标题： 九个弹性脆性断裂的圆：一组用于评估断裂模型的挑战问题 显示英文标题

标题： Nine circles of elastic brittle fracture: A series of challenge problems to assess fracture models

摘要： 自21世纪以来，利用数学和计算领域的现代进展，文献中提出了大量计算模型，旨在描述在机械、热和/或其他类型载荷作用下材料中裂纹形核和传播的过程。 总体而言，每个新提案都侧重于问题的某一方面，而忽略了其他已被广泛接受的方面。 这种方法导致了大量模型，这些模型最多只能在有限条件下描述裂纹，而在一般情况下可能会预测出严重错误甚至非物理的行为。 为了解决这一困境，本文引入了一种审查过程，形式为九个挑战性问题，任何用于描述裂纹形核和传播的计算模型都必须能够令人信服地处理这些问题，才能有可能普遍描述裂纹的形核和传播。 重点是基本的设置，即各向同性弹性脆性材料在准静态机械载荷下的情况。 这些挑战性问题经过精心选择，以确保： $i$) 它们可以使用标准测试设备进行实验； $ii$) 可以用明确的裂纹描述进行无歧义分析；并且，最关键的是， $iii$) 它们整体上涵盖了过去一个世纪积累的关于裂纹形核和传播的已确立的实验知识范围。 为了演示的目的，在介绍之后，每个挑战性问题都用两种裂纹相场模型进行求解。 显示英文摘要

摘要： Since the turn of the millennium, capitalizing on modern advances in mathematics and computation, a slew of computational models have been proposed in the literature with the objective of describing the nucleation and propagation of fracture in materials subjected to mechanical, thermal, and/or other types of loads. By and large, each new proposal focuses on a particular aspect of the problem, while ignoring others that have been well-established. This approach has resulted in a plethora of models that are, at best, descriptors of fracture only under a restricted set of conditions, while they may predict grossly incorrect and even non-physical behaviors in general. In an attempt to address this predicament, this paper introduces a vetting process in the form of nine challenge problems that any computational model of fracture must convincingly handle if it is to potentially describe fracture nucleation and propagation in general. The focus is on the most basic of settings, that of isotropic elastic brittle materials subjected to quasi-static mechanical loads. The challenge problems have been carefully selected so that: $i$) they can be carried out experimentally with standard testing equipment; $ii$) they can be unambiguously analyzed with a sharp description of fracture; and, most critically, $iii$) in aggregate they span the entire range of well settled experimental knowledge on fracture nucleation and propagation that has been amassed for over a century. For demonstration purposes, after their introduction, each challenge problem is solved with two phase-field models of fracture.