Derivation of a Homogenized Bending–Torsion Theory for Rods with Micro-Heterogeneous Prestrain

@article{Bauer2019DerivationOA,
  title={Derivation of a Homogenized Bending–Torsion Theory for Rods with Micro-Heterogeneous Prestrain},
  author={Robert O. Bauer and Stefan Neukamm and Mathias Sch{\"a}ffner},
  journal={Journal of Elasticity},
  year={2019},
  pages={1-37}
}
In this paper we investigate rods made of nonlinearly elastic, composite–materials that feature a micro-heterogeneous prestrain that oscillates (locally periodic) on a scale that is small compared to the length of the rod. As a main result we derive a homogenized bending–torsion theory for rods as Γ $\Gamma $ -limit from 3D nonlinear elasticity by simultaneous homogenization and dimension reduction under the assumption that the prestrain is of the order of the diameter of the rod. The limit… Expand
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