Modeling residual stresses in arterial walls based on anisotropic growth

Abstract

With the aim of obtaining a general local formulation for anisotropic growth in soft biological tissues, a model based on the multiplicative decomposition of the growth tensor is formulated. The two parts of the growth tensor are associated with the main anisotropy directions. Together with an anisotropic driving force, the model enables an effective stress reduction by including growth‐induced residual stresses, which is demonstrated in a numerical example of an idealized arterial segment. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling of Anisotropic Growth and Residual Stresses in Arterial Walls

“…In a previous comparative study [15], an arterial segment with internal pressure and an axial displacement of 15 % of the initial length was considered for a comparison of two different forms of the growth tensor and two different driving forces. Each of the approaches was able to provoke growth-induced circumferential stress smoothening, but the approach presented in Subsection 2.1 turned out to be the most effective, generating the most beneficial stress distributions at the lowest growth requirement, measured by the determinant of the growth tensor.…”