Weak-form Quadrature Element Modelling For Crack Propagation With Minimal Remeshing

There exist cracks caused by various reasons in components of engineering structure,and crack propagation causes the components out of work due to fracture,eventually leading to the failure of the entire structure.How to predict the crack propagation accurately,so as to take appropriate activities to avoid fracture of the components,has been a hot issue of research in the field of engineering.Therefore,it is of great engineering significance and application prospect to carry out the simulation to the whole process of crack propagation by means of numerical methods.According to the theory of fracture mechanics,the stress field near a crack tip determines the crack propagation condition and the crack propagation direction,so the premise of accurate simulation to crack propagation is accurate calculation of the stress field near the crack tip.More recently,a novel weak-form quadrature element method in combi-nation with the subregion generalized variational principle is proposed to obtain the coefficients of the stress field near the crack tip with considerable accuracy,which makes it possible to simulate the crack propagation.Through dividing the circular or rectangular complementary energy region with stresses as the field variable near the crack tip,the total energy consists of the potential energy,the complementary energy and the mixed work on the interface.Using the weakform quadrature element method to deal with the differentiation and integration of the energy based on the same set of discrete nodes,the algebraic equations can be established to solve the coefficients of the stress field near the crack tip by the variational stationary condition,and then the stress field near the crack tip can be obtained.Once the stress field near the crack tip is known,the crack propagation condition and direction are determined using certain cracking criterion.Due to the global coarse mesh feature of the developed method,an automatic distance search algorithm is implemented in the present study,and only minimal global remeshing,instead of local fine remeshing,is needed to follow the crack propagation.Through superimposing the displacement of the potential energy region in each crack propagation step,the deformation of the model in the whole process of crack propagation can be represented accurately,thus the purpose of simulating crack propagation can be achieved at last.In order to use the weak-form quadrature element method to deal with the cracking model with complicated boundary conditions and to broaden the applicability of the proposed method,this thesis introduces two kinds of methods for constructing element mapping functions,which can accurately map the curved boundary.To show the characteristics of the proposed method,several benchmark problems are investigated using the proposed method.As can be seen from the results,the proposed method not only can simulate the crack propagation with minimal remeshing,but also has better computational efficiency and accuracy in comparison with other existing methods.