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In the attached manuscript, we have coupled the extended finite element method (X-FEM) to the fast marching method (FMM) for non-planar crack growth simuations. Unlike the level set method, the FMM is ideally-suited to advance a monotonically growing front. The FMM is a single-pass algorithm (no iterations) without any time-step restrictions. The perturbation crack solutions due to Gao and Rice (IJF, 1987) and Lai, Movchan and Rodin (IJF, 2002) are used for the purpose of comparisons.

      This paper studies a gel formed by a network of cross-linked polymers and a species of mobile molecules. The gel is taken to be a dielectric, in which both the polymers and the mobile molecules are nonionic. We formulate a theory of the gel in contact with a solvent made of the mobile molecules, and subject to electromechanical loads. A free-energy function is constructed for an ideal dielectric gel, including contributions from stretching the network, mixing the polymers and the small molecules, and polarizing the gel.

Foods are good examples of composite materials that everyone can relate to.  From foams like ice creams to emulsions like spreads to hydrogels like jams to viscoelastic solids like cheese to porous, brittle solids like crisps, the properties of these multiphasic, heterogeneous materials are most important in the mouth where they are broken down via mechanical, chemical or thermal means.  Unlike many structural materials where the design strategy is to achieve the highest strength or toughness, foods are designed to break down in a particular manner and only under particular condit