Yield Criterion and the Hardening Rule for a Plastic Solid

The work‐hardening of an initially isotropic material is mathematically described by a hardening rule which specifies the modification of the initial yield condition in the process of continued plastic deformation. Although such rules have been proposed by various investigators and shown to be in good agreement with the experimental results, they are based on different specific assumptions. In the present work it is shown that all the existing hardening rules can be obtained from a general mathematical concept which is based upon the isotropic representation of a scalar valued function which is a function of two symmetric 3 × 3 matrices. A more general form has then been derived which accounts for the second‐order effect relating to axial strain accumulation in cyclic torsion.