Fracture is a highly nonlinear problem, especially under a large deformation in cross-linked elastomers. Existing constitutive theories and fracture models fail to predict the fracture behavior of cross-linked elastomers because of the absence of the random polymer network structure. Meanwhile, few numerical methods can present the realistic fracture process of a polymer network. In this study, we propose a mesoscopic network mechanics method to present the entire large deformation and fracture process of the polymer network in cross-linked elastomers. The microstructure of a cross-linked elastomer is abstracted as a polymer network model where nodes are referred to as crosslinkers and connections between nodes are referred to as polymer chains. A hybrid total energy form of the network model is proposed including the free energy of polymer chains and volumetric deformation energy. In addition, using a proposed stretch criterion of polymer chains to realize chain scission, this mesoscopic network mechanics method is numerically implemented by coding. Two-dimensional network models with uniform and randomly distributed chain lengths, as well as models with different types of pre-cracks, are constructed and simulated under uniaxial tension tests using our method. Our method reproduces the entire hyper-elastic large deformation and fracture process of polymer network models. The random network models show a lower Young's modulus and a less significant strain-hardening stage, indicating that the structural randomness is the primary cause of accuracy degradation for existing hyperelastic constitutive models under large deformations. The results also reveal that the structural randomness of the polymer network is a primary reason for the ductile fracture and the low notch sensitivity of cross-linked elastomers.

断裂是一个高度非线性的问题，特别是在交联弹性体的大变形下。由于缺乏无规聚合物网络结构，现有的本构理论和断裂模型无法预测交联弹性体的断裂行为。同时，很少有数值方法可以呈现聚合物网络的真实断裂过程。在这项研究中，我们提出了一种细观网络力学方法来呈现交联弹性体中聚合物网络的整个大变形和断裂过程。交联弹性体的微观结构被抽象为聚合物网络模型，其中节点称为交联剂，节点之间的连接称为聚合物链。提出了网络模型的混合总能量形式，包括聚合物链的自由能和体积变形能。此外，利用提出的聚合物链的拉伸准则来实现断链，这种细观网络力学方法通过编码在数值上实现。使用我们的方法在单轴拉伸试验下构建和模拟具有均匀和随机分布的链长的二维网络模型以及具有不同类型预裂纹的模型。我们的方法再现了聚合物网络模型的整个超弹性大变形和断裂过程。随机网络模型显示较低的杨氏模量和不太显着的应变硬化阶段，表明结构随机性是现有超弹性本构模型在大变形下精度下降的主要原因。结果还表明，聚合物网络的结构随机性是导致交联弹性体韧性断裂和缺口敏感性低的主要原因。