Applicability of a constant Young's modulus in geometrically nonlinear elasticity (Q2714411)

The paper considers geometrically non-linear, but physically linear isotropic elastic laws between three different conjugate stress and strain measures. The stress-strain response is determined by these laws for a uniaxial tensile test. As one would expect, the differences between the three curves become large, when the strains grow. Although the sense of a geometrically non-linear and physically linear modeling can be and has been questioned, it is a nice example for students to demonstrate the characteristics of such models.NEWLINENEWLINENEWLINEThe author assumes that ``in reality'' there is a linear dependence of the nominal stress on the stretch, and any deviation from that particular linear law is considered as ``error''. However, this assumption is not substantiated, and it remains open where this belief of the author comes from. In finite elasticity all stress and strain tensors have equal rights, and it depends on the individual material, which law can be fitted closest to the experimental data.