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.
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BibTeX
@article{stefano2026unified,
title = {{A Unified Configurational Framework for Interface and Bulk Defects in Eshelbian Linear Elasticity}},
author = {Salvatore Di Stefano and Claudia Binetti and Giuseppe Puglisi and Stefano Giordano},
journal = {Journal of Elasticity},
year = {2026},
month = aug,
doi = {10.1007/s10659-026-10222-3},
url = {https://hal.science/hal-05760008v1},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - JOUR
TI - A Unified Configurational Framework for Interface and Bulk Defects in Eshelbian Linear Elasticity
AU - Salvatore Di Stefano
AU - Claudia Binetti
AU - Giuseppe Puglisi
AU - Stefano Giordano
PY - 2026
DA - 2026/08/17
JO - Journal of Elasticity
DO - 10.1007/s10659-026-10222-3
UR - https://hal.science/hal-05760008v1
AB - 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.
SN - 0374-3535
SN - 1573-2681
ER -