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.