Our aim is to estimate regional mechanical properties of the annulus fibrosus (AF) using a multi-relaxation tensile test and to examine the relevance of using the transverse dilatations in the identification procedure. We collected twenty traction specimens from both outer (n = 10) and inner (n = 10) sites of the anterior quadrant of the annulus fibrosus of one pig spine. A 1-h multi-relaxation tensile test in the circumferential direction allowed us to measure the force in the direction of traction and the dilatations in all three directions. We performed a specific-sample finite element inverse analysis to identify variations, along the radial position, of material and structural parameters of a hyperelastic compressible and anisotropic constitutive law. Our experimental results reveal that the outer sites are subjected to a significantly greater stress than the inner sites and that both sites exhibit an auxetic behavior. Our numerical results suggest that the inhomogeneous behavior arises from significant variations of the fiber angle taken into account within the hyperelastic constitutive law. In addition, we found that the use of the measured transverse dilatations in the identification procedure had a strong impact on the identified mechanical parameters. This pilot study suggests that, in quasi-static conditions, the annulus fibrosus may be modeled by a hyperelastic compressible and anisotropic law with a fiber angle gradient from inner to outer periphery.

我们的目的是使用多重松弛拉伸试验评估纤维环（AF）的区域力学性能，并研究在鉴定程序中使用横向扩张的相关性。我们从一只猪脊柱纤维环前象限的外部（n = 10）和内部（n = 10）位置收集了二十个牵引标本。在圆周方向上进行了1小时的多松弛试验，使我们能够测量牵引方向上的力和所有三个方向上的膨胀。我们进行了特定样本的有限元反分析，以识别沿径向位置的超弹性可压缩和各向异性本构关系的材料和结构参数的变化。我们的实验结果表明，外部位置比内部位置承受的应力要大得多，并且两个位置都表现出发胀行为。我们的数值结果表明，不均匀的行为是由超弹性本构律中考虑的纤维角度的显着变化引起的。此外，我们发现在识别过程中使用测量的横向膨胀对识别的机械参数有很大的影响。这项初步研究表明，在准静态条件下，纤维环可以通过超弹性可压缩和各向异性定律建模，纤维定律从内周到外周。我们的数值结果表明，不均匀的行为是由超弹性本构律中考虑的纤维角度的显着变化引起的。此外，我们发现在识别过程中使用测量的横向膨胀对识别的机械参数有很大的影响。这项初步研究表明，在准静态条件下，纤维环可以通过超弹性可压缩和各向异性定律建模，纤维定律从内周到外周。我们的数值结果表明，不均匀的行为是由超弹性本构律中考虑的纤维角度的显着变化引起的。此外，我们发现在识别过程中使用测量的横向膨胀对识别的机械参数有很大的影响。这项初步研究表明，在准静态条件下，纤维环可以通过超弹性可压缩和各向异性定律建模，纤维定律从内周到外周。