A mesoscopic network mechanics method to reproduce the large deformation and fracture process of cross-linked elastomers

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.