Data-Driven Multiscale Topology Optimization of Soft Functionally Graded Materials with Large Deformations

TL;DR

This paper presents a comprehensive topology optimization framework for designing multiscale soft functionally graded materials that exhibit nonlinear behaviors under large deformations, integrating microstructure reconstruction, homogenization, neural network surrogates, and advanced sensitivity analysis.

Contribution

It introduces a novel multiscale topology optimization method that combines microstructure generation, data-driven material modeling, and nonlinear analysis for soft FGMs.

Findings

Generated distinct topologies differing from linear elasticity designs.

Produced spatially varying microstructures tailored for large deformation behaviors.

Demonstrated the effectiveness of the integrated optimization framework through numerical experiments.

Abstract

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: (1) a novel microstructure reconstruction algorithm that generates composite architecture materials from a reduced design space using physically interpretable parameters; (2) a new material homogenization approach that estimates effective properties by combining the stored energy functions of multiple soft constituents; (3) a neural network-based topology optimization that incorporates data-driven material surrogates to enable bottom-up, simultaneous optimization of material and structure; and (4) 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.