A two-scale computational homogenization approach for elastoplastic truss-based lattice structures

Abstract

Advancements in metal additive manufacturing have enabled the fabrication of alloy-based lattice structures with complex geometrical features, driving the need for efficient modeling frameworks. Despite progress in the homogenization of metamaterials, most existing studies have focused on the elastic behavior of lattice structures (whether linear or nonlinear), while the inelastic behavior, particularly elastoplasticity, remains largely unexplored. This study develops a two-scale homogenization framework to model such structures, focusing on post-yielding deformations, using a combined nonlinear exponential isotropic-kinematic hardening model for the lattice struts. The framework is applied to three types of stretching-dominated lattice topologies, including triangular, X-braced, and X-Plus-braced unit cells. The macroscopic structure is represented as a two-dimensional continuum, while the microscale lattice is modeled as a network of truss elements, significantly reducing computational cost. The framework is validated through numerical examples, including a double-clamped beam, a square plate under tension, and a dog-bone specimen under cyclic loading. It is demonstrated that the homogenization framework accurately captures force-displacement responses as well as full-field local solutions during loading, unloading, and reverse loading. Comparisons with direct numerical simulations show that the framework provides precise results in both the elastic and elastoplastic regimes, demonstrating the importance of satisfying the principle of scale separation to ensure accuracy, particularly in the plastic regime. • A two-scale computational homogenization approach, considering a two-dimensional macroscopic continuum and microscopic truss structures, is developed for elastoplastic lattice structures. • Three stretching-dominated lattice topologies, including triangular, X-braced and X-Plus-braced lattices are studied. • The homogenization approach provides highly accurate solutions in loading, unloading and reverse loading scenarios. • Examining the principle of scale separation shows that the accuracy of the homogenization scheme increases when the component under investigation is composed of more lattice structures. • The accuracy of the homogenization approach is slightly higher in the elastic regime.

Topics & Concepts