Aug 2026· Journal of elasticity· Vol 158· 0 citations· 100 references
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.
Inspired by the classical Plateau-Douglas problem for soap films bounded by two closed curves, we solve an analogous problem for fluid interfaces with fixed surface area and resistance to out-of-plane bending. The boundaries are planar but need not be symmetric or concentric. The equilibrium surfaces minimize the Willm...
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Interfaces of crystalline materials are strongly affected by the anisotropy of interface energy. A key quantity in this context is the interface stiffness tensor, which characterizes the response of the interface energy to changes in interface orientation and plays a role in determining the driving force for interface...
We derive energy scaling laws for thin elastic sheets with topological defects --- disclinations and dislocations --- for a fully nonlinear 3D model. For disclinations, the scaling laws are tight in the thickness parameter, and improve upon previous results by applying simultaneously to positive and negative disclinati...
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To describe the evolution of grain boundaries based on the underlying microscopic mechanisms of line defects (disconnections) and the integrated effects of a diverse range of thermodynamic driving forces, Zhang, et al. in 2017 formulated a continuum equation. We prove the global-in-time existence, uniqueness, and regul...
P. Zhu, Xiaoxue Qin, Yang Xiang· 0 citations
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