Computational Homogenization of Architectured Materials

Abstract

Architectured materials involve geometrically engineered distributions of microstructural phases at a scale comparable to the scale of the component, thus calling for new models in order to determine the effective properties of materials. The present chapter aims at providing such models, in the case of mechanical properties. As a matter of fact, one engineering challenge is to predict the effective properties of such materials; computational homogenization using finite element analysis is a powerful tool to do so. Homogenized behavior of architectured materials can thus be used in large structural computations, hence enabling the dissemination of architectured materials in the industry. Furthermore, computational homogenization is the basis for computational topology optimization which will give rise to the next generation of architectured materials. This chapter covers the computational homogenization of periodic architectured materials in elasticity and plasticity, as well as the homogenization and representativity of random architectured materials.

Effect of prestress on phononic band gaps induced by inertial amplification

“…( 10) and the numerical results (magenta square markers). The values of k ef f introduced in the analytical model are directly calculated from the deformed numerical configuration according to standard homogenization procedures 65,66 .…”

Experimental and computational analysis of the mechanical properties of composite auxetic lattice structures

“…By computing the volume averaged response under a physical stimulus over a virtual sample that is considered a representative volume element (RVE), one can identify the effective properties of a heterogeneous medium [74][75][76][77][78].…”

Computational Investigation of the Effective Mechanical Behavior for 3D Pre-Buckled Auxetic Lattices

“…Another main interest of computational homogenization resides in obtaining an equivalent constitutive model that can be implemented in a finite element analysis, saving extensive computation time by avoiding to explicitly represent and account for the underlying microstructure. This strategy is commonly used for architectured materials [5], allowing for fast computation of their effective properties. In this work, linear elastic properties of auxetics are investigated first, before extending the study to elastoplasticity.…”

“…Architectured materials are a rising class of advanced materials that bring new possibilities in terms of functional properties, filling the gaps and pushing the limits of Ashby's materials performance maps [1]. The term architectured materials encompasses any material obtained through a design process aiming at fulfilling a specific set of requirements, in terms of functionality, behavior, or performance, induced by a particular morphology, i.e., the relative topological arrangement between multiple phases, such that some of its materials properties, e.g., yield strength/density, are improved in comparison with those of its constituents due to structure and composite effects [1][2][3][4][5].…”