On the use of QR kinematics in studying the Eshelby energy–momentum tensor

Abstract

We study the Eshelby energy–momentum tensor using QR kinematics, obtained from an upper-triangular decomposition of the deformation gradient. In recent years, a QR decomposition of the deformation gradient has gained attention because of its utility in experiments and constructing constitutive models. In this framework, the constitutive relations can be developed using scalar, conjugate, stress/strain, base pairs that have minimum couplings between them. In this paper, in addition to these scalar stress attributes, we introduce driving force attributes that are thermodynamic conjugates to the dissipative strain attributes. A one-to-one relation between the driving force attributes and the components of Eshelby’s energy–momentum tensor, defined in this framework, has been established. These kinetic and kinematic quantities play a key role in the constitutive formulation of a dissipative process. Finally, a classical J2 plasticity model has been derived to illustrate the role of these driving force attributes.