Semidiscrete Modeling of Dislocation-Disclination Systems: Finite Element Formulation
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.
Related
- Memory-Augmented Phase-Field Modeling: Onsager Formulation, Internal-Variable Lifting, and Structure-Preserving Computation
- A Gaussian Process State Space Formulation for Materials Constitutive Modeling: Application to Quasi-brittle Materials
- Gradient flow formulation and discrete approximation of reaction-cross-diffusion systems with size exclusion
- A Projected Semiexplicit Integrator for Dissipative Systems with Configuration-Dependent Kinetic Energy: Contact-Herglotz Formulation and Benchmarks
- Numerical approximation of nonlinear fractional dynamical systems for coastal wave modeling: rigorous analysis of convergence and computational efficiency
BibTeX
@misc{cesana2026semidiscrete,
title = {{Semidiscrete Modeling of Dislocation-Disclination Systems: Finite Element Formulation}},
author = {Pierluigi Cesana and Edoardo Fabbrini and Andrés A. León Baldelli and Marco Morandotti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29614},
eprint = {2609.29614},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29614},
}
RIS
TY - UNPB
TI - Semidiscrete Modeling of Dislocation-Disclination Systems: Finite Element Formulation
AU - Pierluigi Cesana
AU - Edoardo Fabbrini
AU - Andrés A. León Baldelli
AU - Marco Morandotti
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.29614
UR - https://arxiv.org/abs/2609.29614
AB - 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.
ER -