Approximation of the Mechanical Response of Large Lattice Domains Using Homogenization and Design of Experiments

Abstract

Lattice-based workpieces contain patterned repetition of individuals of a basic topology (Schwarz, ortho-walls, gyroid, etc.) with each individual having distinct geometric grading. In the context of the design, analysis and manufacturing of lattice workpieces, the problem of rapidly assessing the mechanical behavior of large domains is relevant for pre-evaluation of designs. In this realm, two approaches can be identified: (1) numerical simulations which usually bring accuracy but limit the size of the domains that can be studied due to intractable data sizes, and (2) material homogenization strategies that sacrifice precision to favor efficiency and allow for simulations of large domains. Material homogenization synthesizes diluted material properties in a lattice, according to the volume occupancy factor of such a lattice. Preliminary publications show that material homogenization is reasonable in predicting displacements, but is not in predicting stresses (highly sensitive to local geometry). As a response to such shortcomings, this paper presents a methodology that systematically uses design of experiments (DOE) to produce simple mathematical expressions (meta-models) that relate the stress–strain behavior of the lattice domain and the displacements of the homogeneous domain. The implementation in this paper estimates the von Mises stress in large Schwarz primitive lattice domains under compressive loads. The results of our experiments show that (1) material homogenization can efficiently and accurately approximate the displacements field, even in complex lattice domains, and (2) material homogenization and DOE can produce rough estimations of the von Mises stress in large domains (more than 100 cells). The errors in the von Mises stress estimations reach 42 % for domains of up to 24 cells. This result means that coarse stress–strain estimations may be possible in lattice domains by combining DOE and homogenized material properties. This option is not suitable for precise stress prediction in sensitive contexts wherein high accuracy is needed. Future work is required to refine the meta-models to improve the accuracies of the estimations.

Predictions of the Elastic–Plastic Compressive Response of Functionally Graded Polymeric Composite Lattices Manufactured by Three-Dimensional Printing

“…Several studies [8][9][10] have experimentally and/or numerically explored the structural response of metal-or polymer-based strut-and surface-based lattices, however only a few scrutinized FGLs [2,11,12]. To-date, finite element analyses of these structures have primarily focused on their elastic behaviour, despite lattice materials and FGLs offering great advantages over monolithic materials in terms of specific energy absorption [5], which is considerably high during their plastic response.…”

“…The authors observed a good agreement of the FEN model with the experimental data. Besides the explicit geometric models, the homogenisation approach [12,[15][16][17][18][19] served as a computationally efficient alternative to determine the equivalent effective properties of a heterogeneous lattice. In [17,19], it was coupled with the modified Hill yield criterion and showed good agreement for variable density and surface-based lattices.…”