Calibrating surface hyperelastic constitutive models in soft solids.

Soft solids such as silicone gels, with bulk shear modulus ranging from ∼10 to 1000kPa, exhibit strongly strain-dependent surface stresses. Moreover, unlike conventional stiffer materials, the effects of surface stress in these materials manifest at length scales of tens of micrometers rather than nanometers. However, the calibration of constitutive parameters for surface hyperelasticity has proved to be challenging. Using a reasonably general surface constitutive model, we explore the possibility of obtaining its parameters from force-twist, torque-twist, and force-extension (force-compression) responses of a soft cylinder held between two inert, rigid plates. The motivation behind using these responses is derived from the fact that the roles of the surface constitutive parameters, under suitably ideal conditions, are neatly separated from each other and the three responses easily yield values of the three parameters. Moreover, through large deformation finite-element simulations with coupled bulk and surface hyperelasticity, we delineate the extent to which deviation from the ideal conditions may be tolerated. Using an example with previously reported material parameters, we estimate that, for cylindrical specimens with a radius of the order of 100μm, the capability to measure forces and torques of the order of 1-100μN and 10^{3}-10^{5}μN-μm, respectively, will be required to determine the parameters accurately.