Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems

The focus of this paper is on interpolation schemes for fictitious domain and topology optimization approaches with structures undergoing large displacements. Numerical instability in the finite element simulations can often be observed, due to excessive distortion in low stiffness regions. A new energy interpolation scheme is proposed in order to stabilize the numerical simulations. The elastic energy density in the solid and void regions is interpolated using the elastic energy densities for large and small deformation theory, respectively. The performance of the proposed method is demonstrated for a challenging test geometry as well as for topology optimization of minimum compliance and compliant mechanisms. The effect of combining the proposed interpolation scheme with different hyperelastic material models is investigated as well. Numerical results show that the proposed approach alleviates the problems in the low stiffness regions and for the simulated cases, results in stable topology optimization of structures undergoing large displacements.