Integrated experimental and numerical comparison of different approaches for planar biaxial testing of a hyperelastic material

Planar biaxial testing has been applied to a variety of materials to obtain relevant information for mechanical characterization and constitutive modeling in presence of complex stress states. Despite its diffusion, there is currently no standardized testing procedure or a unique specimen design of common use. Consequently, comparison of results obtained with different configurations is not always straightforward and several types of optimized shapes have been proposed. The purpose of the present work is to develop a procedure for comprehensive comparison of results of biaxial tests carried out on the same soft hyperelastic material, using different types of gripping methods and specimen shapes (i.e., cruciform and square). Five configurations were investigated experimentally using a biaxial test rig designed and built by the authors, using digital imaging techniques to track the displacements of markers apposed in selected positions on the surfaces. Then, material parameters for a suitable hyperelastic law were determined for each configuration examined, employing an inverse method which combines numerical simulations with the finite element method (FEM) and optimization algorithms. Finally, efficiency of examined biaxial configurations was assessed comparing stress reductions factor, degree and uniformity of biaxial deformation, and operative strain ranges.