MatTO: A Modular Framework for Material and Topology Optimization of Stimulus-Responsive Soft Materials

Abstract

Design of stimulus-responsive soft materials plays a fundamental role in applications in soft robotics, sensing, and actuation. Their design space can extend beyond structural topology to include material composition and orientation. For example, in hard-magnetic soft materials (hMSMs), magnetic particle volume fraction and remanent magnetization direction fields can be designed together with the topology field. Our prior work proposed a joint material–structural optimization framework for hMSMs and demonstrated that simultaneous optimization of material and topology can lead to non-intuitive designs while providing additional design freedom. In this work, we show that this approach can be made material-independent and applied to different classes of materials in which the optimization fields represent different physical variables. Specifically, we propose the open-source framework MatTO to provide this generalized design capability. Through eleven numerical examples involving hMSMs, liquid crystal elastomers, and anisotropic and isotropic magneto-active elastomers in two and three dimensions, we demonstrate the applicability of the framework across different material classes and design variables. We discuss the main components of the framework and provide details for defining new problems and extending it to additional material models. The open-source repository is available at CEADpx/matto. A common energy-based constitutive structure is assumed, and the open-source FEniCSx software is used for finite-element analysis. Future extensions will consider plastic deformation, phase-field fracture, and time- and path-dependent models.