Opening of the artery as a result of the existence of residual stresses

Associated people

J. Schröder, S. Brinkhues, M. von Hoegen

Abstract

In a variety of investigations of the mechanical behavior of arteries it is assumed, that an unloaded artery exhibits an internal zero-stress state. This assumption does not reflect the real behavior, which can be observed in experiments: when an axial section is cutted in longitudinal direction, the artery springs open. This ``cutted'' configuration is often assumed to be stress-free. In various works dealing with the numerical simulation of arterial walls, it is accounted for residual stresses by closing an opened, unstressed artery by an initial bending to form a load-free, but internally stressed configuration. However, such configuration is not available for real purposes. In this research project we propose a novel approach  for the incorporation of residual stresses in human arteries. In contrast to the approach described above, we focus directly on the gradients of appropriate stresses in radial direction. Motivated by the arrangement of the embedded fibers, the gradients of the fiber stresses in radial direction are considered and smoothed by dint of residual stresses. This approach is applicable for arbitrary two- or three-dimensional arterial geometries and thus an appropriate solution for such complex physiological problems.

References

Brinkhues, S. & Schröder, J. (2011), "On the incorporation of residual stresses in arterial walls", Proceedings of Applied Mathematics and Mechanics, Vol. 11, pp. 83--84.

Schröder, J. & von Hoegen, M. (2015), "An engineering tool to estimate eigenstresses in three-dimensional patient-specific arteries", submitted to Computer Methods in Applied Mechanics and Engineering, Preprint Report 115