English

On material-uniform elastic bodies with disclinations and their homogenization

Mathematical Physics 2025-12-29 v3 Differential Geometry math.MP Classical Physics

Abstract

In this note, we define material-uniform hyperelastic bodies (in the sense of Noll) containing discrete disclinations and dislocations, and study their properties. We show in a rigorous way that the size of a disclination is limited by the symmetries of the constitutive relation; in particular, if the symmetry group of the body is discrete, it cannot admit arbitrarily small, yet non-zero, disclinations. We then discuss the application of these observations to the derivations of models of bodies with continuously-distributed defects.

Keywords

Cite

@article{arxiv.2412.14319,
  title  = {On material-uniform elastic bodies with disclinations and their homogenization},
  author = {Cy Maor},
  journal= {arXiv preprint arXiv:2412.14319},
  year   = {2025}
}

Comments

Dedicated to Marcelo Epstein, in celebration of his 80th birthday. Version 2: some minor changes in presentation, typos fixed. Version 3: a remark added before Proposition 3.4, some little errors fixed in Example 3.5