Topology optimization of composite hyperelastic material using SPIMFO-method

Fiber reinforced materials are used in assorted engineering application and for this reason, new additive manufacturing technologies have been developed for this type of materials. With these technologies, it is possible to construct composite structures with different shapes and desired fiber orientation. Therefore, reinforced composite structures can be designed based on an optimized fiber orientation. Because of it, several works propose different methods to tailor fiber directions. Albeit, the determination of fiber optimized orientation is a problem usually subjected to multiple local minima issues, unless discrete material optimization methods are used. In addition, in these works, usually a linear relation between stress and strain is considered, which limits simulations to small displacements, strains and rotations. Recently, a method named SPIMFO has been developed where the angle is considered a continuous variable and the local minima issues are circumvented. Thus, this work proposes to determine the optimized fiber orientation of a fiber reinforced composite structure by using the SPIMFO method with a constitutive equation in fully nonlinear range based on transversely isotropic neo-Hookean model. A new method to measure the fiber continuity named index of average continuity is proposed and implemented. The results obtained by using the proposed method are compared to results obtained by using a discrete model named NDFO-m, which is proposed in a previous work.