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

2025-06-29

AI Summary

This study addresses the challenge of automated multiscale design for soft functionally graded materials (FGMs) exhibiting nonlinear mechanical responses under large deformations. Methodologically, we propose a topology optimization framework integrating microstructure reconstruction algorithms, data-driven homogenization modeling, neural-network-enhanced co-optimization architecture, and derivative-free nonlinear sensitivity analysis. Key innovations include physics-informed parametric constitutive modeling, stored-energy-function coupling, adaptive Newton–Raphson solvers, and energy-based interpolation strategies. The resulting gradient microstructural topologies exhibit pronounced spatial gradation under large deformations—overcoming limitations of linear elasticity assumptions—while ensuring physical interpretability and computational efficiency. This work establishes a new paradigm for intelligent, nonlinear design of soft functional materials, with direct applicability to soft robotics, actuators, and tissue engineering.

Technology Category

• Intelligent Robots: Learning & Optimization for ROB
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Multi-instance/Multi-view Learning

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• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• Design multiscale soft FGMs with nonlinear material behaviors
• Automate topology optimization for large deformation applications
• Integrate data-driven methods for material and structure optimization

Innovation

• Microstructure reconstruction algorithm with interpretable parameters
• Material homogenization via stored energy functions
• Neural network-based data-driven topology optimization