Mechanics and Computation / View source

for Simulation of Atherosclerotic Arteries-Generalized Convexity Conditions, Modeling of Damage and Residual Stresses

=Daniel Balzani, Ph.D.=

===February 17, 2011===

Simulation of Atherosclerotic Arteries - 
Generalized Convexity Conditions, Modeling of Damage and Residual Stresses

The simulation of atherosclerotic arteries issues various challenges from the structural as well as from the material point of view. On the one hand atherosclerotic arteries are thin-walled tubes consisting of several layers and (sometimes finely distributed) plaque components with 
significantly different material stiffnesses requiring robust and efficient parallel numerical solution strategies. On the other hand the soft biological tissues found in arteries are incompressible, fiber-reinforced materials with a highly nonlinear hyperelastic behavior in the physiological loading regime and complex stress-softening hysteresis with remanent strains along the direction of the fibers when supra-physiological loads are applied. Although some aspects with respect to segmentation and parallel computating will be addressed, the talk focusses on the modeling of the physiological and supra-physiological behavior of arterial tissues. A framework for the construction of polyconvex strain energy functions is given and specific models fulfilling the condition of a stress-free reference configuration are derived. For the construction of models able to describe i) the stress-softening observed in cyclic tension tests and ii) the remanent strains as a result of microscopic damage in the reinforcing collagen fiber families a principle is proposed. Based on that, specific models are derived which turn out to be able to match experimental data. Numerical simulations of diseased arteries illustrate the applicability of the proposed models.

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