论文标题
准脆性裂缝的变分不对称相位模型：能量溶液及其计算
A variational asymmetric phase-field model of quasi-brittle fracture: Energetic solutions and their computation
论文作者
论文摘要
我们通过应用速率非依赖性过程的能量公式并获得裂缝的正则配方，从而得出了梯度损伤模型的变异公式。该模型在牵引和压缩时表现出不同的行为，并且具有依赖状态的耗散电位，该耗散势可以诱导与路径无关的工作。我们将展示该公式如何提供自然框架，以建立具有基本变化结构的一致数值方案，并以双面能量不平等的形式衍生出其他必要的全球最优化条件。这些条件将构成我们的标准，以便在应用最小化方案的应用中更好地选择将裂纹传播描述为基础增量功能的全局最小化器的绝对发展。我们将对二维基准测试问题应用程序，并将结果与欧拉 - 拉格朗日方程的弱形式的解决方案进行比较。我们将观察到，通过在我们的解决方案方法中包括两侧的能量不平等，我们描述了某些基准问题，当损坏开始显现时是一个平衡路径，这与通过简单地求解基本功能的平稳条件获得的损伤时有所不同。
We derive the variational formulation of a gradient damage model by applying the energetic formulation of rate-independent processes and obtain a regularized formulation of fracture. The model exhibits different behavior at traction and compression and has a state-dependent dissipation potential which induces a path-independent work. We will show how such formulation provides the natural framework for setting up a consistent numerical scheme with the underlying variational structure and for the derivation of additional necessary conditions of global optimality in the form of a two-sided energetic inequality. These conditions will form our criteria for making a better choice of the starting guess in the application of the alternating minimization scheme to describe crack propagation as quasistatic evolution of global minimizers of the underlying incremental functional. We will apply the procedure for two- and three-dimensional benchmark problems and we will compare the results with the solution of the weak form of the Euler-Lagrange equations. We will observe that by including the two-sided energetic inequality in our solution method, we describe, for some of the benchmark problems, an equilibrium path when the damage starts to manifest, which is different from the one obtained by solving simply the stationarity conditions of the underlying functional.
