A programmable environment for shape optimization and shapeshifting problems

Abstract

Soft materials underpin many domains of science and engineering, including soft robotics, structured fluids, and biological and particulate media. In response to applied mechanical, electromagnetic or chemical stimuli, such materials typically change shape, often dramatically. Predicting their structure is of great interest to facilitate design and mechanistic understanding, and can be cast as an optimization problem where a given energy function describing the physics of the material is minimized with respect to the shape of the domain and additional fields. However, shape-optimization problems are very challenging to solve, and there is a lack of suitable simulation tools that are both readily accessible and general in purpose. Here we present an open-source programmable environment, Morpho, and demonstrate its versatility by showcasing a range of applications from different areas of soft-matter physics: swelling hydrogels, complex fluids that form aspherical droplets, soap films and membranes, and filaments. This study introduces an extensible framework—Morpho—for shape optimization, enabling researchers to predict the structure of soft materials, such as complex fluids, gels, particulate and biological materials.