Zusammenfassung
Constitutive relations are fundamental to the solution of problems in
continuum mechanics, and are required in the study of, for example,
mechanically dominated clinical interventions involving soft biological
tissues. Structural continuum constitutive models of arterial layers
integrate information about the tissue morphology and therefore allow
investigation of the interrelation between structure and function in
response to mechanical loading. Collagen fibres are key ingredients in
the structure of arteries. In the media (the middle layer of the artery
wall) they are arranged in two helically distributed families with a
small pitch and very little dispersion in their orientation (i.e. they
are aligned quite close to the circumferential direction). By contrast,
in the adventitial and intimal layers, the orientation of the collagen
fibres is dispersed, as shown by polarized light microscopy of stained
arterial tissue. As a result, continuum models that do not account for
the dispersion are not able to capture accurately the stress-strain
response of these layers. The purpose of this paper, therefore, is to
develop a structural continuum framework that is able to represent the
dispersion of the collagen fibre orientation. This then allows the
development of a new hyperelastic free-energy function that is
particularly suited for representing the anisotropic elastic properties
of adventitial and intimal layers of arterial walls, and is a
generalization of the fibre-reinforced structural model introduced by
Holzapfel & Gasser (Holzapfel & Gasser 2001 Comput. Meth. Appl. Mech.
Eng. 190, 4379-4403) and Holzapfel et al. (Holzapfel et al. 2000 J.
Elast. 61, 1-48). The model incorporates an additional scalar structure
parameter that characterizes the dispersed collagen orientation. An
efficient finite element implementation of the model is then presented
and numerical examples show that the dispersion of the orientation of
collagen fibres in the adventitia of human iliac arteries has a
significant effect on their mechanical response.
Nutzer