Optimization of Carbon Black Polymer Composite Microstructure for Rupture Resistance

Optimization of material microstructure is strongly tied with the performance of composite materials at the macroscale and can be used to control desired macroscopic properties. In this paper, we study the optimal location of carbon black (CB) particle inclusions in a natural rubber (NR) matrix with the objective to maximize the rupture resistance of such polymer composites. Hyperelasticity is used to model the rubber matrix and stiff inclusions, and the phase field method is used to model the fracture accounting for large deformation kinematics. A genetic algorithm is employed to solve the inverse problem in which three parameters are proposed as optimization objective, including maximum peak force, maximum deformation at failure-point, and maximum fracture energy at failure-point. Two kinds of optimization variables, continuous and discrete variables, are adopted to describe the location of particles, and several numerical examples are carried out to provide insight into the optimal locations for different objectives.