A new constitutive framework for arterial wall mechanics and a comparativestudy of material models

In this paper we develop a new constitutive law for the description of the (passive) mechanical response of arterial tissue. The artery is modeled as a thick-walled nonlinearly elastic circular cylindrical tube consisting of two layers corresponding to the media and adventitia (the solid mechanicall y relevant layers in healthy tissue). Each layer is treated as a fiber-rein forced material with the fibers corresponding to the collagenous component of the material and symmetrically disposed with respect to the cylinder axi s. The resulting constitutive law is orthotropic in each layer. Fiber orien tations obtained from a statistical analysis of histological sections from each arterial layer are used. A specific form of the law, which requires on ly three material parameters for each layer, is used to study the response of an artery under combined axial extension, inflation and torsion. The cha racteristic and very important residual stress in an artery in vitro is acc ounted for by assuming that the natural (unstressed and unstrained) configu ration of the material corresponds to an open sector of a tube, which is th en closed by an initial bending to form a load-free, but stressed, circular cylindrical configuration prior to application of the extension, inflation and torsion. The effect of residual stress on the stress distribution thro ugh the deformed arterial wall in the physiological state is examined. The model is fitted to available data on arteries and its predictions are a ssessed for the considered combined loadings. It is explained how the new m odel is designed to avoid certain mechanical, mathematical and computationa l deficiencies evident in currently available phenomenological models. A cr itical review of these models is provided by way of background to the devel opment of the new model.