Inelastic Constitutive Modeling of Arterial and Ventricular Walls

Abstract

The constitutive laws of arterial and ventricular walls are reviewed and their mechanical modeling is discussed. After a brief review of the constitutive modeling of arterial and ventricular walls, an anisotropic inelastic constitutive model of arteries is developed. The hysteresis loops under cyclic loading are assumed to be caused by the dependence of the behavior on the loading path and the loading rate. The elastic part of the deformation is represented by postulating a transversely isotropic strain energy density function, while the inelastic part is formulated by incorporating the transverse isotropy into the viscoplastic model proposed in a previous paper by the authors. A three-dimensional transversely isotropic constitutive model of ventricular walls is then proposed by dividing the stress into the sum of the passive and active parts. The passive part is represented by a strain energy density function similar to the arterial wall, and the active part is formulated by introducing internal variables describing the activities and the sarcomere length. The applicability of the current models is also discussed by comparing them with the corresponding results of experiments.