Caner Ferhun C, Carol Ignacio
ETSECCPB (School of Civil Engineering), UPC (Technical University of Catalonia), Jordi Girona 1-3, Edif. D2, E-08034 Barcelona, Spain.
J Biomech Eng. 2006 Jun;128(3):419-27. doi: 10.1115/1.2187036.
This paper presents a nonlinearly elastic anisotropic microplane formulation in 3D for computational constitutive modeling of arterial soft tissue in the passive regime. The constitutive modeling of arterial (and other biological) soft tissue is crucial for accurate finite element calculations, which in turn are essential for design of implants, surgical procedures, bioartificial tissue, as well as determination of effect of progressive diseases on tissues and implants. The model presented is defined at a lower scale (mesoscale) than the conventional macroscale and it incorporates the effect of all the (collagen) fibers which are anisotropic structural components distributed in all directions within the tissue material in addition to that of isotropic bulk tissue. It is shown that the proposed model not only reproduces Holzapfel's recent model but also improves on it by accounting for the actual three-dimensional distribution of fiber orientation in the arterial wall, which endows the model with advanced capabilities in simulation of remodeling of soft tissue. The formulation is flexible so that its parameters could be adjusted to represent the arterial wall either as a single material or a material composed of several layers in finite element analyses of arteries. Explicit algorithms for both the material subroutine and the explicit integration with dynamic relaxation of equations of motion using finite element method are given. To circumvent the slow convergence of the standard dynamic relaxation and small time steps dictated by the stability of the explicit integrator, an adaptive dynamic relaxation technique that ensures stability and fastest possible convergence rates is developed. Incompressibility is enforced using penalty method with an updated penalty parameter. The model is used to simulate experimental data from the literature demonstrating that the model response is in excellent agreement with the data. An experimental procedure to determine the distribution of fiber directions in 3D for biological soft tissue is suggested in accordance with the microplane concept. It is also argued that this microplane formulation could be modified or extended to model many other phenomena of interest in biomechanics.
本文提出了一种用于动脉软组织被动状态下计算本构模型的三维非线性弹性各向异性微平面公式。动脉（及其他生物）软组织的本构模型对于精确的有限元计算至关重要，而有限元计算对于植入物设计、手术过程、生物人工组织以及确定渐进性疾病对组织和植入物的影响而言必不可少。所提出的模型定义在比传统宏观尺度更低的尺度（细观尺度）上，它除了考虑各向同性的整体组织外，还纳入了所有（胶原）纤维的影响，这些纤维是在组织材料内沿各个方向分布的各向异性结构成分。结果表明，所提出的模型不仅能够重现霍尔扎菲尔的最新模型，还通过考虑动脉壁中纤维取向的实际三维分布对其进行了改进，这赋予了该模型在软组织重塑模拟方面的先进能力。该公式具有灵活性，因此在动脉的有限元分析中，其参数可以调整，以便将动脉壁表示为单一材料或由多层组成的材料。给出了材料子程序的显式算法以及使用有限元方法与运动方程动态松弛进行显式积分的算法。为了避免标准动态松弛的缓慢收敛以及显式积分器稳定性所要求的小时间步长，开发了一种确保稳定性和尽可能快的收敛速度的自适应动态松弛技术。使用具有更新惩罚参数的惩罚方法来强制实现不可压缩性。该模型用于模拟文献中的实验数据，结果表明模型响应与数据非常吻合。根据微平面概念，提出了一种确定生物软组织三维纤维方向分布的实验方法。还论证了这种微平面公式可以修改或扩展，以对生物力学中许多其他感兴趣的现象进行建模。
