Affine versus non-affine deformation in soft biological tissues, measured by the reorientation and stretching of collagen fibres through the thickness of compressed porcine skin

Skin is a complex three-dimensional structure of cells, collagen fibres and other proteins. However most mechanical analyses treat skin as a two-dimensional membrane, neglecting the through thickness structure. In this paper we investigate through thickness reorientation of collagen fibres. The mode of deformation of skin is also considered. For modelling purposes deformation is usually assumed to be affine. This assumption was tested by constructing a simple geometrical, affine deformation model to predict the through thickness reorientation of collagen fibres, from their initial through thickness angle and the measured deformations of skin samples during compression. The measured reorientation of collagen fibres was found to be very variable, however the average reorientations were consistent with the predictions of the model, with the inclusion of a systematic error. The variation in the reorientation of individual fibres can be explained by the variations in the structure at a micrometre scale. The systematic deviation of reorientations from the model predictions can be explained by a non-affine relationship between the collagen fibres and ground substance at a micrometre scale. However, non-affine deformations at a micrometre scale caused by irregularities of structure are likely to average out at a millimetre scale, because at this level material is evenly distributed.