Finite element algorithm for implementing variants of physically nonlinear defining equations in the calculation of an ellipsoidal shell

The defining equations at the loading step are obtained in three variants. In the first variant, the relations between strain increments and stress increments are obtained by differentiating the equations of the theory of small elastic-plastic deformations using the hypothesis of plastic incompressibility of the material. In the second variant, the assumption of plastic incompressibility was not used. The relations between the first invariants of stress and strain tensors were considered to be known from the extension test. In the third variant, the defining equations at the loading step are obtained without dividing the strain increments into elastic and plastic parts based on the hypothesis of proportionality of the components of the strain increment deviators and the components of the stress increment deviators using the relations between the first invariants of the stress and strain increment tensors determined experimentally. The numerical example shows the preference of the third variant of the defining equations.