论文标题
分数Visco-elasto塑料的一般返回映射框架
A General Return-Mapping Framework for Fractional Visco-Elasto-Plasticity
论文作者
论文摘要
我们为幂律Visco-elasto-Plasticity开发了一个分数返回映射框架。在我们的方法中，分数粘弹性是通过Scott-Blair元素的典型组合来解释的，以构建一系列众所周知的分数线性粘弹性模型，例如Kelvin-Voigt，Maxwell，Kelvin-Zener和Poynting-Thomson。我们还考虑了Fung模型的分数准线性版本，以说明应力/应变非线性。分数粘弹性模型与分数粘膜塑料装置结合使用，并与涉及Scott-Blair元素的串行组合的分数粘弹性模型结合使用。然后，我们开发了一个通用的返回映射过程，该过程完全隐含了线性粘弹性模型，而对于准线性案例，该过程完全隐含了。我们发现，在校正阶段，离散的应力投影和塑料滑动对于所有考虑的模型都具有相同的形式，尽管具有不同的属性和依赖时间依赖的投影项。使用分析和参考解决方案进行了一系列数值实验，以证明所提出的框架的收敛性和计算成本，该框架至少对于一般加载条件至少是一阶准确的。我们的数值结果表明，开发的框架更加灵活，保留了现有方法的数值准确性，同时由于CPU时间减少了$ 50 \％$，因此在Visco-Plastic范围内更具计算机处理。我们的公式特别适合在生物组织中的分数演算的新兴应用，这是呈现多个粘弹性幂律和粘性塑性性的标志。
We develop a fractional return-mapping framework for power-law visco-elasto-plasticity. In our approach, the fractional viscoelasticity is accounted through canonical combinations of Scott-Blair elements to construct a series of well-known fractional linear viscoelastic models, such as Kelvin-Voigt, Maxwell, Kelvin-Zener and Poynting-Thomson. We also consider a fractional quasi-linear version of Fung's model to account for stress/strain nonlinearity. The fractional viscoelastic models are combined with a fractional visco-plastic device, coupled with fractional viscoelastic models involving serial combinations of Scott-Blair elements. We then develop a general return-mapping procedure, which is fully implicit for linear viscoelastic models, and semi-implicit for the quasi-linear case. We find that, in the correction phase, the discrete stress projection and plastic slip have the same form for all the considered models, although with different property and time-step dependent projection terms. A series of numerical experiments is carried out with analytical and reference solutions to demonstrate the convergence and computational cost of the proposed framework, which is shown to be at least first-order accurate for general loading conditions. Our numerical results demonstrate that the developed framework is more flexible, preserves the numerical accuracy of existing approaches while being more computationally tractable in the visco-plastic range due to a reduction of $50\%$ in CPU time. Our formulation is especially suited for emerging applications of fractional calculus in bio-tissues that present the hallmark of multiple viscoelastic power-laws coupled with visco-plasticity.
