Mesh refitting approach: a simple method to model mixed-mode crack propagation in nonlinear elastic solids
Y. Sudhakar, Wolfgang A. Wall
2017
Advanced Modeling and Simulation in Engineering Sciences
We devise a finite element methodology to trace quasi-static through-thickness crack paths in nonlinear elastic solids. The main feature of the proposed method is that it can be directly implemented into existing large scale finite element solvers with minimal effort. The mesh topology modifications that are essential in propagating a crack through the finite element mesh are accomplished by utilizing a combination of a mesh refitting procedure and a nodal releasing approach. The mesh refitting
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... procedure consists of two steps: in the first step, the nodes are moved by solving the elastostatic equations without touching the connectivity between the elements; in the next step, if necessary, quadrilateral elements attached to crack tip nodes are split into triangular elements. This splitting of elements allows the straightforward modification of element connectivity locally, and is a key step to preserve the quality of the mesh throughout the simulation. All the geometry related operations required for crack propagation are addressed in detail with full emphasis on computer implementation. Solving several examples involving single and multiple cracks, and comparing them with experimental or other numerical approaches indicate that the proposed method captures crack paths accurately. Objective and motivation One of the main reasons why devising a computational methodology to deal with fracture mechanics is challenging, is the fact that cracks propagate in arbitrary directions through the material. If the dynamics of the crack were known apriori, one can design an optimal mesh that allows the propagation of a crack through the pre-existing mesh at each instant. Since this is not the usual case, the mesh has to be repeatedly modified to accommodate the advancement of cracks within the finite element (FE) mesh. The objective of this work is to devise a simple procedure to achieve the required mesh modifications, which enables us to model complex crack paths through nonlinear elastic solids. The present work is motivated by our interest in developing computational methodologies for fluidstructure-fracture interaction (FSFI) [1] that model the following phenomenon: when a flexible structure interacts with the fluid flow, the fluid loading induces elastic deformation © The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
doi:10.1186/s40323-017-0088-x
fatcat:7isuc7rmdbevbk4vy2upjb2f3y