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Abstract

We derive an effective plate theory for internally stressed thin elastic layers as are used, e.g., in the fabrication of nano- and microscrolls. The shape of the energy minimizers of the effective energy functional is investigated without a priori assumptions on the geometry. For configurations in two dimensions (corresponding to Euler-Bernoulli theory) we also take into account a non-interpenetration condition for films of small but non-vanishing thickness.

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References

  1. Friesecke G., James R.D. and Müller S. (2002). Rigorous derivation of nonlinear plate theory and geometric rigidity. C. R. Acad. Sci. Paris 334: 173–178

    MATH  Google Scholar 

  2. Friesecke G., James R.D. and Müller S. (2002). A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. Comm. Pure Appl. Math. 55: 1461–1506

    Article  MATH  Google Scholar 

  3. Friesecke G., James R.D. and Müller S. (2006). A hierarchy of plate models derived from nonlinear elasticity by Gamma-convergence. Arch. Rational Mech. Anal. 180: 183–236

    Article  MATH  Google Scholar 

  4. Grundmann M. (2003). Nanoscroll formation from strained layer heterostructures. Appl. Phys. Lett. 83: 2444–2446

    Article  Google Scholar 

  5. Pakzad M.R. (2004). On the Sobolev space of isometric immersions. J. Differ. Geom. 66: 47–69

    MATH  Google Scholar 

  6. Paetzelt H., Gottschalch V., Bauer J., Herrnberger H. and Wagner G. (2006). Fabrication of A(III)-B(II) nano- and microtubes using MOVPE grown materials. Phys. Stat. Sol. (A) 203: 817–824

    Article  Google Scholar 

  7. Schmidt B.(2006). Effective theories for thin elastic films. PhD thesis, University of Leipzig, Leipzig

    Google Scholar 

  8. Schmidt, B.: Plate theory for stressed heterogeneous multilayers of finite bending energy. Max-Planck Institut für Mathematik in den Naturwissenschaften, Leipzig, preprint 86/2006

  9. Schmidt B. (2006). Effective theories for thin elastic films. University of Leipzig, Leipzig

    Article  Google Scholar 

  10. Schmidt O.G. and Eberl K. (2001). Thin solid films roll up into nanotubes. Nature 410: 168

    Article  Google Scholar 

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Correspondence to Bernd Schmidt.

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Schmidt, B. Minimal energy configurations of strained multi-layers. Calc. Var. 30, 477–497 (2007). https://doi.org/10.1007/s00526-007-0099-4

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  • DOI: https://doi.org/10.1007/s00526-007-0099-4

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