Constitutive models are of fundamental importance to many biomedical problems such as the rupture prediction of aortic aneurysms. Existing structure-based constitutive models such as the widely used Gasser–Ogden–Holzapfel (GOH) model usually need to specify the number of fiber family which may be difficult to identify for many kinds of tissues. In this study, we developed a novel hyperelastic model for biological tissues which does not need the information of the number of fiber family. We illustrated that a single generalized structure tensor (GST) with one parameter can characterize the structure of arbitrary planar fiber distribution as long as an in-plane symmetric axis exists. Based on the GST, we developed three novel fiber strain energy functions. Moreover, we proposed a novel second kind of Poisson effect which can capture deformation coupling properties of bio-tissues that the traditional well-known Poisson effect can hardly capture. According to the second kind of Poisson effect, the models constructed from the three novel strain energy functions exhibit different deformation couplings, referred to as strong, medium and weak coupling. The model of medium coupling has the best fitting for experimental data of porcine aortic tissues, and the model of weak coupling has the worst fitting. The newly proposed second kind of Poisson effect is a useful and essential supplement to the traditional Poisson effect and can be applied to investigate the accuracy of nonlinear constitutive models.

本构模型对于许多生物医学问题（例如主动脉瘤破裂的预测）具有根本的重要性。现有的基于结构的本构模型（例如，广泛使用的Gasser–Ogden–Holzapfel（GOH）模型）通常需要指定可能难以识别的多种组织的纤维家族数。在这项研究中，我们开发了一种新颖的生物组织超弹性模型，该模型不需要纤维家族数目的信息。我们说明，只要存在一个面内对称轴，具有一个参数的单个广义结构张量（GST）就可以表征任意平面纤维分布的结构。基于GST，我们开发了三种新颖的纤维应变能函数。而且，我们提出了一种新型的泊松效应，它可以捕获传统的著名泊松效应难以捕获的生物组织的变形耦合特性。根据第二种泊松效应，由三个新的应变能函数构造的模型表现出不同的变形耦合，称为强耦合，中耦合和弱耦合。中等耦合模型最适合猪主动脉组织的实验数据，而弱耦合模型最不适合猪主动脉组织的实验数据。新提出的第二种泊松效应是对传统泊松效应的有用且必不可少的补充，可用于研究非线性本构模型的准确性。根据第二种泊松效应，由三个新的应变能函数构造的模型表现出不同的变形耦合，称为强耦合，中耦合和弱耦合。中等耦合模型最适合猪主动脉组织的实验数据，而弱耦合模型最不适合猪主动脉组织的实验数据。新提出的第二种泊松效应是对传统泊松效应的有用且必不可少的补充，可用于研究非线性本构模型的准确性。根据第二种泊松效应，由三个新的应变能函数构造的模型表现出不同的变形耦合，称为强耦合，中耦合和弱耦合。中等耦合模型最适合猪主动脉组织的实验数据，而弱耦合模型最不适合猪主动脉组织的实验数据。新提出的第二种泊松效应是对传统泊松效应的有用且必不可少的补充，可用于研究非线性本构模型的准确性。而弱耦合模型的拟合效果最差。新提出的第二种泊松效应是对传统泊松效应的有用且必不可少的补充，可用于研究非线性本构模型的准确性。而弱耦合模型的拟合效果最差。新提出的第二种泊松效应是对传统泊松效应的有用且必不可少的补充，可用于研究非线性本构模型的准确性。