Enhancement of Protocols for Simple Shear of Isotropic Soft Hyperelastic Samples

The classic deformation known as simple shear has been investigated within the framework of nonlinear elasticity for isotropic incompressible hyperelastic materials in a large variety of contexts, most notably in the analysis of the mechanical behaviour of soft matter. One of the major difficulties in providing a realistic physical interpretation of this idealised homogeneous deformation is the fact that the conventional mathematical model of simple shear using a plane stress assumption to determine the hydrostatic pressure implies that a normal traction must be applied to the slanted faces of the deformed specimen. However, such a traction is not applied in practice. To resolve this dilemma, we retain the classic plane stress assumption to determine the hydrostatic pressure but modify the basic kinematics to consider a simple shear deformation superposed on a uniform lateral extension or compression of the specimen. The amount of lateral stretch is treated as a stabilising factor determined so that the predicted normal traction is minimised and thus the fidelity of the model with experimental protocols is enhanced. This new approach is illustrated for a variety of classical strain-energy densities for isotropic hyperelastic materials that have been used to model the mechanical behaviour of soft matter.