Abstract
The goal of this paper is to study pure strain deformations of deformable surfaces, i.e., deformations deprived of rotations in the sense of the polar decomposition theorem. The problem is treated with the broader class of general pure strain maps in the background. It is shown that determination of all pure strain deformations of a given surface reduces to a single second-order quasi-linear PDE. It is also proved that this problem is equivalent to a geometrical problem of finding all surfaces with a given third fundamental form (the inverse of the Gauss map) and prescribed lines of principal curvature.
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Szwabowicz, M.L. Pure Strain Deformations of Surfaces. J Elasticity 92, 255–275 (2008). https://doi.org/10.1007/s10659-008-9161-5
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DOI: https://doi.org/10.1007/s10659-008-9161-5