Finite-element modeling of soft solids with liquid inclusions

Surface tension is an important factor in the behavior of fluids but typically has a minimal or negligible effect in solids. However, when a solid is soft and its characteristic dimension is small, forces due to surface tension can become important and significantly affect elastic deformation, leading to interesting elasto-capillary phenomena. We have developed a finite-element formulation accounting for surface tension and large deformations in three-dimensional settings and demonstrate the simulation capability by examining a class of problems involving fluid-filled droplet inclusions in a soft solid matrix. Specifically, we (1) consider the response of isolated droplets under far-field loading and (2) micromechanically model composite materials made up of a finite volume fraction of fluid-filled inclusions in a soft solid matrix. In the latter case, recent experimental work in the literature has shown that when the matrix material is sufficiently compliant, the presence of droplets leads to stiffening-counter to the intuitive notion of the presence of fluid-filled inclusions leading to a more compliant composite material. We show that our numerical simulation capability predicts all experimentally observed phenomena related to fluid-filled inclusions in soft solids. Furthermore, we consider the large-deformation response of composite materials with fluid-filled inclusions-a situation difficult to address using analytical methods.