular periodic lattices with varying rigidity, owing to their node connectivity, are additively manufactured using a brittle photopolymer and then tested to failure under compressive loads. Micromechanical models are developed to elucidate the experimental results and uncouple the effects of microstructure and strut failure on the resulting macroscopic strength. Our results indicate that stress concentrations at the nodes, where struts intersect, are significantly affecting brittle failure and need to be accounted for in predictive modeling frameworks. Towards this goal, both beam- and solid-based finite element models are considered and their efficacy in capturing the response and critical stresses is examined in detail. We finally show the dependence of lattice strength to relative density and compare the trends with well-known scaling formulas based on dimensional analysis and beam theory.