Topology optimization for microstructures of viscoelastic composite materials

The viscoelastic response of materials is often utilized for wide applications such as vibration reduction devices. This paper extends the bi-directional evolutionary structural optimization (BESO) method to the design of composite microstructure with optimal viscoelastic characteristics. Both storage and loss moduli of composite materials are calculated through the homogenization theory using complex variables. Then, the BESO method is established based on the sensitivity analysis. Through iteratively redistributing the base material phases within the unit cell, optimized microstructures of composites with the desirable viscoelastic properties will be achieved. Numerical examples demonstrate the effectiveness of the proposed optimization method for the design of viscoelastic composite materials. Various microstructures of optimized composites are presented and discussed. Meanwhile, the storage and loss moduli of the optimized viscoelastic composites are compared with available theoretical bounds.