On material-uniform elastic bodies with disclinations and their homogenization
arXiv:2412.14319 · doi:10.1177/10812865251322412
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.
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
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