Load relaxation of a flat rigid circular indenter on a gel half space

When a saturated elastic gel is suddenly indented to a fixed displacement, δ, by a flat circular rigid indenter, the solvent cannot escape immediately, this gives rise to a pressure gradient in the solvent and the solvent flows until the pressure in it goes to zero everywhere, and all the stresses are transferred to the elastic network. This load transfer process causes, the indenter load, F, to decrease with time t, with a characteristic time constant, τ, which is given by a²/D_c, where D_c is the cooperative diffusion coefficient and a is the radius of the circular punch. This load relaxation behavior can be used to extract the elastic moduli and the cooperative diffusion coefficient of the gel. A detailed finite element analysis shows the load relaxation as a function of normalized time (t/τ) and how it depends on the shear modulus G and the Poisson's ratio ν of the drained gel. Using this result, we found that the energy release rate available for detaching the punch in a pull-off test can be estimated. It is found that the energy release rate decreases with time for a fixed displacement.