Asymptotic Rigidity of Layered Structures and Its Application in Homogenization Theory

@article{Christowiak2018AsymptoticRO,
  title={Asymptotic Rigidity of Layered Structures and Its Application in Homogenization Theory},
  author={Fabian Christowiak and Carolin Kreisbeck},
  journal={Archive for Rational Mechanics and Analysis},
  year={2018},
  volume={235},
  pages={51-98}
}
  • Fabian Christowiak, Carolin Kreisbeck
  • Published 2018
  • Mathematics
  • Archive for Rational Mechanics and Analysis
  • In the context of elasticity theory, rigidity theorems allow one to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff components arranged into fine parallel layers. We show that strict global constraints of anisotropic nature occur in the limit of vanishing layer thickness, and give a characterization of the class of effective deformations. The optimality of the scaling… CONTINUE READING
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    SHOWING 1-10 OF 56 REFERENCES
    Homogenization of layered materials with rigid components in single-slip finite crystal plasticity
    • 4
    • PDF
    Quantitative Homogenization in Nonlinear Elasticity for Small Loads
    • 9
    • PDF
    High contrast homogenisation in nonlinear elasticity under small loads
    • 2
    • PDF
    A quantitative geometric rigidity result in SBD
    • 7
    • PDF
    Piecewise rigidity
    • 34
    • PDF
    Differential Inclusions and Young Measures Involving Prescribed Jacobians
    • 15
    • PDF