Nonlinear topology optimization of flexoelectric soft dielectrics at large deformation

Abstract

We propose a novel nonlinear topology optimization framework tailored for flexoelectric soft dielectrics undergoing large deformation. A numerical method based on Isogeometric analysis (IGA) is introduced to nonlinear soft dielectrics at finite strain, ensuring the C1-continuity for flexoelectric problems. We outline the process of consistent linearizations and IGA discretizations. Additionally, we introduce an innovative and efficient Strain Density Function (SDF) interpolation scheme for optimizing electromechanical coupling factors (ECFs). In this scheme, the interpolation of electromechanical and hyper-elastic energy terms is grounded in the SIMP model, while a linear material interpolation model is employed for the dielectric energy. Our numerical analysis highlights the remarkable performance of the proposed SDF interpolation scheme in nonlinear electromechanical optimization scenarios. An energy remedy scheme is applied to void regions to eliminate the instability of nonlinear optimization, effectively preventing distortion deformations in low-stiffness elements. Furthermore, we investigate the influence of size effect and larger deformation on the optimization of flexoelectric soft materials. The proposed topology optimization framework adeptly leverages the interplay between size effect and larger deformation, resulting in a notable improvement in ECFs within the optimized structures. Finally, the electromechanical coupling factors (ECFs) of the optimized structures in all the examined cases exhibit enhancements up to 9 times as compared to the reference guess designs.