Stiffness and strength evaluation of lattice-based mechanical metamaterials by decoupled two-scale analysis

Abstract

There is an emerging class of artificial materials, so-called mechanical metamaterials. By deliberately designing microscopic internal mechanisms, these materials exhibit exotic properties, which distinguish the mechanical metamaterials from natural materials. As additive manufacturing technology has been rapidly developed and its manufacturing quality has been improved, those conceptual artificial materials are ready to fabricate. This paper presents a decoupled two-scale analysis framework to efficiently evaluate the stiffness and strength characteristics of lattice-based mechanical metamaterials. Structural characteristics of lattice-based mechanical metamaterials are effectively captured by accommodating a computational homogenization method to lattice-based structures. In the computational homogenization procedure, a unit cell of the periodically distributed structure is modeled as representative finite elements. Equivalent stiffness properties of the unit cell are calculated based on the computational homogenization procedure. The equivalent structural properties are then used to perform macroscopic structural analysis of lattice-based structures in an effective manner. Similarly, a local/microscopic stress distribution within the periodic lattice unit cell is recovered by transforming macroscopic sectional loads, which are obtained from the macroscopic structural analysis, through a stress amplification matrix. The microscopic stress distribution obtained with the two-scale analysis can be used for strength evaluation. Subsequently, numerical results are validated by comparing them with experimental results providing actual behaviors of lattice-based mechanical metamaterials. This work presents the novel use of the multi-scale analysis scheme combining the computational homogenization method and the stress field transformation method enabling structural evaluations to design mechanical metamaterials with structural integrity. This study also demonstrates the feasibility and capability of the presented approach to effectively predict stiffness and strength characteristics of lattice-based structures.