Topology optimization of fibers orientation in hyperelastic composite material

Abstract

Material properties of composite materials reinforced with fibers can be improved for a specific application y tailoring fiber orientation. Likewise, it is necessary to ensure fiber continuity to avoid stress concentration in this material. Various methods for optimizing the fiber orientation have been proposed in the last years. However, if fiber angle is considered as a design variable local minima issues may arise. This can be circumvented by using methods where candidate angles are chosen a priori. All these methods consider the hypotheses of small displacement, strain and rotation. Nevertheless, the formulation for this optimization problems must be extended for large displacement and rotations. Thus, this work proposes to develop a model based on topology optimization where displacement, strain, and rotations are not limited. The constitutive equation used is based on transversely isotropic neo-Hookean material for fully nonlinear range. The fiber optimization method is based on Normal Distribution Fiber Optimization (NDFO) method where the values of angles are inserted directly into a normal distribution function and fiber continuity is ensured by using a modified Helmholtz filter. Numerical examples are presented to illustrate the performance of the method. Linear-elastic and neo-Hookean model results are compared to evaluate differences between both hypotheses.