Using micro-planes concrete damage model in discrete least squares meshless method for predicting the crack growth

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In the present study, the author’s previously developed micro-planes concrete damage model has been implemented in the Discrete Least Squares Meshless method (DLSM) for assessment of the crack performance in concrete domains. DLSM is a true meshless method needing no partition in the local approximation as well as in the assembling of the local approximations in order to obtain a global solution. Instead it uses a collection of the un-structured nodal points in place of the elements and discretizes the governing differential equations with the discrete least squares approach. This can reduce considerably the pre-processing efforts of the calculations. However, DLSM like other meshless methods loses its efficiency when it is applied for the analysis of the solid domains dealing with the growing cracks. In recent years, some researchers have utilized some techniques to overcome this problem such as visibility, transparency and diffraction for precisely detecting the crack discontinuity in the case of a static non-growing crack, but these methods require some reciprocal corrective operations within each step of the calculation process extending the time of processing. In this study, however, a new, straightforward and general applicable method has been used for accommodating this issue using the advantages of the Moving Least Squares (MLS) shape functions constructed based on the Voronoi tessellation algorithm and micro-planes concrete damage constitutive model. Voronoi based MLS shape functions have been implemented for evaluating the crack effects accurately as a discontinuity during the analysis processing and micro-planes concrete damage approach used for proper detecting the crack growth trajectory. In the proposed method, the domain of interest is divided into the Voronoi cells based on the classical Voronoi tessellation approach, a cell for each node, and then the support domain of each node located inside the domain as well as on or near the crack faces is determined based on a neighboring criterion. During each step of the analysis for all the integration points, damages are computed according to the micro-planes concrete damage model and the crack path for the next step will be defined. After the end of the iterations in each step, both the stiffness tensor and internal load vector are modified based on the final stress fields obtained on and near the crack. The accuracy and efficiency of the proposed method have been investigated by solving some benchmark examples and comparing the obtained results with the analytical or valid finite element analyses’ results.