Research On Crack Propagation With Minimal Remeshing Based On The Subregion Generalized Variational Principle And Finite Element Method

Finite element method(FEM)has become the most widely used numerical method because of its advantages in standardization and commercialization.However,the traditional finite element method has difficulties on studying the crack problem of linear elastic materials.A very fine mesh at the crack tip is necessary to describe the singular stress field near the crack tip.Moreover,it is necessary to set the crack surface as the edge of the element and the crack tip as the node of the element.For these reasons,remeshing in global computation domain is required at each crack propagation step,which greatly increases the time-costing.In order to overcome these shortcomings,many special crack-tip elements,such as crack-tip singular element and mixed crack element,have been proposed.However,these singular elements will complicate the construction of governing equations,and at the same time,they bring difficulties on remeshing.In this paper,by combining the subregion generalized variational principle and the finite element method,crack propagation problems are studied.The main contents and conclusions are as follows:(1)Rectangular complementary energy region,a substitute for commonly used circular complementary energy region,will be used,and the governing equation for calculating stress intensity factor will be deduced.Although rectangular complementary energy region slightly increases the difficulty on integrating of complementary energy and boundary mixed work,it reduces the difficulty on dealing with curved boundary of potential energy element and allows regular mesh in computation domain.Because the integrand function of complementary energy and boundary mixed work is complex,Romberg's integration method,which has better stability,is chosen in this paper.(2)Fortran is used to automatically divide computation domain into many meshes in numerical examples,and the stress intensity factors of four typical examples are calculated.The results are compared with those by other literatures.The influence of corresponding parameters on the accuracy of stress intensity factor calculation is analyzed in detail,and the suggestion values of parameters are given.The suggestion values of these parameters are instructive to the initial meshing of crack propagation simulation.(3)Based on the stress intensity factor(SIF)with high precision,the mixed mode crack propagation criterion is used to study the crack growth problem.In this paper,a new remeshing technique is proposed.Its characteristics are that only one mesh is remeshed in each propagation step,which improves the efficiency of crack propagation simulation.The crack propagation paths under different mesh sizes are compared,and it is found that the crack propagation paths converge fast with the mesh densification.By comparing with the paths in the references,the results show that the method presented in this paper is effective in the simulation of crack growth.(4)For the complex multi-crack problem,this paper validates the present method in handling crack intersection.By proposing the remeshing treatment in the process of crack intersection,two numerical examples involving multi-cracks are performed,which validates the effectiveness of the proposed method in handling the complex multi-crack problems.