A novel hyperelastic model for biological tissues with planar distributed collagen fibers and a second kind of Poisson effect

Abstract 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 adventitia 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.