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

Modeling crack initiation and propagation in brittle materials is of great importance to be able predict sudden loss load-carrying capacity prevent catastrophic failure under severe dynamic loading conditions. Second-order phase-field fracture models have gained wide adoption given their ability capture the formation complex patterns, e.g. via merging branching, suitability for implementation within context conventional finite element method. Higher-order also been proposed increase regularity exact solution thus spatial convergence rate its numerical approximation. However, they require special techniques enforce necessary continuity phase field solution. In this paper, we derive a fourth-order model two independent ways; namely, from Hamilton’s principle higher-order micromechanics-based approach. The latter approach novel, provides physical interpretation terms model. addition, propose continuous/discontinuous Galerkin (C/DG) method use computing approximate This employs Lagrange polynomial shape functions guarantee C0-continuity at inter-element boundaries, enforces required C1 with aid additional variational interior penalty weak form. equation coupled momentum balance problems hyper-elastic materials. Two benchmark are presented compare behavior C/DG mixed methods.