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Constitutive modelling of arteries. (English) Zbl 1197.74075
This review article is concerned with mathematical modeling of mechanical properties of soft biological tissues that constitute arterial walls. Many important aspects of the mechanical behavior of arterial tissues can be treated on the basis of finite elasticity theory. Therefore, the present work is primarily focused on the constitutive modeling of anisotropic and highly nonlinear elastic properties of the arterial wall. The work is focused mainly on the developments over the last decade based on the theory of deformation invariants, structural orientation of collagen fibers, the dispersion in the orientation and the associated anisotropy of material properties. The main features of the relevant theory are summarized briefly, and a particular form of elastic strain energy density function is discussed and then applied to an artery considered as a thick-walled circular cylindrical tube in order to illustrate its extension and inflation behavior. Various models for healthy and diseased tissues are discussed. The authors mainly examine the passive behavior of arterial wall materials. Nevertheless, a section is devoted to reviewing the limited literature within the continuum mechanics framework on the active response of arterial walls. Also a final section is added which provides a brief summary of the current state of arterial wall mechanical modeling and points to key areas that need further modeling effort in order to improve understanding of biomechanics of arteries.
The work is well written and can find many readers working in the area of mathematical modeling of soft biological tissues.

MSC:
74L15 Biomechanical solid mechanics
74B20 Nonlinear elasticity
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
92C10 Biomechanics
92-02 Research exposition (monographs, survey articles) pertaining to biology
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