Comparison of approaches to model viscoelasticity based on fractional time derivatives
Comparison of approaches to model viscoelasticity based on fractional time derivatives
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DOI：
10.1016/j.commatsci.2014.11.012
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发表时间：
2015-02
影响因子：
3.3
通讯作者：
C. Zopf;S. Hoque;M. Kaliske
中科院分区：
文献类型：
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作者：
C. Zopf;S. Hoque;M. Kaliske
提出了描述大应变下的本构分数齐纳模型的两种方法。两种粘弹性齐纳模型均由非线性弹性弹簧和分数阶麦克斯韦单元并行组成。分数阶麦克斯韦单元表示公式的粘弹性行为。本文提出了一种考虑有限应变理论的分数阶粘弹性材料模型。此外，还推导了基于两种不同算法的本构方程，以捕获该材料模型中的分数时间积分。分数元素的考虑使得具有相对较少材料参数的高度非弹性、时间依赖材料的表征成为可能。对于分数单元，材料参数α决定了流变单元在弹簧（α= 0）和阻尼器（α= 1）之间的行为转变。通过几种有限元模拟与材料试验结果的对比，验证了传统的非递归算法和一种新的递归算法处理分数阶元素的精度和效率。模拟得到了有限应变和隐式时间积分方案。最后，进行了有限元模拟，发现了显式时间积分方案的扩展本构模型，并与实际成形过程进行了比较，说明了大规模模拟的性能，发现它是相当有效的。
Two approaches to describe a constitutive fractional Zener model at large strain are presented. Both viscoelastic Zener models consist of a nonlinear elastic spring and a fractional Maxwell element in parallel. The fractional Maxwell element represents the viscoelastic behaviour of the formulation. Here, development of a new fractional viscoelastic material model under consideration of finite strain theory is presented. Additionally, the constitutive equations based on two different algorithmic approaches to capture the fractional time integration within this material model are derived. The consideration of fractional elements enables the characterization of highly inelastic, time dependent materials with relatively few material parameters. For the fractional element, a material parameter α determines the transition of the rheological element’s behaviour between spring (α= 0) and dashpot (α= 1). Accuracy and efficiency of a classical (non-recursive) and a new recursive algorithm to handle the fractional elements have been verified and validated by the comparison of several finite element (FE) simulations to material test results. The simulations found on finite strains and an implicit time integration scheme. Finally, a FE moulding simulation, found the extended constitutive model for the explicit time integration scheme has been carried out to illustrate the performance for large scale simulations in comparison to a real forming process and found to be quite efficient.