Lin Che-Yu, Chen Yi-Cheng, Lin Chen-Hsin, Chang Ke-Vin
Institute of Applied Mechanics, College of Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan.
Department of Mechanical Engineering, College of Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan.
Polymers (Basel). 2022 May 23;14(10):2124. doi: 10.3390/polym14102124.
The viscoelastic properties of materials such as polymers can be quantitatively evaluated by measuring and analyzing the viscoelastic behaviors such as stress relaxation and creep. The standard linear solid model is a classical and commonly used mathematical model for analyzing stress relaxation and creep behaviors. Traditionally, the constitutive equations for analyzing stress relaxation and creep behaviors based on the standard linear solid model are derived using the assumption that the loading is a step function, implying that the loading rate used in the loading process of stress relaxation and creep tests is infinite. Using such constitutive equations may cause significant errors in analyses since the loading rate must be finite (no matter how fast it is) in a real stress relaxation or creep experiment. The purpose of this paper is to introduce the constitutive equations for analyzing stress relaxation and creep behaviors based on the standard linear solid model derived with a finite loading rate. The finite element computational simulation results demonstrate that the constitutive equations derived with a finite loading rate can produce accurate results in the evaluation of all viscoelastic parameters regardless of the loading rate in most cases. It is recommended that the constitutive equations derived with a finite loading rate should replace the traditional ones derived with an infinite loading rate to analyze stress relaxation and creep behaviors for quantitatively evaluating the viscoelastic properties of materials.
诸如聚合物等材料的粘弹性特性可以通过测量和分析应力松弛和蠕变等粘弹性行为来进行定量评估。标准线性固体模型是用于分析应力松弛和蠕变行为的经典且常用的数学模型。传统上，基于标准线性固体模型分析应力松弛和蠕变行为的本构方程是在加载为阶跃函数的假设下推导得出的，这意味着在应力松弛和蠕变试验的加载过程中使用的加载速率是无穷大的。使用这样的本构方程可能会在分析中导致显著误差，因为在实际的应力松弛或蠕变实验中加载速率必须是有限的（无论多快）。本文的目的是介绍基于以有限加载速率推导的标准线性固体模型来分析应力松弛和蠕变行为的本构方程。有限元计算模拟结果表明，在大多数情况下，以有限加载速率推导的本构方程在评估所有粘弹性参数时，无论加载速率如何，都能产生准确的结果。建议使用以有限加载速率推导的本构方程来取代传统的以无穷大加载速率推导的本构方程，以分析应力松弛和蠕变行为，从而定量评估材料的粘弹性特性。
