Study Of Smoothed Finite Element Method Implementations Of The Phase-field Regularized Cohesive Zone Model

As one of the most commonly used construction materials,concrete is prone to cracks under the action of internal or external effect,which may lead to degeneration of its mechanical properties and thereby affect the integrity,safety and durability of the corresponding structures.It is of great significance to investigate the initiation and evolution of concrete crack,and to quantify its effects on the structure.With the continuous development of computer technology and computational mechanics theory,numerical simulation methods that have the advantages of high repeatability,low cost of manpower and material resources,and ability to eliminate the influence of accidental factors,are becoming an important method to study the entire process of concrete crack generation and evolution.The newly proposed phase-field regularized cohesive zone model(PF-CZM)for conctete is an outstanding numerical method for the simulation of cracking process.In this method a continuous phase-field is introduced to characterize discontinuous cracks.With no need of cumbersome crack tracking strategies,the model is able to accurately simulate complex crack behavior of concrete structures using a few standard material parameters and thus has broad application prospects in the field of damage and failure analysis in concrete structures.Nevertheless,on the finite element method(FEM)implementation of the model,very fine mesh is demanded in order to ensure sufficient analytical accuracy,which greatly decelerates the analysis efficiency.The smooth finite element method(S-FEM)proposed by Liu et al.is expected to alleviate the above issue: it is well documented that for elastic problems,the SFEM can effectively improve the calculation accuracy of the finite element method with the same set of mesh.In this work,the cell-based S-FEM(CS-FEM)for quadrilateral element and the edgebased S-FEM(ES-FEM)for triangular element was selected to solve the PF-CZM,by analyzing of the characteristics of typical type of S-FEMs.The feasibility of the proposed method is further demonstrated by analyzing its construction of shape function and general numerical procedure.Based on the MATLAB platform,CS-FEM and ES-FEM implementation of PF-CZM are programed.Several benchmark tests of damage and failure in concrete were simulated for validation and comparison with the results given by FEM.It is shown that the implementation can correctly solve the PF-CZM and provides higher coarse mesh accuracy in comparision with FEM.Among them,CS-FEM’s accuracy advantage is not obvious due to the its inability to improve the discontinuity of the gradient field between elements as its smooth domains are discretized within elements.And ES-FEM has obvious advantages of coarse mesh accuracy because the smooth domain is constructed across elements.Therefore,this paper recommends ES-FEM implementation of PF-CZM,which can loosen the strict condition on the element size and thus improve the analysis efficiency.