Topology optimization is a very powerful design method that can find the mechanically optimal material arrangement by setting the design domain, boundary conditions, and materials to be used in advance and performing inverse analysis using computers. Topology optimization has attracted much attention in recent years with the development of lamination technology such as 3D printers, and it has already been put to practical use in the design of many aircraft components. However, most of these designs assume a linear problem, and there has been little progress in designing nonlinear problems that match real-world phenomena. This is due to the fact that path dependence and other effects unique to nonlinear problems complicate sensitivity analysis and require a large amount of computation time. However, the method of Kato et al (2015). allows some steps of sensitivity analysis to be omitted under certain conditions, making the computational cost of the method practical. In this study, We extend the work of Kato et al. and propose a topology optimization method to improve the toughness of von-Mises elastoplastic and/or damaged multimaterials. We verify the accuracy of the sensitivity by comparing the obtained analytical sensitivity with the sensitivity obtained by finite difference approximation, and further discuss the results based on the optimization results obtained by running the calculations.