The meso-structures analysis of truss-like lightweight materials based on symmetric groups

Abstract

Truss-like lightweight materials (TLLMs) with superior mechanical performance and excellent energy absorption capability are extensively used in aerospace and automobile industries. The performance of TLLM was closely related to its meso-structure, but the lack of innovation and variety in the geometric configuration of TLLM’s meso-structure limits the reinforcement effect and strength enhancement. Hence, it is important to thoroughly study the theoretical design method for TLLM’s meso-structure. Inspired by the symmetric feature of TLLM’s meso-structures, the symmetric groups were applied to describe, classify and design TLLM’s meso-structures. First of all, it was found that the representative volume unit (RVU) of TLLM corresponded to point groups that contained the symmetry of TLLM’s meso-structure. Space groups, which consist of point groups and space lattices, could be used to describe the geometric configuration of TLLM’s meso-structures. Then, TLLM’s meso-structures were classified according to different types of point groups. Finally, a description and design method for TLLM’s meso-structure based on the symmetric group theory was proposed. In addition, a novel TLLM’s meso-structure was deduced through the symmetric operations of space group, which could verify the feasibility of the method. Therefore, the present study provides a basis for the design of high-performance TLLMs.