Shirazi-Adl A
Department of Mechanical Engineering, Ecole Polytechnique de Montréal, Quebec, Canada.
J Biomech. 1989;22(4):357-65. doi: 10.1016/0021-9290(89)90050-x.
An axisymmetric finite element model of a body-disc-body unit has been developed and used to study the relative effects of two distinct direction-dependent material representations of the disc annulus on the predicted state of stresses in the disc. The annulus fibrosus is modelled either as nonhomogeneous fibre reinforced composite or alternatively as homogeneous orthotropic with transverse isotropy. In order to have identical states of displacements and hence strains, the unknown properties of the latter model are chosen to be equivalent with those of the former. The fibre slopes of 20 degrees, 30 degrees, and 40 degrees are considered in this study. The stresses in the annulus matrix in the circumferential planes parallel to the fibre layers are predicted to be significantly different depending on the annulus model used. In the nonhomogeneous model, the fibre membranes while under tensile forces, in turn, apply compression to the annulus matrix and, hence, decrease the annulus normal stresses in the above planes. Had the membranes carried compressive forces, a reverse trend would have resulted. The foregoing relative differences are dependent on the fibre orientation, and the magnitude of the tensile forces carried by the fibre layers. The latter also depends, amongst others, on the orientation of the fibres, decreasing as the fibre slope increases from 20 degrees to 30 degrees and 40 degrees. On the basis of the annulus micro-structure and the relative mechanical functions of its components, namely the annulus bulk and the collagenous fibre layers, it appears that nonhomogeneous fibre reinforced composite model of the disc annulus is more realistic resulting in a more accurate computation of stresses in the annulus fibrosus.
已开发出一种身体-椎间盘-身体单元的轴对称有限元模型，并用于研究椎间盘纤维环两种不同的方向依赖性材料表示对椎间盘应力预测状态的相对影响。纤维环要么被建模为非均质纤维增强复合材料，要么被建模为具有横向各向同性的均质正交各向异性材料。为了使位移状态相同，从而使应变相同，后一种模型的未知属性被选择为与前一种模型的属性等效。本研究考虑了20度、30度和40度的纤维斜率。根据所使用的纤维环模型，预计在与纤维层平行的圆周平面内，纤维环基质中的应力会有显著差异。在非均质模型中，纤维膜在承受拉力时，反过来会对纤维环基质施加压力，从而降低上述平面内的纤维环法向应力。如果膜承受压力，就会产生相反的趋势。上述相对差异取决于纤维取向以及纤维层所承受的拉力大小。后者还取决于纤维的取向等因素，随着纤维斜率从20度增加到30度和40度而减小。基于纤维环的微观结构及其组成部分（即纤维环主体和胶原纤维层）的相对力学功能，椎间盘纤维环的非均质纤维增强复合材料模型似乎更现实，从而能更准确地计算纤维环中的应力。
