Microstructure design of porous viscoelastic composites with prescribed relaxation moduli by multi-material topology optimization

Abstract

This paper presents a multi-material topology optimization method for designing the microstructures of porous viscoelastic composites with prescribed relaxation moduli. It is assumed that the composite materials are microscopically composed of periodic unit cells. The effective relaxation moduli of the composites are obtained using the homogenization method. The density-based topology optimization is utilized, and a related material interpolation scheme is introduced. The design objective is to determine an optimal material distribution that exhibits the prescribed modulus in both the glassy and rubbery regions. The design sensitivity is derived analytically using the adjoint variable method. A filtering scheme is adopted to impose a minimum length scale for each material phase. Several numerical examples are presented to demonstrate the effectiveness of the proposed method. Various microstructures with prescribed relaxation moduli are presented and discussed. In addition, the bounds on the relaxation moduli of the optimized microstructures are compared with theoretical bounds.