Dislocations and Disclinations: Local Incompatibility and Global Geometry

par Marco Valerio d'Agostino (INSA Lyon)

mardi 10 nov. 2026, 11:00 → 11:59 Europe/Paris

125

Dislocations and disclinations are the fundamental defects in crystalline materials, arising from translational and rotational incompatibilities respectively. The geometric description of them requires a distinction to be made between incompatibility that is distributed throughout the material and incompatibility that is concentrated along singular cores. Even if the material is locally Euclidean away from its cores the global geometry of the material may still have non-trivial affine monodromy.

In this talk I'll present a geometric framework in which the regular part of a material body is endowed with a Riemannian metric, a linear connection and a smooth field of crystalline lattices. I'll go on to discuss the respective roles of torsion, curvature and non-metricity and how linear and affine transport complement these local descriptions. There'll be a particular emphasis on the relationship between holonomy and monodromy, the difference between local compatibility and global obstructions and the geometric interpretation of Burgers vectors and Frank rotations. Some concrete examples will be used to illustrate both the information which can be captured by these tools and their limitations.