title: Numerical implementation of constitutive model for arterial layers with distributed collagen fibre orientations.
abstract: Several constitutive models have been proposed for the description of mechanical behaviour of soft tissues containing collagen fibres. Some of the commonly used approaches accounting for the dispersion of fibre orientations are based on the summation of (mechanical) contributions of differently oriented fibre families. This leads to the need of numerical integration on the sphere surface, and the related numerical consumption is the main disadvantage of this category of constitutive models. The paper is focused on the comparison of various numerical integration methods applied to a specific constitutive model applicable for arterial walls. Robustness and efficiency of several integration rules were tested with respect to application in finite element (FE) codes. Among all the analysed numerical integration rules, the best results were reached by Lebedev quadrature; the related parameters for the specific constitutive model are presented in the paper. The results were implemented into the commercial FE code ANSYS via user subroutines, and their applicability was demonstrated by an example of FE simulation with non-homogenous stress field.
authors.affiliation: a Institute of Solid Mechanics, Mechatronics and Biomechanics, Brno University of Technology , Technicka 2896/2, 616 69 , Brno , Czech Republic.
authors.forename: Pavel
authors.initials: P
authors.lastname: Skacel
authors.forename: Jiri
authors.initials: J
authors.lastname: Bursa
mesh_terms: D001158:Arteries / Q000033:anatomy & histology* / Q000502:physiology*; D001696:Biomechanical Phenomena; D003094:Collagen / Q000502:physiology*; D019295:Computational Biology / Q000379:methods*; D003198:Computer Simulation; D008954:Models, Biological
chemical_list: D003094:Collagen
keywords: Hyperfit software; arterial wall mechanics; constitutive modelling; distribution of collagen fibre orientation; numerical integration on the sphere