Loading restrictions for the Blatz-Ko hyperelastic model—application to a finite element analysis

In this paper, we consider the Blatz-Ko constitutive model for compressible elastic solids. It is shown that the Cauchy stress tensor leads to a normal loading limitation. This limitation induces slow convergence of the Newton-Raphson algorithm near the maximum authorized normal loading value and divergence if this value is exceeded. In addition, convergence of the Newton-Raphson scheme also depends on ellipticity and strong ellipticity conditions. These various points are discussed in the case of a rectangular specimen subjected to a tensile load and modeled with finite elements.