Polygonal and Polyhedral Elements as a New Computational Paradigm to Study Soft Materials

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Modern advances in materials science have revealed that soft organic solids --- such as electro- and magneto-active elastomers, gels, and shape-memory polymers --- hold tremendous potential to enable new high-end technologies, especially as the next generation of sensors and actuators featured by their low cost together with their biocompatibility, processability into arbitrary shapes, and unique capability to undergo large reversible deformations. The realization of this potential has prompted an upsurge in the computational microscopic and mesoscopic studies of soft materials with the objectives of quantitatively understanding their behavior from the bottom up and ultimately guiding their optimization and actual use in technological applications. Almost all of these studies have made use of standard finite elements, which have repeatedly proved unable to simulate processes involving realistically large deformations. The graduate students involved in the project will benefit from the collaborative computational/theoretical character of the research. Concepts developed from this interdisciplinary research will be adapted into the curriculum and will positively impact engineering education.The main objective of this project is to put forward a new computational technology with the capability to study soft solids undergoing realistically large deformations. A second objective is to deploy this technology to study the nonlinear elastic response of soft solids with complex particulate microstructures (e.g. elastomers reinforced with anisotropic filler particles), ubiquitous in many soft active material systems. From a conceptual point of view, this will be accomplished by making use of mimetic inspired methods (which preserve the underlying properties of physical and mathematical models, thereby improving the predictive capability of computer simulations) to put forward a new discretization approach for arbitrarily shaped elements under finite deformations in the context of finite element and virtual element methods. This work involves collaboration with the University of Milan and Los Alamos National Laboratory.