Extension of the scaled boundary finite element method to treat implicitly defined interfaces without enrichment
- Authors: Natarajan, Sundararajan , Dharmadhikari, Prasad , Annabattula, Ratna , Zhang, Junqi , Ooi, Ean , Song, Chongmin
- Date: 2020
- Type: Text , Journal article
- Relation: Computers and Structures Vol. 229, no. (2020), p.
- Full Text: false
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- Description: In this paper, the scaled boundary finite element method (SBFEM) is extended to solve the second order elliptic equation with discontinuous coefficients and to treat weak discontinuities. The salient feature of the proposed technique is that: (a) it requires only the boundary to be discretized and (b) does not require the interface to be discretized. The internal boundaries are represented implicitly by the level set method and the zero level sets are used to identify the different regions. In the regions containing the interface, edges along the boundary are assigned different material properties based on their location with respect to the zero level set. A detailed discussion is provided on the implementation aspects, followed by a few example problems in both two and three dimensions to show the robustness, accuracy and effectiveness of the proposed approach in modelling materials with interfaces. The proposed technique can easily be integrated to any existing finite element code. © 2019 Elsevier Ltd
Adaptive phase-field modeling of brittle fracture using the scaled boundary finite element method
- Authors: Hirshikesh , Pramod, Aladurthi , Annabattula, Ratna , Ooi, Ean Tat , Song, Chongmin , Natarajan, Sundararajan
- Date: 2019
- Type: Text , Journal article
- Relation: Computer Methods in Applied Mechanics and Engineering Vol. 355, no. (2019), p. 284-307
- Full Text: false
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- Description: In this work, we propose an adaptive phase field method (PFM) to simulate quasi-static brittle fracture problems. The phase field equations are solved using the scaled boundary finite element method (SBFEM). The adaptive refinement strategy is based on an error indicator evaluated directly from the solutions of the SBFEM without any need for stress recovery techniques. Quadtree meshes are adapted to perform mesh refinement. The polygons with hanging nodes in the quadtree decomposition are treated as n−sided polygons within the framework of the SBFEM and do not require any special treatment in contrast to the conventional finite element method. Several benchmark problems are used to demonstrate the robustness and the efficacy of the proposed technique. The adaptive refinement strategy reduces the mesh burden when adopting the PFM to model fracture. Numerical results show an improvement in the computational efficiency in terms of the number of elements required in the standard PFM without compromising the accuracy of the solution.