Design of microstructures of viscoelastic composites for optimal damping characteristics

Abstract An inverse homogenization problem for two-phase viscoelastic composites is formulated as a topology optimization problem. The effective complex moduli are estimated by the numerical homogenization using the finite element method. Sensitivity analysis shows that the sensitivity calculations do not require the solution of any adjoint problem. The objective function is defined so that the topology optimization problem finds microstructures of viscoelastic composites which exhibit improved stiffness/damping characteristics within the specified operating frequency range. Design constraints include volume fraction, effective complex moduli, geometric symmetry and material symmetry. Several numerical design examples are presented with discussions on the nature of the designed microstructures. From the designed microstructures, it is found that mechanism-like structures and wavy structures are formed to maximize damping while retaining stiffness at the desired level.

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