The goal of this project is to create an accessible open-source software package, Morpho, able to solve a wide variety of shape optimization, evolution and shapeshifting problems. These occur in numerous systems that cut across multiple NSF programs involving soft matter, an umbrella term for readily deformable materials, and includes soft robots, plastics, complex fluids, textiles, particulate media, glasses and biological materials as well as other applications in mathematics and computer science involving computational geometry. Shape change is an important feature of these systems, or a goal of the envisioned applications, but predicting their behavior is very challenging. There is presently a lack of appropriate simulation tools readily available to practitioners working in these domains inhibiting quantitative, mechanistic understanding of their behavior and optimization for applications. With Morpho, domain scientists gain a powerful new simulation tool that enables them to tackle larger and more complex shape evolution problems than presently possible. The project also creates a user community by providing extensive training opportunities including an immersive annual workshop, high quality documentation and a virtual community.
Shape optimization and evolution problems are numerically extremely challenging because the final shape is not known ahead of time: The numerical representation must be continuously monitored to ensure the solution obtained is correct and of high quality. The central innovation of Morpho is to regularize ill-posed shape problems by introducing auxiliary functionals that capture some notion of mesh quality. The aim of this work is to extend the range and complexity of problems Morpho can solve in two ways. The first is to allow the user to incorporate arbitrary types of manifolds, field quantities defined on the manifolds, discretizations, functionals and constraints pertinent to their problem. The second is to leverage multilevel algorithms and GPU computing to accelerate the simulations and enable the software to predict the dynamical response of the system given an initial configuration. The project also engages domain scientists in creating and using Morpho through a user-centered development process and a community driven science and education program, incorporating documentation, a repository of example code and tutorials, a virtual community and an annual training workshop. The resulting software and educational materials enable other researchers to simulate shape evolution in several emerging fields involving soft matter and other areas including active materials, soft robots, programmable materials and extreme mechanics.
This award by the NSF Office of Advanced Cyberinfrastructure is jointly supported by the Division of Materials Research within the NSF Directorate of Mathematical and Physical Sciences.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
