GELATO: Multi-Material Topology Optimization of Programmable Gel-Elastomer Structures

2026-05-19

AI Summary

Conventional approaches struggle to design gel-elastomer composite structures with complex programmable shape-morphing capabilities. This work proposes a multi-material topology optimization framework that, for the first time, integrates coordinate-based neural networks with the Flory–Rehner unified constitutive model to establish an end-to-end differentiable implicit design paradigm, enabling simultaneous optimization of structural topology and spatial material distribution. Implemented in JAX with automatic differentiation, the method supports multi-objective, multi-constraint formulations and coupled multi-physics responses. It successfully demonstrates programmable soft actuators, multi-stimuli-responsive organogel–hydrogel composites, and anisotropic hydrogel architectures with co-optimized fiber orientation and topology.

Abstract

Gel-elastomer composites, comprising an active swellable hydrogel and a passive elastomer, are a compelling class of programmable material systems (PMS) capable of shape morphing under multiphysics actuation. The precise design of the topology and material distribution unlocks complex programmability instrumental in wearable electronics, soft robots, and drug delivery; however, the structure-function relationship is highly non-intuitive, rendering both trial-and-error and conventional design approaches largely intractable. To address this, we present a topology optimization (TO) framework for the automated design of such structures, enabling systematic exploration of the design space for target functionalities realized via programmable shape morphing. In particular, we propose a multi-material TO framework that concurrently optimizes the structural topology and the spatial distribution of the gel-elastomer phases. The design is represented via a coordinate-based neural network, and the mechanical response of both phases is described within a unified constitutive framework based on the Flory-Rehner theory. Furthermore, we present an end-to-end differentiable design framework with implicit differentiation that accommodates various objective functions, constraints, and discretizations. We demonstrate the framework on shape-programming structures and soft actuators. The framework is further validated through the design of organogel-hydrogel composites for multi-stimuli responsiveness across chemically distinct solvent environments, and of anisotropic hydrogels wherein the local fiber orientation is optimized concurrently with the topology. The codebase implemented in JAX is publicly shared to support benchmarking and reproducibility.

Problem

• programmable material systems
• multi-material topology optimization
• gel-elastomer composites
• shape morphing
• structure-function relationship

Innovation

• topology optimization
• multi-material design
• programmable matter
• differentiable simulation
• neural implicit representation