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

Abstract

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.