Work

Semidiscrete Modeling of Dislocation-Disclination Systems: Finite Element Formulation

Year: 2026

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.29614

Authors: Cesana, Pierluigi, Fabbrini, Edoardo, Baldelli, Andrés A. León, Morandotti, Marco

Institutions: Kyushu University, Institute of Mathematics for Industry, Kyushu University, Kyoto University, Centre National de la Recherche Scientifique, Sorbonne Université, Institut Jean Le Rond d'Alembert, Politecnico di Torino

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Politecnico di Torino, La Trobe University, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni, Japan Society for the Promotion of Science, Division of Mathematical Sciences, Moonshot Research and Development Program

Awards: G40761899, G5368403867, G8137651613

OpenAlex ID: W7214340834

Cites: 49

Cited by:

Related to: 10