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

Results in Engineering, vol. 25, pp. 103976

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.

Authors 5

1. Hooman Danesh corresponding Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany

2. Lisamarie Heußen Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany

3. Francisco Javier Montáns

   Universidad Politécnica de Madrid · University of Florida

   Affiliation as printed

   Department of Mechanical and Aerospace Engineering, Herbert Wertheim College of Engineering, University of Florida, Gainesville, FL 32611, USA

   ETS de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza Cardenal Cisneros 3, 28040 Madrid, Spain

4. Stefanie Reese Aachen Institute of Applied Mechanics

   RWTH Aachen University · University of Siegen

   Affiliation as printed

   Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany

   University of Siegen, Adolf-Reichwein-Str. 2a, 57076 Siegen, Germany

5. Tim Brepols Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany