Deformation, affine plastic

Since no drastic morphological change occurs during the homogeneous drawing of fibrous structure, one can conclude that the basic elements, i.e. the microfibrils and fibrils, remain basically unaffected. Plastic deformation can proceed only by pulling the adjacent elements in the draw direction in a manner described by the affine transformation (Figure 4). 

Since the deformational forces are proportional to the cross section (A = d2) and the resistance to the lateral surface area (4dl), one would expect a larger displacement effect on fibrils than on microfibrils. The average length of both is practically the same, lf = lmfy but fibril thickness is about ten times that of microfibrils, df — 10dmf. If the mentioned difference in friction coefficient is also considered, one can conclude that most plastic deformation of fibrous structure is the consequence of the nearly affine displacement of fibrils and that only a small fraction is attributable to that of microfibrils. 

It is reasonable to assume that a solid will deform in an affine manner this is the elastic assumption. Note that in metal crystals plastic deformation by dislocation glide on slip planes is not affine. The crystal between the slip planes is not plastically distorted all the deformation occurs at the slip plane. 

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