A coordinate-free approach to the kinematics of membranes
In the kinematics of a three-dimensional continuum the polar decomposition of the so-called deformation gradient into a stretch tensor and a rotation tensor is well known. An analogous decomposition can be developed with respect to a two-dimensional membrane. The standard polar decomposition, however, is connected with some problems resulting from the fact that the two-dimensional tangent space changes with the deformations of the membrane. These difficulties can be removed by introducing a supplementary new polar decomposition taking into account the embedding of the two-dimensional membrane into the three-dimensional Euclidean space.
embedding of the two-dimensional membrane into the three-dimensional Euclidean space
scientific article; zbMATH DE number 3932480