Ramp-hold relaxation solutions for the KVFD model applied to soft viscoelastic media
Ramp-hold relaxation solutions for the KVFD model applied to soft viscoelastic media
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DOI：
10.1088/0957-0233/27/2/025702
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发表时间：
2016-01
影响因子：
2.4
通讯作者：
Hong-mei Zhang;Yue Wang;M. Insana
中科院分区：
文献类型：
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作者：
Hong-mei Zhang;Yue Wang;M. Insana
由于难以通过实验实现阶跃应变，标准阶跃保持载荷松弛曲线可以产生机械性能的可变估计。如果可以导出适当的模型函数，斜坡保持曲线克服了这一限制。基于Kelvin-Voigt分数阶导数（KVFD）模型，利用Boltzmann遗传积分算子对两种压痕几何形状进行积分，得到了载荷松弛的斜坡解析解.结果从与数据拟合的单个模型曲线确定了表征粘弹性行为的三个模型参数：弹性模量E0、分数阶参数α和松弛时间常数τ？>。通过对表现出粘弹性行为的明胶乳液样品进行测量，验证了分析的定量性质。基于KVFD模型的解决方案为一系列粘弹性和实验条件下的载荷松弛行为提供了数学上简单和实验上灵活的描述;例如，一个封闭形式的解决方案可以拟合松弛时间序列的斜坡和保持阶段。实验表明，球形压头和板式压缩机的解与相应的实验弛豫曲线拟合良好，决定系数R2 > 0.98。从球形尖端压痕和板压缩几何形状获得的参数在一个标准偏差内一致，证实了基于斜坡解的KVFD模型产生一致的测量值用于表征粘弹性材料。
The standard step-hold load-relaxation profile can yield variable estimates of mechanical properties due to the difficulty in achieving a step strain experimentally. A ramp-hold profile overcomes this limitation if appropriate model functions can be derived. Utilizing Boltzmann hereditary integral operators for two indentation geometries, analytical ramp solutions for load-relaxation were developed based on the Kelvin–Voigt fractional derivative (KVFD) model. The results identify three model parameters for characterizing viscoelastic behavior from a single model curve fit to the data: the elastic modulus E0, fractional-order parameter α, and relaxation time constant τ ?>. The quantitative nature of the analysis was validated through measurements on gelatin emulsion samples exhibiting viscoelastic behavior. KVFD-model-based solutions provide mathematically simple and experimentally flexible descriptions of load-relaxation behavior for a range of viscoelastic properties and experimental conditions; e.g. one closed-form solution can fit the ramp and the hold phases of the relaxation time series. Experiments show that the solution for a spherical indenter and plate compressor each fit well to the corresponding experimental relaxation curves with a coefficient of determination R2 > 0.98. Parameters obtained from the spherical-tip indentation and plate-compression geometries agree within one standard deviation, confirming that the ramp solution based KVFD model yields consistent measurements for characterizing viscoelastic materials.