The elongation-criterion for fracture toughness of hydrogels based on percolation model

The fracture behavior of hydrogels is a difficult problem. Almost all theories widely used at present are based on comparisons between the energy release rate and the intrinsic fracture energy plus the extra dissipative energy. However, this methodology based on the concept of fracture energy also has its drawbacks, such as inconvenience in measurements, disregarding the complex network configurations, as well as other uncertainties in engineering. In this paper, a framework based on another perspective is proposed to reconsider the fracture behavior of hydrogels. A carefully designed network generating algorithm is used to simulate the growth process of a hydrogel network. Then, the simulated hydrogel network is transformed into a corresponding logical network to express the interaction between chains. In our theory, the elongation ratio of a hydrogel is used to build a new fracture criterion. The percolation theory is then introduced to find out the critical fracture elongation ratio. Finally, considering the uncertainties in hydrogel samples, the probability distribution of the experimental results and the theoretical predictions are compared to validate our theoretical framework.