论文标题
通过通风应力函数方法的楔形脱节和边缘位错的系统模型
Semi-discrete modeling of systems of wedge disclinations and edge dislocations via the Airy stress function method
论文作者
论文摘要
我们提出了旋转和翻译类型晶格缺陷的变分理论。我们专注于平面楔形脱节，披露偶极子和边缘位错的有限系统，在运动学不兼容的约束下，我们将其作为解决各向同性弹性能量的最小问题的解决方案。在平面线性化运动学的假设下运行，我们根据通风应力功能制定了机械平衡问题，为此，我们在不兼容的弹性的情况下引入了严格的分析公式。我们的主要结果需要分析其单一极限制度的渐近学中披露偶极和边缘位错的能量等效性。通过通过核心半径采用正则化方法，我们表明，随着核心半径的消失，公开偶极子的渐近能量扩展与边缘位错系统的能量相吻合。这证明，从披露偶极子方面，Eshelby对边缘位错的运动学表征也是从充满活力的角度精确的。
We present a variational theory for lattice defects of rotational and translational type. We focus on finite systems of planar wedge disclinations, disclination dipoles, and edge dislocations, which we model as the solutions to minimum problems for isotropic elastic energies under the constraint of kinematic incompatibility. Operating under the assumption of planar linearized kinematics, we formulate the mechanical equilibrium problem in terms of the Airy stress function, for which we introduce a rigorous analytical formulation in the context of incompatible elasticity. Our main result entails the analysis of the energetic equivalence of systems of disclination dipoles and edge dislocations in the asymptotics of their singular limit regimes. By adopting the regularization approach via core radius, we show that, as the core radius vanishes, the asymptotic energy expansion for disclination dipoles coincides with the energy of finite systems of edge dislocations. This proves that Eshelby's kinematic characterization of an edge dislocation in terms of a disclination dipole is exact also from the energetic standpoint.
