Extended Finite Element Simulation Of Crack Propagation Under Load

Cracks are common in solid building structures.Cracks occur and extend when structural materials are stressed beyond their strength.In building structural components,the appearance and extension of cracks will affect the mechanical performance of components and even lead to the failure of structural components,Threatening people's lives and property security.Therefore,it is necessary to conduct an in-depth study on the crack propagation path.The research results of crack cracking path under load are great significance to the effective control of crack propagation,the design and reinforcement of structural components,and the improvement of the stress performance and safety coefficient of building structures.Traditional finite element method is a commonly used numerical simulation method,but there are many deficiencies in the simulation of the cracked wall.The reason is that the traditional finite element method requires the crack to be on the grid when dividing the grid and the crack extends uncertainly,which brings greater difficulty and more calculation amount to the simulation.The emergence of extended finite elements provides strong support for solving the above problems.The extended finite element method is considered to be the most effective method to simulate the cracked wall at present.On the MATLAB platform,this paper conducted numerical simulation of the single crack and the cross crack of the homogenized plate in unit on the basis of extended finite element.The main research contents and achievements are as follows:(1)For a single crack,this paper presents sub-domain division scheme of general unit,unit of crack crossing and unit of containing crack tip.Based on these,combined with single crack displacement field expression and stiffness integration scheme,the expansion of single crack in the unit is realized.The crack can not only extend in one direction in the unit,but also extend towards the opposite direction.(2)For the cross-crack,this paper gives the displacement field expression when the crack occurs,the single element sub-domain division scheme and the stiffness matrix integration scheme.On this basis,the crack propagation of a single element with crosscrack under load is realized.(3)Achieving simulation of crack propagation in homogeneous plates under load.Based on single unit,the appropriate constitutive model,the cracking criterion and an accurate numerical integration scheme is adopted to realize the accurate simulation of crack cracking of the homogeneous plate under load.The influence of crack tip range,meshing density and extended step size on crack extending simulation accuracy are also studied.