Variants of physical equations in a curvilinear coordinate system and their comparison based on mixed FEM

In arbitrary curvilinear coordinate system under elastoplastic deformation, a comparative analysis of three variants of the constitutive equations at the loading step was performed. In the first variant, the equations of the theory of plastic flow were used, according to which the strain increment had been divided into elastic and plastic parts. The cumbersomeness of the algorithm for obtaining expressions for the components of the plastic strain increments tensor in an arbitrary curvilinear coordinate system is shown, which leads to the lack of the possibility of obtaining the matrix dependence of physical equations at the loading step. In the second variant, to obtain plastic strain increments, the hypothesis of their proportional dependence on the components of the stress increments deviator was used. The constitutive equations were also obtained by summation of the elastic strains increment and plastic strains increment. In the third variant, the hypothesis of the division of strain increments into elastic and plastic parts was not used. The physical equations were written using the assumption that there was a proportional dependence between the components of the strain increment deviators and stress increment deviators. Using the example of calculating the shell of revolution, the preference of the third variant of the constitutive equations for elastoplastic deformation is shown.