Distortion energy-based topology optimization design of hyperelastic materials

Highly stretchable material is widely used in the engineering field ranging from soft robots to stretchable electronics. Some highly stretchable 3D-architected mechanical metamaterials have been developed recently. However, failure of material is still the most critical design constraint when stretchability of the structure is considered, and existing topology optimization methods based on, e.g., von Mises stress failure criterion, are not accurate when applied to design hyperelastic materials under large deformation. To address this issue, this paper presents a topology optimization method based on distortion energy for designing nonlinear hyperelastic material against failure. For this purpose, a new objective function based on distortion energy for hyperelastic materials is proposed in the p-norm form. The adjoint method is applied to obtain the sensitivities, and the corresponding optimization problem is solved by the method of moving asymptotes. Excessive mesh distortion in low-density area is addressed through an interpolation scheme of the strain energy known as the fictitious domain method. Four numerical design examples are presented to demonstrate the validity and effectiveness of the proposed algorithm in significantly reducing local distortion energy concentration. One of these examples involves design of highly stretchable metamaterial where the optimized design is shown to sustain three times the finite strain of its base material under uniaxial tension without failure. Therefore, the proposed method has great potential in designing extremely stretchable materials such as stretchable electronics in the future.