This paper discusses the finite element modeling of cracking of quasi-brittle materials under cyclic loading. A damage based crack model is proposed, which considers tensile and compressive damage, irreversible strains upon unloading in compression, as well as micro-crack closure-reopening effects with special attention to the sliding of open cracks (MCRS). The model is implemented in conjunction with a mixed strain/displacement finite element formulation which provides enhanced accuracy and guarantees mesh size and bias independent results. Two distinct damage models are developed. The first one is based on the classical fixed orthotropic crack models and the second is an isotropic version. Both of them incorporate the necessary elements to furnish full MCRS capabilities. The model is demonstrated through several examples of application and comparison with experimental evidence, in mode I, mode II and mixed mode monotonic and cyclic loading.

中文翻译：

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具有完全关闭、重新打开和滑动功能的多裂纹模型的架构

本文讨论了循环载荷作用下准脆性材料开裂的有限元建模。提出了一种基于损伤的裂纹模型，该模型考虑了拉伸和压缩损伤、压缩卸载时的不可逆应变，以及微裂纹闭合-重新打开效应，特别关注开裂（MCRS）的滑动。该模型与混合应变/位移有限元公式结合实施，可提供更高的精度并保证网格尺寸和偏置无关的结果。开发了两种不同的损坏模型。第一个基于经典的固定正交各向异性裂纹模型，第二个是各向同性版本。它们都包含必要的元素以提供完整的 MCRS 功能。