Numerical modeling of large deformations of elastoplastic solids in terms of logarithms of principal stretches

Numerical technique for solving the problem of large elastoplastic deformations of three-dimensional bodies based on the finite element method is proposed. The original variant of the multiplicative decomposition of the deformation gradient is used. Constitutive equations and the plastic flow law are formulated in terms of logarithms of principal stretches and have a scalar form. The solution of the problem is based on step-by-step loading with iteration refinement. The relationships for the Mises medium, necessary for calculations, are constructed. Separation of elastic and plastic deformations is realized using the implicit Euler integration scheme for plastic flow equations. A numerical example is presented.