Data-driven multiscale nonlinear topology optimization of functionally graded soft composites under large deformations

Functionally graded materials (FGMs) made of soft constituents have emerged as promising material-structure systems in potential applications across many engineering disciplines, such as soft robots, actuators, energy harvesting, and tissue engineering. Designing such systems remains challenging due to their multiscale architectures, multiple material phases, and inherent material and geometric nonlinearities. The focus of this paper is to propose a general topology optimization framework that automates the design innovation of multiscale soft FGMs exhibiting nonlinear material behaviors under large deformations. Our proposed topology optimization framework integrates several key innovations: (i) a novel microstructure reconstruction algorithm that generates composite architecture materials from a reduced design space using physically interpretable parameters; (ii) a new material homogenization approach that estimates effective properties by combining the stored energy functions of multiple soft constituents; (iii) a neural network-based topology optimization that incorporates data-driven material surrogates to enable bottom-up, simultaneous optimization of material and structure; and (iv) a generic nonlinear sensitivity analysis technique that computes design sensitivities numerically without requiring explicit gradient derivation. To enhance the convergence of the nonlinear equilibrium equations amid topology optimization, we introduce an energy interpolation scheme and employ a Newton–Raphson solver with adaptive step sizes and convergence criteria. Numerical experiments show that the proposed framework produces distinct topological designs, different from those obtained under linear elasticity, with spatially varying microstructures. Our framework’s effectiveness and robustness are validated across a range of objective functions and boundary conditions involving large deformations.