Skacel Pavel, Bursa Jiri
a Institute of Solid Mechanics, Mechatronics and Biomechanics, Brno University of Technology , Technicka 2896/2, 616 69 , Brno , Czech Republic.
Comput Methods Biomech Biomed Engin. 2015;18(8):816-28. doi: 10.1080/10255842.2013.847928. Epub 2013 Oct 29.
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.
已经提出了几种本构模型来描述含有胶原纤维的软组织的力学行为。一些考虑纤维取向离散性的常用方法是基于不同取向纤维族的（力学）贡献之和。这导致需要在球面上进行数值积分，而相关的数值计算量是这类本构模型的主要缺点。本文着重比较应用于适用于动脉壁的特定本构模型的各种数值积分方法。针对在有限元（FE）代码中的应用，测试了几种积分规则的稳健性和效率。在所有分析的数值积分规则中，勒贝德夫求积法取得了最佳结果；本文给出了特定本构模型的相关参数。通过用户子程序将结果实现到商业有限元代码ANSYS中，并通过一个具有非均匀应力场的有限元模拟示例证明了其适用性。
