0578000 - MÚ 2024 RIV DE eng J - Journal Article
Šilhavý, Miroslav
Renormalized energy of a dislocation loop in a 3D anisotropic body.
Journal of Elasticity. Roč. 154, 1-4 (2023), s. 355-381. ISSN 0374-3535. E-ISSN 1573-2681
Institutional support: RVO:67985840
Keywords : dislocations * incompatible distortion field * regularized energy * prelogarithmic energy factor
OECD category: Applied mathematics
Impact factor: 1.8, year: 2023
Method of publishing: Open access
https://doi.org/10.1007/s10659-023-10017-w

The paper presents a rigorous analysis of the singularities of elastic fields near a dislocation loop in a body of arbitrary material symmetry that extends over the entire three-space. Explicit asymptotic formulas are given for the stress, strain and the incompatible distortion near the curved dislocation. These formulas are used to analyze the main object of the paper, the renormalized energy. The core-cutoff method is used to introduce that notion: first, a core in the form of a curved tube along the dislocation loop is removed, then, the energy of the complement is determined (= the core-cutoff energy). As in the case of a straight dislocation, the core-cutoff energy has a singularity that is proportional to the logarithm of the core radius. The renormalized energy is the limit, as the radius tends to 0, of the core-cutoff energy minus the singular logarithmic part. The main result of the paper are novel formulas for the coefficient of logarithmic singularity (the ‘prelogarithmic energy factor’) and for the renormalized energy.
Permanent Link: https://hdl.handle.net/11104/0347056