Inelastic Constitutive Models of Blood Vessels in Physiological Conditions

Abstract

An inelastic constitutive model for passive blood vessels and one for active blood vessels are introduced. In the former model, the total deformation is decomposed into inelastic and elastic parts. The elastic part is expressed by postulating an incompressible transversely isotropic strain energy density function. The inelastic part is formulated so as to describe a hysteresis loop in stress-strain relationship under cyclic loading by taking account of the loading path and loading rate dependencies. In the latter model, the total deformation is decomposed into inelastic and non-inelastic parts. In the non-inelastic part of the deformation, the total stress consists of a passive stress and an active stress. The passive stress is expressed by a strain energy density function. The active stress is formulated so as to express a stress development in the muscle direction. Both models describe the mechanical behavior of the arteries well.