This paper explores the computational modeling of nonlocal strain, damage, and fracture in concrete, considering the isolated contribution of two random, spatially variable properties related to the fracture process: Young’s modulus (E) and tensile strength (f_t). Applying a continuum damage model, heterogeneous specimens of concrete with random and spatially varying E or f_t were found to produce substantial differences when contrasted with traditional homogeneous (non-random) specimens. These differences include variable and uncertain strain and damage, wandering of the failure paths, and differing (sometimes lower) peak forces, i.e. increased probabilities of failure in the heterogeneous specimens. It is found that f_t variability contributes more (from 1.7 to up to 4 times more, depending on the parameter) to the overall performance variability of the concrete than E variability, which has a comparatively lower contribution. Performance is evaluated using (1) force-displacement response, (2) individual, average, and standard deviation maps of non-local strain and damage, (3) fracture paths and strain and damage values along the fractures. The modeling methodology is illustrated for two specimen geometries: a square plate with a circular hole, and an L-shaped plate. The computational results correlate well with reported experimental data of fracture in concrete specimens.

本文探讨了混凝土非局部应变，损伤和断裂的计算模型，考虑了与断裂过程有关的两个随机的，空间可变的特性的独立贡献：杨氏模量（E）和抗张强度（f _t）。应用连续损伤模型，随机或空间变化E或f _t的混凝土异质标本与传统的均质（非随机）标本相比，它们被发现会产生实质性差异。这些差异包括可变的和不确定的应变和损坏，失效路径的漂移以及峰值力的不同（有时更低），即异质样本中失效的可能性增加。发现f _t的变化对混凝土整体性能变化的影响比E更大（从1.7到最大4倍，具体取决于参数）。可变性，其贡献相对较低。使用（1）力-位移响应，（2）非局部应变和损伤的个体，平均和标准偏差图，（3）断裂路径以及沿断裂的应变和损伤值对性能进行评估。说明了两种样品几何形状的建模方法：带圆孔的正方形板和L形板。计算结果与报告的混凝土试样断裂实验数据很好地相关。