Abstract Peridynamic (PD) models of bodies without pre-cracks, based on a single fracture parameter (associated with the critical fracture energy), produce different strengths when different horizon sizes are used to simulate crack nucleation under quasi-static conditions. To maintain the same strength and fracture energy under different horizon sizes, extra parameters have to be introduced in the failure model. Bilinear and trilinear bond force-strain relationships have been proposed in the literature for crack propagation in quasi-brittle materials. In this paper we study crack nucleation in a plate with a hole under quasi-static loading using bilinear and trilinear PD models. We provide analytical formulas to calibrate the models to measurable material properties. We show convergence for both strength and fracture toughness. The bilinear PD constitutive model works well for both brittle (e.g. ceramics) and quasi-brittle (e.g. concrete) systems, while the trilinear version is more suited for quasi-brittle fracture behavior. We also find that for quasi-brittle fracture, a model that accounts, stochastically, for the presence of small-scale pores/defects performs better than a homogenized model. A wedge-splitting test in concrete and crack nucleation in a quasi-isotropic composite plate with a circular hole are used to demonstrate the model’s performance. In contrast with other models, the current formulation does not depend on the sample geometry.

中文翻译：

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脆性和准脆性材料中的裂纹成核：近场动力学分析

摘要 无预裂纹体的近场动力学 (PD) 模型基于单个断裂参数（与临界断裂能相关），当使用不同的层级尺寸模拟准静态条件下的裂纹成核时，会产生不同的强度。为了在不同的层位尺寸下保持相同的强度和断裂能，必须在失效模型中引入额外的参数。双线性和三线性键力-应变关系已在文献中提出用于准脆性材料中的裂纹扩展。在本文中，我们使用双线性和三线性 PD 模型研究了准静态载荷下带孔板中的裂纹形核。我们提供分析公式来校准模型到可测量的材料属性。我们展示了强度和断裂韧性的收敛性。双线性 PD 本构模型适用于脆性（例如陶瓷）和准脆性（例如混凝土）系统，而三线性版本更适用于准脆性断裂行为。我们还发现，对于准脆性断裂，随机考虑存在小尺度孔隙/缺陷的模型比均质模型表现更好。通过混凝土中的楔形劈裂试验和带圆孔的准各向同性复合板中的裂纹形核来证明该模型的性能。与其他模型相比，当前的公式不依赖于样品几何形状。随机考虑存在小尺度孔隙/缺陷的模型比均质模型表现更好。通过混凝土中的楔形劈裂试验和带圆孔的准各向同性复合板中的裂纹形核来证明该模型的性能。与其他模型相比，当前的公式不依赖于样品几何形状。随机考虑存在小尺度孔隙/缺陷的模型比均质模型表现更好。通过混凝土中的楔形劈裂试验和带圆孔的准各向同性复合板中的裂纹形核来证明该模型的性能。与其他模型相比，当前的公式不依赖于样品几何形状。