A dynamic description of material brittle failure using a hybrid phase-field model enhanced by adaptive isogeometric analysis

Abstract

The objective of this work is to study dynamic crack propagation in brittle materials under time-dependent loading conditions by using the recently developed adaptive isogeometric phase-field approach. The current approach owns several ingredients including the advantages of the phase-field method (PFM), which can be used to model complex crack morphologies without any fracture criterion, and the isogeometric analysis, which possesses some excellent features such as exact geometry and high-order continuity. In addition, the model is further enhanced by employing the locally refined non-uniform rational B-spline (LR NURBS) basis, which is utilized for spatial discretization and phase-field discretization, while the generalized-α or HHT-α method is employed for the temporal discretization. For the coupled elasto-phase field system, a staggered approach is adopted to compute the unknown field variables. Moreover, a hybrid formulation of the PFM is employed to recover the linearity of momentum equation. The structured mesh adaptive refinement is conducted based on the prescribed threshold on the phase-field variable, thus it can effectively alleviate the burden of computational overhead, which is the main shortcoming of the PFM. Three problems involving dynamic crack growth is solved to show the robustness and the applicability of the proposed approach. It is shown that the proposed approach can obtain accurate results at a fraction of degrees-of-freedom without compromising accuracy in comparison with uniformly refined mesh.