Phase field method has proven capable of producing complex crack patterns in solids. It introduces a continuous phase field to regularize the sharp crack discontinuities. However, the applicability of this method to engineering problems is hindered by its computational costs. In this work, we proposed a mapped phase field method as a possible route to resolve this issue. The core of this method is a map that connects the physical domain to a parametric domain, which is essentially a local reparametrization of the physical domain where large gradients are expected. By the use of this map the strongly varying fields can be approximated by a much smoother function. The reparametrized solution is solved via standard finite element in the parametric domain and then mapped back to the physical domain. A simple analysis shows that, with a properly defined map, such method consumes much less computational resources compared with conventional phase field method, without loss in accuracy. The map can also be easily manipulated to adapt to the evolution of cracks, and thus providing a flexible framework to simulate complex crack patterns without any knowledge of the crack path in advance. The advantages of our proposed method are further shown by four different numerical examples: single edge crack under symmetric and anti-symmetric loading, three-point bending, and L-shape panel under cyclic loading.

相场法已被证明能够在固体中产生复杂的裂纹模式。它引入了一个连续相场来规范尖锐的裂纹不连续性。然而，这种方法对工程问题的适用性受到其计算成本的阻碍。在这项工作中，我们提出了一种映射相场​​方法作为解决这个问题的可能途径。这种方法的核心是将物理域连接到参数域的映射，它本质上是一个局部的预期有大梯度的物理域的重新参数化。通过使用该地图，可以通过更平滑的函数来近似强烈变化的场。重新参数化的解决方案通过参数域中的标准有限元求解，然后映射回物理域。一个简单的分析表明，在正确定义地图的情况下，这种方法与传统的相场方法相比消耗的计算资源要少得多，而且精度没有损失。该地图还可以很容易地进行操作以适应裂缝的演变，从而提供一个灵活的框架来模拟复杂的裂缝模式，而无需事先了解裂缝路径。我们提出的方法的优点通过四个不同的数值例子进一步展示：对称和反对称载荷下的单边裂纹，