A length scale insensitive phase field model for brittle fracture of hyperelastic solids

Fracture of hyperelastic materials such as synthetic rubber, hydrogels, textile fabrics is an essential problem in many engineering fields. The computational simulation of such a fracture is complicated, but the use of phase field models (PFMs) is promising. Indeed, in PFMs, sharp cracks are not treated as discontinuities; instead, they are approximated as thin damage bands. Thus, PFMs can seamlessly model complex crack patterns like branching, merging, and fragmentation. However, previous PFMs for hyperelastic materials, which are mostly based on a PFM with a simple quadratic degradation function without any user-defined parameters, provide solutions that are sensitive to a length scale (that controls the width of the damage band). The current practice of considering this length scale as a material parameter suffers from two issues. First, such a calculated length scale might be too big (compared with the problem dimension) to provide meaningful crack patterns. Second, it might be too small, which results in undesirable computationally expensive simulations. This paper presents a length scale insensitive PFM for brittle fracture of hyperelastic materials. This model is an extension of the model of Wu (2017) with a material parameter dependent rational degradation function, which converges to Cohesive Zone Model (CZM) at least for 1D problems (Wu and Nguyen, 2018), and also can deal with crack nucleation and propagation simultaneously. Results of mode-I and mixed-mode fracture problems obtained with the method of finite elements are in good agreement with previous findings and independent of the discretization resolution. Most importantly, they are independent of the incorporated length scale parameter. Moreover, preliminary results show that the proposed model is as efficient as, if not more than the previous models.