A novel approach for the modelling of disclinations in microstructured media
Contemporary advancements in continuum mechanics increasingly acknowledge the inadequacies of classical theories to model materials with complex microstructures, such as polymers, crystals, and biological tissues. These materials often exhibit emergent behaviours — such as dislocations and disclinations — stemming from microstructural interactions, necessitating generalized models that integrate both macroscopic and microscopic scales. To address such challenges, the so-called microstructured or micromophic media where introduced. By adding some placement-like degrees of freedom, they allowed the emergence of dislocations. However, to our knowledge, no model allowed to obtained disclinations from placement-like kinematic variables alone. In a recent paper we presented a novel two-scale geometric model to address such issue. This model uses a generalisation of Riemann-Cartan manifolds and introduces a new tool, the pseudo-metric. In the first part of this talk, we will present this model. Emphasis will be made on the physical motivations and on the interpretation of the variables. In particular, we will try to use concrete and simple analogies when possible. In the second part, an application of this model to the case of one-dimensionnal structures in small deformations will be presented. In particular, it will be shown how the said model includes several beam models such as Euler-Bernouilli and Timoschenko beams. A discussion on the nature of dislocation and disclination fields in this case will ensue. Finally, a more general case will be discussed, whose (currently) unresolved status opens up the possibility of collaboration with interested researchers.