Arcady V. Sokolov

Mechanics and Mathematics Department. Rostov State University. Zorge str., 5, Rostov-on-Don, 344090. Russia

e-mail: arcady sokolov@mail.ru

Abstract. The nonlinear mechanical behavior of an arterial wall under the effect of a perivascular medium (muscular and areolar tissue) is investigated. The artery is modeled by an anisotropic, incompressible, nonlinear, elastic, two-layer, thick-walled tube under torsion, tension, and in ation. The arterial vessel is assumed to be surrounded by an elastic medium with the property of Winkler's foundation. An analytical expression for the components of the stress tensor is established. Comparative analysis of perivascular media is carried out.

Keywords and phrases. Deformation of a blood vessel, Model of an arterial wall, Nonlinear anisotropic theory of elasticity, Large deformations.

2000 Mathematics Subject Classification. Primary: 92C10. Secondary: 74B20.

Resumen. Se investiga el comportamiento mecánico no lineal de una pared arterial bajo el efecto de un medio perivascular (tejido areolar y muscular). La arteria es modelada por un tubo no-isotrópico no-comprimible, no lineal, de dos capas y de paredes gruesas bajo torsión tensión e inflación. Se asume que el vaso está rodeado por un medio elástico con soporte de tipo Winkler. Se establece una expresión analítica para las componentes de el tensor de tensión. Se lleva a cabo un análisis comparativo del medio perivacular.

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(Recibido en septiembre de 2005. Aceptado en noviembre de 2005)