A Unified Configurational Framework for Interface and Bulk Defects in Eshelbian Linear Elasticity

Abstract Within the framework of Eshelbian mechanics and linear elasticity, we develop a kinematic and energetic formulation for treating different classes of defects. Central to the approach is a defect map, through which interface discontinuities and bulk material inhomogeneities are described within a common notation. The driving force is derived as an energy-release rate, leading to a single identity in which defect-dependent mechanical effects, material inhomogeneity, and boundary/interface contributions are explicitly separated. For affine modes of defect evolution—translation, rotation, and dilatation—the formulation recovers the corresponding classical integrals as special cases. In particular, the analysis shows that path independence is not automatic, but follows under the assumptions required for the balance of the different contributions to the driving force. Finally, a prototypical one-dimensional example is discussed to describe the physical meaning of the deduced analytical expression of the total driving force.