Large-scale simulation of arterial walls: mechanical modeling

In: Proceedings in Applied Mathematics and Mechanics (PAMM), Jg. 7 (2007) ; 1, Special Issue: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007, S. 4020017-4020018
ISSN: 1617-7061
Zeitschriftenaufsatz / Fach: Bauwissenschaften
Biological soft tissues appearing in arterial walls are characterized by a nearly incompressible, anisotropic hyperelastic material behavior in the physiological range of deformations. For the representation of such materials we apply a polyconvex strain energy function in order to ensure the existence of minimizers and in order to satisfy the Legendre-Hadamard condition automatically. When arteries are overstretched, discontinuous damage is observed. For the modeling of this effect we apply a damage model, which basically assumes that the damage occurs mainly in fiber direction. For the numerical simulation we consider an atherosclerotic artery and apply a high internal pressure which is comparable to the pressure applied during a balloon-angioplasty. The 3D-discretization results in a large system of equations, therefore, a parallel algorithm using FETI-DP is applied to solve the boundary value problem.