A phase-field description of brittle fracture is employed in the reported four-point bending analyses of monolithic and laminated glass plates. Our aims are: (i) to compare different phase-field fracture formulations applied to thin glass plates, (ii) to assess the consequences of the dimensional reduction of the problem and mesh density and refinement, and (iii) to validate for quasi-static loading the time/temperature-dependent material properties we derived recently for two commonly used polymer foils made of Polyvinyl Butyral or Ethylene-Vinyl Acetate. As the nonlinear response prior to fracture, typical of the widely used Bourdin-Francfort-Marigo model, can lead to a significant overestimation of the response of thin plates under bending, the numerical study investigates two additional phase-field fracture models providing the linear elastic phase of the stress-strain diagram. The typical values of the critical fracture energy and tensile strength of glass lead to a phase-field length-scale parameter that is challenging to resolve in the numerical simulations. So, we show how to determine the fracture energy concerning the applied dimensional reduction and the value of the length-scale parameter relative to the thickness of the plate. The comparison shows that the phase-field models provide very good agreement with the measured stresses and resistance of laminated glass, despite the fact that only one/two cracks localised using the quasi-static analysis, whereas multiple cracks evolved during the experiment. It has also been observed that the stiffness and resistance of the partially fractured laminated glass can be well approximated using a 2D plane-stress model with initially predefined cracks, which provides a better estimation than the one-glass-layer limit.}

中文翻译：

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准静态弯曲下单片和夹层玻璃薄板的相场断裂建模

在报道的单片和夹层玻璃板的四点弯曲分析中采用了脆性断裂的相场描述。我们的目标是：(i) 比较应用于薄玻璃板的不同相场断裂公式，(ii) 评估问题的尺寸减少以及网格密度和细化的后果，以及 (iii) 验证准静态加载我们最近为两种常用的由聚乙烯醇缩丁醛或乙烯-醋酸乙烯酯制成的聚合物箔得出的时间/温度相关材料特性。由于断裂前的非线性响应（广泛使用的 Bourdin-Francfort-Marigo 模型的典型特征）可能导致明显高估薄板在弯曲下的响应，数值研究研究了两个额外的相场断裂模型，提供了应力-应变图的线弹性相。玻璃的临界断裂能和拉伸强度的典型值导致相场长度尺度参数在数值模拟中难以解决。因此，我们将展示如何确定与应用的尺寸缩减相关的断裂能量以及相对于板厚度的长度尺度参数值。比较表明，相场模型与夹层玻璃的测量应力和电阻非常吻合，尽管使用准静态分析只有一个/两个裂纹局部化，而在实验过程中产生了多个裂纹。