Stress rate and the Lagrangian formulation of the finite-strain plasticity for a von Mises kinematic hardening model
The use of the Jaumann stress rate, in kinematic hardening finite-strain plasticity, in the case of simple shear generates oscillations in the stress field. Alternate theories have been introduced to define other stress rates by making use of the polar decomposition and consequently producing increasing shear stress. In this work, a Lagrangian formulation is introduced which, for the case of simple shear produces monotonically increasing stress-strain relationships. The yield criterion is originally expressed in terms of the Cauchy stress and subsequently transformed to the Lagrangian reference frame. The associated flow rule used here preserves the normality rule in the second Piola-Kirchhoff stress space and is equivalent to that of the Cauchy stress space. This approach preserves the accuracy of the interpretation of the material behavior in the Eulerian reference frame and it also bypasses the use of the Jaumann stress rate in the formulation of kinematic hardening finite-strain plasticity.
kinematic hardening finite-strain plasticity
monotonically increasing stress-strain relationships
transformed to the Lagrangian reference frame
scientific article; zbMATH DE number 3970203