On constitutive inequalities and bifurcation in elastic-plastic solids with a yield-surface vertex
A constitutive inequality for time-independent elastic-plastic models of polycrystalline metals at finite strain is derived from the known constitutive framework for single metal crystals obeying the normality and symmetry postulates. Consequences of the inequality are examined for a general class of nonlinear constitutive rate equations at a yield- surface vertex. It is demonstrated that existence of a strain-rate potential and the normality flow rule can be inferred from the inequality alone. With the help of the constitutive inequality, it is proved that bifurcation in velocities is ruled out by positive definiteness of the quadratic functional based on the tangent moduli. Micromechanically-based justification for linearization of the bifurcation problem along a regular deformation path is obtained in that way, without the need of specifying the full constitutive law. As another example of application of the constitutive inequality, explicit restrictions on phenomenological models of material behaviour at a yield-surface vertex are derived.
scientific article; zbMATH DE number 4094914
scientific article