2019/04/28 by Juan Michael Sargado, Sargado, Juan Michael, Eirik Keilegavlen +5 · 1 citation
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1904.12395
openalex publication_date 2019/04/28 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
Numerical simulations of brittle fracture using phase-field approaches often\nemploy a discrete approximation framework that applies the same order of\ninterpolation for the displacement and phase-field variables. Most common is to\nuse linear finite elements to discretize the linear momentum and phase-field\nequations. However the use of P1 Lagrange shape functions to model the\nphase-field is not optimal, since the latter develops cusps for fully developed\ncracks that in turn occur at locations correspoding to Gauss points of the\nassociated FE model for the mechanics. Such feature is challenging to reproduce\naccurately with low order elements, and consequently element sizes must be made\nvery small relative to the phase-field regularization parameter in order to\nachieve convergence of results with respect to the mesh. In this paper, we\ncombine the standard P1 FE discretization of stress equilibrium with a\ncell-centered finite volume approximation of the phase-field evolution equation\nbased on the two-point flux approximation that is constructed on the same\nsimplex mesh. Compared to a pure FE formulation utilizing linear elements, the\nproposed framework results in looser restrictions on mesh refinement with\nrespect to the phase-field length scale. Furthermore, initialization of the\nhistory field is straightforward and accomplished through a local procedure.\nThe ability to employ a coarser mesh relative to the traditional implementation\nis shown for several numerical examples, demonstrating savings in computational\ncost on the order of 50 to 80 percent for the studied cases.\n