A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method. (August 2022)

• Record Type: Journal Article
• Authors: Svolos, Lampros; Mourad, Hashem M.; Manzini, Gianmarco; Garikipati, Krishna
• Is Part Of: Journal of the mechanics and physics of solids. Volume 165(2022)
• Publication Date: 2022-08
• Subjects: Fracture -- Phase-field modeling -- Discontinuous Galerkin method -- Mixed finite element method; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2022.104910
• Languages: English
• ISSNs: 0022-5096

Abstract

Abstract: Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order phase-field fracture models have gained wide adoption given their ability to capture the formation of complex fracture patterns, e.g. via crack merging and branching, and their suitability for implementation within the context of the conventional finite element method. Higher-order phase-field models have also been proposed to increase the regularity of the exact solution and thus increase the spatial convergence rate of its numerical approximation. However, they require special numerical techniques to enforce the necessary continuity of the phase field solution. In this paper, we derive a fourth-order phase-field model of fracture in two independent ways; namely, from Hamilton's principle and from a higher-order micromechanics-based approach. The latter approach is novel, and provides a physical interpretation of the higher-order terms in the model. In addition, we propose a continuous/discontinuous Galerkin (C/DG) method for use in computing the approximate phase-field solution. This method employs Lagrange polynomial shape functions to guarantee C 0 -continuity of the solution at inter-element boundaries, and enforces the required C 1 regularity with the aid of additional variational and interior penalty terms in the weak form. The phase-field equation is coupled with the momentum balance equation to model dynamic fracture problems in hyper-elastic materials. Two benchmark problems are presented to compare the numerical behavior of the C/DG method with mixed finite element methods. Highlights: Modeling dynamic fracture in hyper-elastic materials with the phase-field method. A fourth-order phase-field model is derived from a micromechanics-based approach. A continuous/discontinuous Galerkin method is used for the phase-field equation. Comparison between the C/DG method and mixed finite element methods. Sensitivity analysis with respect to penalty parameters is conducted.