Orientation preservation and Newton–Raphson convergence in the case of an hyperelastic sphere subjected to an hydrostatic pressure Original Research Article

In this paper, we show that the incremental Newton–Raphson algorithm diverges if the orientation is not preserved. To illustrate this point, we treat the example of a compressible hyperelastic sphere subjected to an hydrostatic pressure. The selected model is the Blatz–Ko behaviour law. We also show that it is possible to choose an optimal step loading. This step guarantees at the same time the orientation preservation, the Newton–Raphson convergence and a minimum computing time.