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T. Christian Gasser

Department of Solid Mechanics, Royal Institute of Technology (KTH)

Anisotropic constitutive modeling of soft biological tissues based on finite deformation continuum mechanics

Abstract:

Biomechanical simulations can effectively assist and improve clinical interventions, provide diagnostic information and be of potential aid in tissue engineering. The reliability of such simulations largely depends on the underlying constitutive descriptions, and hence, constitutive modeling of soft biological tissues became an active field of research within the last few decades [1]. Continuum based constitutive relations describe the gross behavior that results from the internal constitution and allow the investigation of structural and functional interrelation in response to mechanical loading. This knowledge is crucial for the predictive capability of constitutive models and to gain insights into the physiological and the pathological load carrying mechanisms of soft biological tissues, i.e. to understand the interplay of mechanical load and cell signaling [1].

The fibrous (collagen) structure of many soft biological tissues determines their macroscopic mechanical properties, and hence, the present seminar discusses different approaches to incorporate structural information into macroscopic constitutive models. To this end the framework of finite strain continuum mechanics is employed and generalized structural tensors [2] are introduced to represent the tissue's microstructure. Anisotropic constitutive models, i.e. stress strain laws are derived in compliance with the laws of thermodynamics and towards a numerical implementation within the Finite Element Method. Consequently, a consistent linearization of the constitutive descriptions is provided, which in turn facilitates an incremental solution of the arising nonlinear system of equations. Finally, structural simulations, aiming at assessing the rupture risk of Abdominal Aortic Aneurysm, demonstrate the feasibility of the proposed approaches.

References
[1] J.D. Humphrey, Cardiovascular Solid Mechanics. Cells, Tissues, and Organs, Springer-Verlag, New York, 2002.
[2] T.C. Gasser, R.W. Ogden and G.A. Holzapfel. Review - Hyperelastic modelling of arterial layers with distributed collagen fibre orientations, J. Royal Soc. Lond. Interface, 3 (2006), 15 - 35.