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Fractional Creep Model of Viscoelasticity of Hami Melon

机译：哈密​​瓜粘弹性的分数蠕变模型

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摘要

Hami Melon is considered as viscoelastic material. The creep process of Hami Melon is simulated by combining standard linear viscoelasticity with fractional order derivative. The standard viscoelasticity creep model was generalized by applying the Riemann—Liouville fractional calculus operators. The analytical expressions of the creep function for the obtained fractional standard linear viscoelasticity model were given by using the Boltzmann superposition principle and discrete inverse Laplace transform. The analytical solutions of the fractional model were used to fit the experimental data for viscoelasticity of Hami Melon. The comparison results showed that the fractional standard linear viscoelasticity model is more efficient than the Burgers viscoelasticity model with integer order in describing the stress—strain constitutive relations for the viscoelasticity of Hami Melon. The fractional model is a simple form with a few parameters which can be adjusted in the calculation processes. We believe the proposed fractional model can provide theory basis about forecasting creep damage.
机译：哈密​​瓜被认为是粘弹性材料。哈密​​瓜的蠕变过程是通过将标准线性粘弹性与分数阶导数相结合来模拟的。标准粘弹性蠕变模型通过应用Riemann-Liouville分数微积分算子进行了推广。利用玻尔兹曼叠加原理和离散逆拉普拉斯变换，给出了所得分数标准线性粘弹性模型的蠕变函数的解析表达式。分数模型的解析解用于拟合哈密瓜粘弹性的实验数据。比较结果表明，分数标准线性粘弹性模型在描述哈密瓜粘弹性的应力-应变本构关系上比具有整数阶的Burgers粘弹性模型更有效。分数模型是具有一些参数的简单形式，可以在计算过程中对其进行调整。我们认为，提出的分数模型可以为预测蠕变损伤提供理论基础。

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