Complete mechanical characterization of soft media using nonspherical rods

Hydrogels have been used as substrates for studying the cellular processes by many researchers. The stiffness of such gels was also characterized previously. However, in most of the cases, these soft Poisson's ratio was assumed incompressible and Poisson's ratio is assumed to be one-half. This may not be true in many cases, and might alter the calculation of the stiffness of the gels. In this study, we present equations for the complete characterization of soft media, i.e., calculation of Young's modulus, shear modulus, and Poisson's ratio. The method involves the individual measurement of either the displacement or rotation of cylindrical rods embedded in the soft media, under the application of an external force or torque. Equations involving shear modulus and Poisson's ratio for rotation of the rod and Young's modulus and Poisson's ratio for the displacement of the rod are independently derived. In addition, the displacement and rotation of the rods embedded in an elastic medium, under the application of either a force or a torque, respectively, were also calculated using finite element analysis. These values compared well with the displacements and rotations obtained using closed form equations.