Modeling of Anisotropic Growth and Residual Stresses in Arterial Walls

Zahn, Anna; Balzani, Daniel

doi:10.14311/app.2017.7.0085

Cited by 5 publications

(1 citation statement)

References 16 publications

(22 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to cure the need for describing the structure of the growth-related deformation gradient a-priori, more recent works (e.g. Zahn and Balzani 2017 ) have developed formulations in which the growth-related deformation gradient tensor is constructed with respect to the eigenvectors corresponding to the principal stress state. Nevertheless, defining general and flexible formulations that can adapt to various boundary value problems remains a challenging task and ongoing topic of research, as pointed out already by e.g.…”

Section: Introductionmentioning

confidence: 99%

A macroscopic approach for stress-driven anisotropic growth in bioengineered soft tissues

Lamm

Jockenhövel

Brepols

et al. 2022

Biomech Model Mechanobiol

View full text Add to dashboard Cite

The simulation of growth processes within soft biological tissues is of utmost importance for many applications in the medical sector. Within this contribution, we propose a new macroscopic approach for modelling stress-driven volumetric growth occurring in soft tissues. Instead of using the standard approach of a-priori defining the structure of the growth tensor, we postulate the existence of a general growth potential. Such a potential describes all eligible homeostatic stress states that can ultimately be reached as a result of the growth process. Making use of well-established methods from visco-plasticity, the evolution of the growth-related right Cauchy–Green tensor is subsequently defined as a time-dependent associative evolution law with respect to the introduced potential. This approach naturally leads to a formulation that is able to cover both, isotropic and anisotropic growth-related changes in geometry. It furthermore allows the model to flexibly adapt to changing boundary and loading conditions. Besides the theoretical development, we also describe the algorithmic implementation and furthermore compare the newly derived model with a standard formulation of isotropic growth.

show abstract

Section: Introductionmentioning

confidence: 99%

A macroscopic approach for stress-driven anisotropic growth in bioengineered soft tissues

Lamm

Jockenhövel

Brepols

et al. 2022

Biomech Model Mechanobiol

View full text Add to dashboard Cite

show abstract

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

Zahn

Balzani

2018

Z Angew Math Mech

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Finite element simulation of three dimensional residual stress in the aortic wall using an anisotropic tissue growth model

Liu

Zhang

Liu

et al. 2019

Journal of the Mechanical Behavior of Biomedical Materials

View full text Add to dashboard Cite

Modeling of Anisotropic Growth and Residual Stresses in Arterial Walls

Cited by 5 publications

References 16 publications

A macroscopic approach for stress-driven anisotropic growth in bioengineered soft tissues

A macroscopic approach for stress-driven anisotropic growth in bioengineered soft tissues

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

Finite element simulation of three dimensional residual stress in the aortic wall using an anisotropic tissue growth model

Contact Info

Product

Resources

About