Orientation preservation and Newton-Raphson convergence in the case of an hyperelastic sphere subjected to an hydrostatic pressure. (English) Zbl 1026.74074

Summary: 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 hydrostatic pressure. The selected model is Blatz-Ko material. 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.


74S05 Finite element methods applied to problems in solid mechanics
74B20 Nonlinear elasticity
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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