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

TL;DR

This paper introduces a two-scale computational homogenization method for elastoplastic analysis of truss-based lattice structures, significantly reducing computational costs while accurately capturing complex material behaviors.

Contribution

The study develops a novel two-scale homogenization approach with real-time information exchange for elastoplastic lattice structures, improving efficiency over direct numerical simulations.

Findings

The method accurately predicts forces and displacements in lattice structures.

It reduces computational cost by modeling microscale trusses as 1D elements.

Scale separation is crucial for the method's validity.

Abstract

The revolutionary advancements in metal additive manufacturing have enabled the production of alloy-based lattice structures with complex geometrical features and high resolutions. This has encouraged the development of nonlinear material models, including plasticity, damage, etc., for such materials. However, the prohibitive computational cost arising from the high number of degrees of freedom for engineering structures composed of lattice structures highlights the necessity of homogenization techniques, such as the two-scale computational homogenization method. In the present work, a two-scale homogenization approach with on-the-fly exchange of information is adopted to study the elastoplastic behavior of truss-based lattice structures. The macroscopic homogenized structure is represented by a two-dimensional continuum, while the underlying microscale lattices are modeled as a network of one-dimensional truss elements. This helps to significantly reduce the associated computational cost by reducing the microscopic degrees of freedom. The microscale trusses are assumed to exhibit an elastoplastic material behavior characterized by a combination of nonlinear exponential isotropic hardening and linear kinematic hardening. Through multiple numerical examples, the performance of the adopted homogenization approach is examined by comparing forces and displacements with direct numerical simulations of discrete structures for three types of stretching-dominated lattice topologies, including triangular, X-braced and X-Plus-braced unit cells. Furthermore, the principle of scale separation, which emphasizes the need for an adequate separation between the macroscopic and microscopic characteristic lengths, is investigated.