Inhomogeneous deformation of elastomer gels in equilibrium under saturated and unsaturated conditions

A variational method is employed to obtain governing equations and boundary conditions describing finite strain equilibrium configurations of elastomeric gels. Three situations are considered: a liquid saturated gel, an unsaturated gel, and a gel in equilibrium with a vapor of its own liquid. Surface tractions can lead to equilibrium transitions between these cases. The liquid saturated gel is regarded as immersed in a liquid bath. If this bath becomes depleted, then the gel is unsaturated. The degree of unsaturation – a measure of the amount of liquid that would restore a state of saturation – affects the subsequent mechanical behavior. If the unsaturated system is further allowed to condense or evaporate its liquid component at the gel surface, then a new state of equilibrium is achieved. The transition between the unsaturated case and the case of being in equilibrium with the vapor phase corresponds to the chemical potential variable of the gel changing its value from one that is determined by a volume constraint to the value of the chemical potential in the vapor phase. A finite element method is created on the basis of the variational method and demonstrated in the context of eversion, a deformation that imposes very large finite strains. Liquid migration within the gel is not modeled as our focus is on equilibrium states that occur after all such non-equilibrium processes come to rest.