On behavior of transversely isotropic incompressible hyperelastic materials under multiaxial stretching

Abstract

Abstract Nowadays, mechanical behavior of soft materials are characterized by using standard tests: uniaxial traction, simple shear (or combination) and equibiaxial tension. However, the multiaxial testing data are necessary in order to characterize the anisotropy, which is posing formidable technical challenges. We propose a new method to investigate multiaxial behavior of fiber-reinforced hyperelastic solids. The test protocol consists to deform a thin rectangular sample by coupling both the pure shear and simple shear loadings. The specimen is mounted and oriented by an angle in the plane of a special device, which is attached to a universal testing machine. So, the direction of stretching is dictated by in such way that, the stress-strain relations depend on and magnitude of the displacement prescribed on the sample edge, i.e. . The shape factor of the sample is assumed to dictate the direction of transverse isotropy in the reference configuration. Thereby, the direction of stretching could be taken neither parallel nor perpendicular to the stretching-direction. But also, it could be chosen parallel to the direction of transverse isotropy. Based on, we have revisited the standard results, established new ones, and investigated the anisotropy. We demonstrated that, the Cauchy stress fields are depending on the multiaxiality in the core region of the sample. So, the experimental data arising from this test could be used for both parameter calibration and/or validation of transversely isotropic incompressible hyper elastic models.