Fractional-order viscoelasticity applied to describe uniaxial stress relaxation of human arteries
Fractional-order viscoelasticity applied to describe uniaxial stress relaxation of human arteries
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DOI：
10.1088/0031-9155/53/17/006
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发表时间：
2008-09-07
影响因子：
3.5
通讯作者：
Guinea, Gustavo V.
中科院分区：
文献类型：
--
作者：
Craiem, Damian;Rojo, Francisco J.;Guinea, Gustavo V.
粘弹性模型可用于更好地理解生理和病理条件下的动脉壁力学。动脉壁揭示了非常缓慢的时间依赖性衰减在单轴应力松弛实验中，与弱幂律函数一致。准线性粘弹性（QLV）理论被成功地应用于模拟这样的响应，但减少松弛函数参数的准确估计可能是非常困难的。在这项工作中，一个替代的松弛函数的基础上分数微积分理论，提出了描述应力松弛实验条从健康的人尿道。在三个增量应力水平下记录应力松弛（1 h）。将新的三参数弛豫函数与QLV理论相结合，对实验数据进行拟合。它是基于一个修改的Voigt模型，包括一个分数阶的元素，称为弹簧罐。应力松弛预测准确、快速。每个参数的敏感性图在其最佳值附近呈现最小值。最小二乘误差保持在2%以下。α = 0.1-0.3级的值证实了主要的弹性行为。该模型的其他两个参数可以与弹性和粘性常数，解释所观察到的弛豫函数的时间过程。分数阶模型集成到QLV理论证明捕捉动脉壁机械响应的基本特征。
Viscoelastic models can be used to better understand arterial wall mechanics in physiological and pathological conditions. The arterial wall reveals very slow time-dependent decays in uniaxial stress-relaxation experiments, coherent with weak power-law functions. Quasi-linear viscoelastic (QLV) theory was successfully applied to modeling such responses, but an accurate estimation of the reduced relaxation function parameters can be very difficult. In this work, an alternative relaxation function based on fractional calculus theory is proposed to describe stress relaxation experiments in strips cut from healthy human aortas. Stress relaxation (1 h) was registered at three incremental stress levels. The novel relaxation function with three parameters was integrated into the QLV theory to fit experimental data. It was based in a modified Voigt model, including a fractional element of order a, called spring-pot. The stress-relaxation prediction was accurate and fast. Sensitivity plots for each parameter presented a minimum near their optimal values. Least-squares errors remained below 2%. Values of order alpha = 0.1-0.3 confirmed a predominant elastic behavior. The other two parameters of the model can be associated to elastic and viscous constants that explain the time course of the observed relaxation function. The fractional-order model integrated into the QLV theory proved to capture the essential features of the arterial wall mechanical response.