Topology optimization of micro-structured materials featured with the specific mechanical properties

TL;DR

This paper presents a level set-based topology optimization method for designing micro-structured materials with specific mechanical properties, using energy-based homogenization to evaluate effective properties and optimizing microstructures for desired elastic behaviors.

Contribution

It introduces a novel combination of energy-based homogenization and parametric level set methods for microstructure topology optimization targeting specific mechanical properties.

Findings

Successfully optimized microstructures with maximum bulk and shear moduli.

Achieved negative Poisson's ratio microstructures.

Demonstrated effectiveness through numerical examples.

Abstract

Micro-structured materials consisting of an array of microstructures are engineered to provide the specific material properties. This present work investigates the design of cellular materials under the framework of level set, so as to optimize the topologies and shapes of these porous material microstructures. Firstly, the energy-based homogenization method (EBHM) is applied to evaluate the material effective properties based on the topology of the material cell, where the effective elasticity property is evaluated by the average stress and strain theorems. Secondly, a parametric level set method (PLSM) is employed to optimize the microstructural topology until the specific mechanical properties can be achieved, including the maximum bulk modulus, the maximum shear modulus and their combinations, as well as the negative Poisson's ratio (NPR). The complicated topological shape optimization of the material microstructure has been equivalent to evolve the sizes of the expansion coefficients in the interpolation of the level set function. Finally, several numerical examples are fully discussed to demonstrate the effectiveness of the developed method. A series of new and interesting material cells with the specific mechanical properties can be found.