A Semiempirical Model for Post‐Yield Stress Instability in the Stress–Strain Response of 3D Lattice Structures under Compressive Loads

Abstract

Mechanical behavior of lattice structures is important for a range of engineering applications. Herein, a new semiempirical model is proposed that describes the entire range of stress–strain response of lattice structures, including the stress‐instability region which is modeled as an oscillator. The model can be fit to individual stress–strain curves to extract elastic modulus, yield stress, collapse stress, post‐yield collapse ratio, densification strain, and the energy absorbed per unit volume. The model is fit to 119 unique experimental stress–strain curves from 13 research papers in literature covering four different lattice designs, namely, octet truss, body‐centered cubic with vertical members, body‐centered cubic, and hexagonal. Manufacturing methods (additive and conventional) and materials (metals and polymers) were also included in the analysis. The fitted model yields several new insights into the compression behavior of previously tested lattice structures and can be applied to additional lattice designs. Among other results, analysis of variance (ANOVA) reveals that the octet truss lattice demonstrates the highest post‐yield collapse ratio and the smallest normalized energy absorption per unit volume amongst the lattice structures investigated. The proposed model is a powerful tool for designers to quantitatively compare and select 3D lattice structures with the desired mechanical characteristics.