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.

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A simultaneous shape and stacking sequence optimization algorithm is presented for laminated composite free-form shells, by which the coupled effect of shape and stacking sequence can be considered. The optimization objective is determined as maximizing fundamental natural frequency to obtain largest stiffness of shells. Nonuniform rational B-spline (NURBS) is employed to represent free-form geometrical shapes. The coordinates of NURBS control points and fiber orientations are set up as continuous and discrete optimization variables, respectively, and optimized simultaneously. To improve the efficiency of the mixed continuous-discrete optimization, multi-island genetic algorithm (MIGA) is employed to search for the global result. Through several numerical examples, the performance of the proposed approach is demonstrated in comparison with the two-phase optimization method; the effect of boundary conditions and the setup of control points on optimal results are investigated, respectively.