Numerical Simulation Of Propagation Of Cracks With Extended Finite Element Method In Concrete

In the actual engineering structure,the structure due to the strength of more than their own tensile strength will produce cracks,and the material itself often has a variety of defects such as cracks,inclusions,holes,etc.,which will affect the structural performance of the force.It is necessary to analyze the structure with the existence of cracks to ensure the normal use of the structure of the project.The traditional finite element method is a typical and often used numerical simulation method,but there are bottlenecks in the simulation of the structure with cracks.This is mainly because the traditional extended finite element method requires that the grid be overlapped with the crack edge and the crack propagation is uncertain.It greatly increases the difficulty and time of the calculation.The extended finite element method is developed on the basis of the traditional finite element method.It can be independent of meshing when dealing with crack,and it shows great superiority in dealing with crack model and is considered to be the most effective when dealing with crack in the numerical methods.In this paper,the extended finite element method is used to simulate the crack propagation and crossover,and the numerical simulation of the dynamic expansion of the cohesive crack is carried out.The main contents and conclusions are as follows:(1)On the basis of the unit decomposition method,the basic principle of the extended finite element method is described in detail,and how to use the le vel set method to characterize the geometric information of the crack.In the extended finite element method,the integral weak form and the discrete equation are obtained when there is no interaction force and cohesion in the crack interface,and the stif fness matrix expression in the two cases is obtained.(2)In the static crack study(ie,the linear elastic fracture model),the unit,the node coding form and the improved unit subdomain division scheme are proposed.The calculation process of the static crack model is combed,and the static single crack,the relationship between the vertical displacement of the top node and the node is obtained by numerical simulation of the cross crack model.(3)In the dynamic crack propagation model,an interface cohes ive constitutive model is proposed,which can consider the influence of the normal and tangential stresses of the crack interface,and an improved numerical integration scheme is proposed to integrate The division of the points is greatly simplified.On th is basis,the calculation process of crack dynamic expansion is proposed.The numerical simulation of the three-point support beam is carried out.The crack propagation path,the load-CMOD relationship curve,the vertical displacement curve of the load-load point and so on are analyzed.The results show that the numerical analysis and the experimental result are fitting well.The influence of several parameters such as extended step size setting and crack tip radius is analyzed,and the appropriate va lue is put forward.