The phase field model (PFM) has emerged as a popular computational framework for analyzing and simulating complex fracture problems. Despite PFM's inherent capacity to model relatively complex fracture phenomena such as nucleation, branching, deflection, etc., the computational costs involved in the analysis are quite high. Hence, a multi-level adaptive mesh refinement framework is proposed for a unified phase field model (PFCZM) to improve the computational efficiency. The proposed adaptive framework can be implemented for structured as well as unstructured meshes, making it suitable for analyzing complex fracture problems. This framework adaptively generates local mesh refinement at the discrete crack tip, based on an active element error indicator, until the damage is initiated, hence completely avoiding the pre-requisite of local mesh refinement. Further, the gradient of energy degradation and the gradient of dissipated fracture energy based error indicators are proposed to capture the fracture domain and regions ahead of the crack tip, respectively. The Newest vertex and Maubach's refinement routines are implemented as the element level-based hierarchical refinement strategies. Unlike recently proposed adaptive strategies for PFCZM involving elements with hanging nodes, the proposed adaptive framework inherently addresses the conformity and reflectivity of the discretized domain efficiently. The robustness and accuracy of the framework is checked against four benchmark fracture problems, demonstrating a significant reduction in computational costs with sufficient accuracy.

中文翻译：

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一种使用非结构化共形简化进行统一相场断裂建模的多级自适应网格细化策略


相场模型 （PFM） 已成为分析和模拟复杂断裂问题的常用计算框架。尽管 PFM 具有模拟相对复杂的断裂现象（如成核、分支、挠度等）的固有能力，但分析所涉及的计算成本相当高。因此，为统一相场模型 （PFCZM） 提出了一种多级自适应网格细化框架，以提高计算效率。所提出的自适应框架可以实现结构化和非结构化网格，使其适用于分析复杂的断裂问题。该框架根据激活的单元误差指示器，在离散裂纹尖端自适应地生成局部网格细化，直到损伤开始，从而完全避免了局部网格细化的先决条件。此外，提出了能量退化梯度和基于耗散裂隙能量的误差指标梯度，以分别捕获裂缝域和裂缝尖端之前的区域。Newest vertex 和 Maubach 的细化例程被实现为基于元素级别的分层细化策略。与最近提出的涉及具有悬挂节点的元件的 PFCZM 自适应策略不同，所提出的自适应框架从本质上有效地解决了离散化域的一致性和反射率。根据四个基准断裂问题检查了框架的稳健性和准确性，表明在足够准确的情况下，计算成本显著降低。