Minimal energy configurations of strained multi-layers. (English) Zbl 1129.49045
Summary: 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.
MSC:
| 49S05 | Variational principles of physics |
| 74K20 | Plates |
| 74G65 | Energy minimization in equilibrium problems in solid mechanics |
References:
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