Using automatic differentiation with checkpointing for elastoplastic topology optimization

The topology optimization of elastoplastic materials is complicated by path dependency and nonlinearity, which greatly increase the computational costs. We propose an elastoplastic topology optimization framework aimed at eliminating the complexity of sensitivity analysis design while greatly improving the computational efficiency. The proposed method utilizes automatic differentiation (AD) for the sensitivity analysis, which eliminates the need for labor-intensive formulations and programming. This is combined with checkpointing to drastically mitigate the immense memory consumption of AD by retaining only the minimum data necessary for gradient computation with the tradeoff of a manageable increase in computation time. To demonstrate the versatility of the proposed method, a general von Mises elastoplastic model that incorporates both isotropic and kinematic hardening via nonlinear piecewise linear approximation was applied to a multi-material optimization problem involving the maximization of energy absorption and plastic work under volume constraints. Numerical examples confirmed the accuracy of the AD-based sensitivity analysis regardless of the objective function and demonstrated that applying checkpointing effectively resolved the memory bottleneck for AD. The proposed method demonstrates the methodological feasibility of AD-based sensitivity analysis for topology optimization problems involving multiple elastoplastic materials, providing an important foundation toward full-scale practical applications in the future.