COVER BASED REFINEMENT IN THE NUMERICAL MANIFOLD METHOD AND ITS APPLICATION IN CRACK PROPAGATION

The numerical manifold method (NMM) is a cover-based method with two different covers, namely mathematical cover and physical cover. The weight functions are defined on the mathematical covers and the unknown displacement coefficients are defined on the physical covers. A cover based refinement with the NMM to model two-dimensional crack propagation is described. The refined points of this method are pre-determined for a given element. Not all manifold elements are required to be refined, instead, only the frontal elements and relevant elements satisfied some conditions are required. The refinement is not based on the elements but based on the corresponding mathematical covers of those elements. The updated process is different for various boundary conditions of frontal elements and will be discussed. When a mathematical cover is updated, the corresponding physical covers and elements are updated. Furthermore, the loop of the considered domain is required to be updated as well. In order to demonstrate the utility of the proposed technique, three numerical examples are analyzed to validate and explain the present method. The results show that the refined method is more accurate, since the crack can propagate inside an element. Therefore, the refined method is suitable for improving the accuracy of considered problems without significantly increasing the degrees of freedom.