An updated-Lagrangian damage mechanics formulation for modeling the creeping flow and fracture of ice sheets
An updated-Lagrangian damage mechanics formulation for modeling the creeping flow and fracture of ice sheets
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用于模拟冰盖蠕动流和破裂的更新拉格朗日损伤力学公式
DOI：
10.1016/j.cma.2016.09.034
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发表时间：
2017
影响因子：
7.2
通讯作者：
Bassis, Jeremy
中科院分区：
文献类型：
--
作者：
Jiménez, Stephen;Duddu, Ravindra;Bassis, Jeremy
一个更新的拉格朗日公式的开发模型不可压缩的斯托克斯（蠕动）流和断裂的冰盖使用显式积分和隐式梯度非局部损伤的方法。本文在平面应变近似下，采用高阶混合有限元方法，在当前参考区域上对不可压非线性粘性Stokes流的控制方程进行了离散。离散化后的非线性系统采用Picard迭代法求解，并在每一时间步采用网格更新方法获得更新后的参考域。裂缝（决口）的启动和传播建模使用标量（各向同性）损伤变量，并实施损伤控制或元素删除策略，以避免数值精度和收敛问题所产生的完全损坏的有限元决口尖端附近。该公式在开源有限元软件FEniCS中实现，并详细介绍了相关的数值算法。数值验证和基准研究的基础上制造的非线性斯托克斯解决方案和恒定速度和重力驱动的蠕变流实验进行建立的可行性的制定。我们表明，从非线性斯托克斯和麦克斯韦粘弹性模型得到的决口传播速率在短时间尺度（天）是很好的协议，所以它是合理的忽略弹性效应，采用斯托克斯模型来模拟冰山崩解。此外，我们表明，在很长的时间尺度（月）的更新拉格朗日斯托克斯制定是更准确的物理比总拉格朗日麦克斯韦粘弹性制定，因为前者占域几何形状的变化。总之，建议的配方的优点是双重的：首先，它是计算效率比麦克斯韦粘弹性模型;第二，它占有限应变蠕变变形累积在很长的时间尺度。
An updated-Lagrangian formulation is developed to model the incompressible Stokes (creeping) flow and fracture of ice sheets using both explicit-integral and implicit-gradient nonlocal damage approaches. The governing equations of incompressible nonlinearly viscous Stokes flow assuming the plane strain approximation are discretized using high-order mixed finite elements over the current reference domain. The discretized nonlinear system is solved using a Picard iteration scheme, and a mesh update method is employed to obtain the updated reference domain at every time step. Fracture (crevasse) initiation and propagation is modeled using a scalar (isotropic) damage variable, and damage control or element removal strategies are implemented to avoid numerical accuracy and convergence issues arising from fully damaged finite elements near the crevasse tip. The formulation is implemented in the open-source finite element software FEniCS, and the relevant numerical algorithms are detailed. Numerical verification and benchmark studies based on manufactured nonlinear Stokes solutions and constant velocity and gravity-driven creep flow experiments are conducted to establish the viability of the formulation. We demonstrate that crevasse propagation rates obtained from nonlinear Stokes and Maxwell viscoelastic models are in good agreement over short time scales (days), so it is reasonable to neglect the elastic effects and employ the Stokes model to simulate iceberg calving. Furthermore, we demonstrate that over long time scales (months) the updated-Lagrangian Stokes formulation is more physically accurate than the total Lagrangian Maxwell viscoelastic formulation because the former accounts for the domain geometry changes. To conclude, the merit of the proposed formulation is two-fold: first, it is computationally more efficient than the Maxwell viscoelastic model; and second, it accounts for finite strain creep deformations accruing over long time scales.
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影响因子：
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作者：
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通讯作者：
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DOI：
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影响因子：
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作者：
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