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Virtual Element Method for modeling crack propagation

Virtual Element Method for modeling crack propagation

Led by:  X. Zhuang
Team:  Minh T.V Nguyen
Year:  2016

The virtual element method (VEM) is a very recent numerical technique for solving partial differential equations. It can be seen as a generalization of the Finite Element Method to arbitrary polygons and polyhedra. What makes VEM become special is that the explicit calculation of integral shape functions is not required. It is possible through introduced polynomial functions and defined degrees of freedom. Due to the fact that VEM is able to generate flexible element mesh type even convex elements or concave elements, it allows us to arbitrarily add more nodes to the large stress concentration areas such as crack tips in crack simulation. In this study, we aim to develop an approach utilizing VEM to model crack growth with minimal remeshing or without remeshing. Nevertheless, the final formulation should fulfill the consistency and stability term in our approach to guarantee the accuracy and the convergence.

Figure: Horizontal stress visualization in Timoshenko's beam problem with arbitrary polygonal elements.