Mechanical modeling of rheometer experiments: Applications to rubber and actin networks

Experiments on cross-linked actin networks in form of a circular cylinder conducted with a rheometer and parallel-plate geometry resemble a torsional problem of a cylinder undergoing large deformation. A commonly used approximation for the analysis of such experiments is simple shear which is inappropriate for the global analysis of the more complex 3D torsion deformation. We compare the solutions of the torsion of a cylinder with simple shear on the basis of three (phenomenological) rubber models and two network models for cross-linked actin. We start with rubber elasticity and show that the approximation for materials with linear shear elasticity may be reasonable. In the case of cross-linked actin networks, however, the strong strain-stiffening behavior causes higher deviations of simple shear from the more realistic torsional mode. Furthermore, we show that the frequently used eight-chain model cannot account for the correct normal stress behavior of cross-linked actin networks. A recently proposed affine network model reproduces the correct sign for the normal stress for both versions of the boundary conditions. The two solutions, however, differ significantly so that an approximation of the deformation mode in a parallel-plate rheometer by simple shear should be used with caution.