An adaptive phase-field model with variable-node elements for fracture of hyperelastic materials at large deformations

In this work, an adaptive phase-field method is proposed for modeling fracture of hyperelastic materials at large deformations. The adaptive mesh refinement is facilitated by the variable-node elements, which are flexible to act as transition elements in the employed quadtree mesh. To control the adaptive process, we propose a combined phase-field and energetic mesh refinement criterion, where the energetic part exploits the strain energy threshold of the AT1 phase-field model which is used in this work. Both the compressible and incompressible neo-Hookean models are taken into account, and the latter is enforced by the plane stress condition to simplify the implementation. Several representative examples are studied to verify the accuracy and efficiency of the proposed adaptive phase-field method, in comparison to the available numerical and experimental reference data as well as the fixed locally pre-refined mesh. The simulated results show that the energetic part of the mesh refinement criterion can effectively prevent the delayed damage evolution when the phase-field initiates. Finally, the fracture process of a hyperelastic composite with inclusions is simulated to demonstrate the capacity of the proposed method for reproducing complex failure phenomena at large deformations.