Higher order methods for simulating fracturing with applications in multi-physics problems

We develop higher order nite element methods for fracture mechanics. The framework is cast within the context of conforming nite elements [3]. The method [1] exploits the a priori knowledge of the singular behavior of the elds to construct an alternate regular solution. Solving for the alternate problem yields optimal rates of convergence and high order of accuracy. The salient feature of the method is the lack of additional degrees of freedom in comparison with its standard Galerking nite element formulation. E ectively for the same computational cost we obtain a higher order of accuracy.
Along with the above we employ interaction integrals for curvilinear fractures as presented in [2] and generalize their denition for the proposed higher order method. Along with the optimality of the convergence of the solution we showcase the accuracy and the convergent behavior of the computed stress intensity factors. The method is verified with respect several analytical solutions. The application of the framework 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 be used to demonstrate the robustness and capabilities of the presented tools.

References
[1] Chiaramonte M.M., Shen Y., and Lew A.J. Higher order methods for fracture mechanics. preprint, 2014.
[2] Chiaramonte M.M., Shen Y., Keer L.M., and Lew A.J. Computing stress intensity factors for curvilinear fractures. preprint, 2014.
[3] Rangarajan R., Chiaramonte M.M., Shen Y. Hunsweck M.J., and Lew A.J. Simulating curvilinear crack propagation with universal meshes. Int Journal For Numerical Methods in Engineering, Submitted.


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