Smooth multi-patch scaled boundary isogeometric analysis for Kirchhoff-Love shells

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   Résumé scientifique

   In this paper we propose a solution strategy for the Cahn-Larch\'e equations, which is a model for linearized elasticity in a medium with two elastic phases that evolve subject to a Ginzburg-Landau type energy functional. The system can be seen as a combination of the Cahn-Hilliard regularized interface equation and linearized elasticity, and is non-linearly coupled, has a fourth order term that comes from the Cahn-Hilliard subsystem, and is non-convex and nonlinear in both the phase-field and displacement variables. We propose a novel semi-implicit discretization in time that uses a standard convex-concave splitting method of the nonlinear double-well potential, as well as special treatment…

2. Apparenté Pas pertinent

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   Résumé scientifique

   We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed method. The two-dimensional and three-dimensional numerical examples are presented to confirm the accuracy and efficiency of the method with several boundary conditions and several types of polygon meshes and polyhedral meshes.

3. Apparenté Pas pertinent

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   Résumé scientifique

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4. Apparenté Pas pertinent

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   Résumé scientifique

   The phase-field fracture free-energy functional is non-convex with respect to the displacement and the phase field. This results in a poor performance of the conventional monolithic solvers like the Newton-Raphson method. In order to circumvent this issue, researchers opt for the alternate minimization (staggered) solvers. Staggered solvers are robust for the phase-field based fracture simulations as the displacement and the phase-field sub-problems are convex in nature. Nevertheless, the staggered solver requires very large number of iterations (of the order of thousands) to converge. In this work, a robust monolithic solver is presented for the phase-field fracture problem. The solver adop…

5. Apparenté Pas pertinent

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   Résumé scientifique

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6. Apparenté Pas pertinent

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   Résumé scientifique

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7. Apparenté Pas pertinent

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   Résumé scientifique

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8. Apparenté Pas pertinent

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   Résumé scientifique

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