A combined growth and remodeling framework for the approximation of residual stresses in arterial walls. Issue 12 (9th August 2018)

• Record Type: Journal Article
• Authors: Zahn, Anna; Balzani, Daniel
• Other Names: Holzapfel Gerhard A. guestEditor.; Cyron Christian J. guestEditor.
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 98:Issue 12(2018)
• Page Start: 2072
• Page End: 2100
• Publication Date: 2018-08-09
• Subjects: arterial walls -- multiplicative stress‐driven growth -- residual stresses -- stress‐driven fiber remodeling; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201700273
• Languages: English
• ISSNs: 0044-2267

Abstract

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. 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.