Constitutive function, residual stress, and state of uniform stress in arteries

Fung (1983) has conjectured that the residual stress in an artery distributes itself in such a way to assure that the circumferential stress is uniform across the artery wall under physiological conditions. In this work, we identify the entire class of constitutive functions for which the circumferential stress is uniform across the artery wall when it is subjected to an internal pressure. It is found that these constitutive functions do not necessarily endow residual stresses. Furthermore, a subset of the class of the constitutive functions is identified for which the circumferential stresses are uniform for the entire range of internal pressures. The constitutive functions in this sub-class are found to have zero residual stress. It is the inhomogeneity, rather than residual stress, that assures uniform circumferential stresses. We also examine the possibility of utilizing these constitutive functions in the design and fabrication of an engineered blood vessel with optimal mechanical properties.