Strain-hardening cementitious composites (SHCC), composed of short fibres embedded within brittle matrix, exhibit distinctive pre-peak strain-hardening characteristics and remarkable tensile ductility. The fracture and failure process of SHCC, involving both hardening and softening stages as a result of matrix multiple micro-cracking and strain localization, is highly complex and poses a significant challenge for numerical modelling. In the present paper, a novel numerical framework, characterized by the bi-layer superposed cohesive zone strategy, is developed for the numerical modelling of fracture and multiple cracking of SHCC, at both the material scale and structural scale. The developed model is based on diffused cohesive interface model, but with adaptions to consider fibre bridging mechanism. The crack interface is simulated by two cohesive elements sharing the same nodes: one for the matrix-cohesion effect and the other for the fibre-bridging effect. Cohesive constitutive relations of matrix cohesion and fibre bridging are carefully assigned. The proposed model is first validated on the material scale through a uniaxial tension test. With the aid of a random material field, multiple-cracking phenomenon and stress fluctuation are successfully predicted by the model. The model is then applied to the structural fracture modelling, where four case studies, including both pure mode I and mixed mode fracture, are performed. The size effect and boundary effect on the fracture behaviour are well captured by the numerical modelling. The model proposed in the current work has the potential to be extended to the multiple cracking modelling of other materials.

中文翻译：

---

应变硬化水泥基复合材料的断裂和多重裂纹建模


应变硬化水泥基复合材料（SHCC）由嵌入脆性基体中的短纤维组成，具有独特的峰前应变硬化特性和显着的拉伸延展性。 SHCC 的断裂和失效过程涉及基体多重微裂纹和应变局部化导致的硬化和软化阶段，非常复杂，对数值模拟提出了重大挑战。本文开发了一种以双层叠加内聚区策略为特征的新型数值框架，用于在材料尺度和结构尺度上对 SHCC 的断裂和多重裂纹进行数值模拟。开发的模型基于扩散内聚界面模型，但进行了调整以考虑纤维桥接机制。裂纹界面由共享相同节点的两个内聚单元来模拟：一个用于基体内聚效应，另一个用于纤维桥接效应。仔细分配了基质内聚力和纤维桥连的内聚本构关系。所提出的模型首先通过单轴拉伸测试在材料尺度上进行验证。借助随机材料场，该模型成功预测了多重裂纹现象和应力波动。然后将该模型应用于结构断裂建模，其中进行了四个案例研究，包括纯模式 I 和混合模式断裂。数值模拟很好地捕捉了断裂行为的尺寸效应和边界效应。当前工作中提出的模型有可能扩展到其他材料的多重裂纹建模。