Publications

A combined growth and remodeling framework for the approximation of residual stresses in arterial walls

Zahn, A. and Balzani, D.

ZAMM ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
Volume: 98 Pages: 2072-2100
DOI: 10.1002/zamm.201700273
Published: 2018

Abstract
A combined model of multiplicative growth and fiber remodeling in the sense of a reorientation of the collagen fibers is proposed for the simulation of adaptation processes in arterial tissues, where both mechanisms are supposed to be governed by the intensity and the direction of the principal stresses. The generalized formulation of the growth tensor includes up to three perpendicular anisotropy directions, which are defined based on the local principal stress state. Remodeling is incorporated in a straightforward manner by formulating a scalar evolution equation for the angle between the existing and the target fiber orientation vectors. In numerical examples on idealized arterial segments, the fiber remodeling algorithm is illustrated and a comparison of different approaches for the growth tensor with respect to stresses in the loaded state, fiber angles and residual stresses is conducted. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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