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The finite element implementation of 3D fractional viscoelastic constitutive models

机译:3D分数粘弹性本构模型的有限元实现

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The aim of this paper is to present the implementation of 3D fractional viscoelastic constitutive theory presented in Alotta et al., 2016 [1] Fractional viscoelastic models exactly reproduce the time dependent behaviour of real viscoelastic materials which exhibit a long "fading memory". From an implementation point of view, this feature implies storing the stress/strain history throughout the simulations which may require a large amount of memory. We propose here a number of strategies to effectively limit the memory required. The form of the constitutive equations are summarized and the finite element implementation in a Newton-Raphson integration scheme is described in detail. The expressions that are needed to be coded in user-defined material subroutines for quasi static and dynamic implicit and explicit analysis (UMAT and VUMAT) in the commercial finite element software ABAQUS are readily provided. In order to demonstrate the accuracy of the numerical implementation we report a number of benchmark problems validated against analytical results We have also analysed the behaviour of a viscoelastic plate with a hole in order to show the efficiency of these types of models. The source codes for the UMAT and VUMAT are provided as online supplements to this paper.
机译:本文的目的是介绍在Alotta等人,2016年提出的3D分数粘弹性本构理论的实现。[1]分数粘弹性模型精确地再现了具有长“衰落记忆”的真实粘弹性材料的时间依赖性行为。从实现的角度来看,此功能意味着在整个模拟过程中存储应力/应变历史记录,这可能需要大量的内存。我们在这里提出许多策略来有效地限制所需的内存。总结了本构方程的形式,并详细描述了牛顿-拉夫森积分方案中的有限元实现。可以轻松提供在用户定义的材料子例程中进行编码的表达式,以便在商业有限元软件ABAQUS中进行准静态和动态隐式和显式分析(UMAT和VUMAT)。为了证明数值实现的准确性,我们报告了一些针对分析结果进行验证的基准问题。我们还分析了带孔的粘弹性板的行为,以显示这些类型的模型的效率。 UMAT和VUMAT的源代码作为本文的在线补充提供。

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