Development of a viscoelastic phase field model for fracture processes with application to ice dynamics

漂浮冰舌中裂缝的扩展导致大型冰山的破裂。这一过程被称为产犊。对冰冻现象的理解对于判断气候变暖的后果非常重要。冰川崩解的增加导致陨冰加速流入海洋，随后海平面上升。为了模拟浮冰舌中复杂的裂纹扩展现象，将基于非线性Maxwell模型的冰粘弹性本构关系与断裂力学相场相结合。在连续的步骤中进行建模，导致材料流动的几何和本构非线性拉格朗日描述以及破裂相场。该模型是在有限元工具箱FENICS中实现的，可以模拟浮冰舌中复杂的裂纹模式。可以考虑裂纹的产生、扩展、阻止和分支。作为应用场景，对格陵兰岛的NioghalfJerdsbrae冰川进行了研究。

The propagation of cracks in floating ice tongues results in the break-off of large icebergs. This process is referred to as calving. The understanding of calving is of great importance for the judgement of the consequences of climate warming. An increased calving leads to an accelerated flow of meteoric ice into the oceans, which is followed by a sea level rise. To model complex crack propagation phenomena in floating ice tongues a viscoelastic constitutive law of ice based on a non-linear Maxwell model is combined with a fracture mechanical phase field. The modeling is pursued in successive steps, resulting in geometrically and constitutively non-linear Lagrangian description of the material flow in conjunction with a fracture phase field. The model is implemented in the finite element toolbox FEniCS and allows for the simulation of complex crack patterns in floating ice tongues. The creation, propagation, arrest, and branching of cracks can be considered. As an application scenario the Nioghalfjerdsbrae glacier in Greenland is investigated.