Murnaghan’s Elastoplastic Material Model

Abstract

Murnaghan’s model of elastic material is generalized to an elastoplastic material. It is assumed that the active process occurs via alternating between the plastic and elastic states. The deformation gradient is replaced by a nonsingular tensor, and constitutive equations in the finite form are written. In addition to Green’s postulate concerning the existence of a stress potential, it is assumed that there exists a stress rate potential, for which rate the objective derivative is uniquely determined. This derivative can be obtained via modifying Green-Nakhdi derivative, wherein the spin of the rotation tensor accompanying the general deformation is replaced by a spin of the rotation tensor accompanying the elastic deformation. A deviator section of the yield surface in the stress space is determined, and differential constitutive equations are formulated. A decrease in the elastic deformation anisotropy under flowing that can lead to an onset of macrocracks is described.