位错-位错偶系统的半离散建模：有限元公式

中文摘要 AI 辅助

我们提出了一种用于求解有限个相互作用的刃型位错和楔形位错偶系统的数值公式。该方法基于对四阶椭圆边值问题的有限元离散化，该问题源于平面应变线性弹性力学平衡方程在存在运动学不相容性时的推导。数值实现采用连续内罚不连续伽辽金框架，并依赖于求解一组有限的局部单元问题。我们的方法通过与解析基准的对比验证，并用于探索若干非平凡的位错-位错偶构型，展示了平移和旋转不相容性如何影响物体的应力状态。

英文摘要

We present a numerical formulation for the resolution of finite systems of interacting edge dislocations and wedge disclinations. The approach is based on a finite element discretization of a fourth-order elliptic boundary value problem arising from the mechanical equilibrium equations of plane-strain linear elasticity in the presence of kinematic incompatibilities. The numerical implementation follows a continuous interior penalty discontinuous Galerkin framework and relies on the solution of a finite set of local cell problems. Our method is validated against analytical benchmarks and used to explore several non-trivial dislocation-disclination configurations, illustrating how translational and rotational incompatibilities shape the stress state of the body.

发表机构

• Graduate School of Science, Kyoto University（京都大学大学院理学研究科）
• Institute of Mathematics for Industry, Kyushu University（九州大学产业数学研究所）
• Sorbonne Université, CNRS, Institut Jean Le Rond d’Alembert（索邦大学、法国国家科学研究中心、让·勒朗·达朗贝尔研究所）
• Dipartimento di Scienze Matematiche “G.˜L.˜Lagrange”, Politecnico di Torino（都灵理工大学“G.L.拉格朗日”数学科学系）

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