论文标题
折断的变异相视野方法的DG/CR离散化
A DG/CR discretization for the variational phase-field approach to fracture
论文作者
论文摘要
裂缝的变分相模型被广泛用于模拟脆性材料中裂纹的成核和传播。它们基于通过两个平滑功能的自由透视裂缝能量的溶液近似：位移和损伤场。它们的数值实现通常基于Nodal $ \ Mathbb {p}^1 $ lagrange有限元元素对两个字段的离散化。在本文中，我们提出了不连续的元素的不合格近似，以造成损坏的位移和不合格元素，其梯度更为各向同性。不合格的处理源于异质扩散问题的处理。我们通过一系列示例说明了提出方法的鲁棒性和多功能性。
Variational phase-field models of fracture are widely used to simulate nucleation and propagation of cracks in brittle materials. They are based on the approximation of the solutions of free-discontinuity fracture energy by two smooth function: a displacement and a damage field. Their numerical implementation is typically based on the discretization of both fields by nodal $\mathbb{P}^1$ Lagrange finite elements. In this article, we propose a nonconforming approximation by discontinuous elements for the displacement and nonconforming elements, whose gradient is more isotropic, for the damage. The handling of the nonconformity is derived from that of heterogeneous diffusion problems. We illustrate the robustness and versatility of the proposed method through series of examples.
