Simple Shear Test in Identification of Constitutive Behaviour of Materials Submitted to Large Deformations — Hyperelastic Materials Case

The present work is directed at evaluation of the simple shear test for identification of constitutive behaviour of materials submitted to large deformations. For that purpose, actual experimental conditions together with theoretical background of the test are analysed on the example of two hyperplastic material models. Advantages and disadvantages of various strain and stress measures used for presentation of simple shear test (SST) results are analysed. The most often presented as the only result of “standard” SST proof chart, i.e. shear nominal stress ↔ shear nominal strain ($σ_{12}^{(N)}↔γ/2$), characterizes the material energetically in the sense that it reveals its capacity for elastic energy storage $dW/V_{0} = σ_{12}^{(N)}dγ$. However, it characterizes the constitutive behaviour of the material only partially, since it is equivalent to shear II Piola Krichoff stress ↔ shear Green-Lagrange strain ($σ_{21}^{(2)}↔ E_{21}^{(2)}$) chart, within the large deformations context. This data alone does not even allow to reconstruct the shear Cauchy stress ↔ shear spatial Hencky strain (($σ_{12}^{(0)}↔ e_{12}^{(0)}$) chart for the tested material. In order to take full advantage of the constitutive information available from simple shear test, it is highly recommended to extend the experimental methodology of “standard” SST proof in such a way as to determine simultaneously two components (shear and normal) of nominal stress tensor in the same SST proof. Such experimental information allows for subsequent recalculation of non-symmetric nominal stress tensor components into Cauchy stress components.