Higher order methods for simulating fracturing with applications in multiphysics problems

We develop higher order fi nite element methods for fracture mechanics. The framework is cast within the contextof conforming fi nite elements [1]. The method [2] exploits the a priori knowledge of the singular behavior of thefi elds to construct an alternate regular solution. Solving for the alternate problem yields optimal rates of conver-gence and high order of accuracy. The salient feature of the method is the lack of additional degrees of freedom incomparison with its standard Galerking fi nite element formulation. Effectively for the same computational cost weobtain a higher order of accuracy. Along with the above we employ interaction integrals for curvilinear fractures aspresented in [3] and generalize their defi nition for the proposed higher order method. Along with the optimality ofthe convergence of the solution we showcase the accuracy and the convergent behavior of the computed stressintensity factors. The method is verifi ed with respect several analytical solutions. The applications of the frame-work are showcased for complex fracturing problems. In particular, simulations of fracture instabilities in thermoelastic materials subjected to large temperature gradients, where oscillatory fracture behavior is expected, will beused to demonstrate the robustness and capabilities of the presented tools. REFERENCES[1] Rangarajan, R., Chiaramonte, M.M., Shen, Y., Hunsweck, M.J., Lew, A.J. Simulating curvilinear crack propagation withuniversal meshes. Int. J. Numer. Meth. Eng., Submitted.[2] Chiaramonte, M.M., Shen, Y., Lew, A.J. Higher order fi nite element methods for fracture mechanics. Preprint, 2013.[3] Chiaramonte, M.M., Shen, Y., Keer, L.M., Lew, A.J. Computing stress intensity factors for curvilinear fractures. Preprint,2013.