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.

翻译：凝胶-弹性体复合材料由活性可膨胀水凝胶与被动弹性体组成，是一类引人注目的可编程材料系统，能够在多物理场驱动下实现形状变形。拓扑结构与材料分布的精确设计可解锁复杂的可编程性，这在可穿戴电子设备、软体机器人和药物递送中至关重要；然而，结构-功能关系高度非直观，使得试错法和传统设计方法大多难以处理。为解决这一问题，我们提出了一种用于此类结构自动化设计的拓扑优化框架，通过可编程形状变形实现对目标功能设计空间的系统探索。具体而言，我们提出了一种多材料拓扑优化框架，可同时优化结构拓扑与凝胶-弹性体相的空间分布。该设计通过基于坐标的神经网络进行表征，并在基于Flory-Rehner理论的统一本构框架内描述两相的力学响应。此外，我们提出了一种采用隐式微分的端到端可微设计框架，可适应多种目标函数、约束条件和离散化方案。我们通过形状编程结构与软体致动器对该框架进行了演示，并进一步通过针对化学性质不同的溶剂环境中多刺激响应性的有机凝胶-水凝胶复合材料设计，以及同时与拓扑协同优化局部纤维取向的各向异性水凝胶设计验证了该框架的可行性。基于JAX实现的代码库已公开共享，以支持基准测试与可重复性研究。