Numerical Simulation Of Brittlefracture Based On Phase Field Method

Brittle fracture,as the main form of component failure,causes huge economic losses and casualties every year.Therefore,it is necessary to study the mechanism of brittle fracture.With the development of computer technology,the partial differential equations that were previously impossible to solve in mathematical theory can give out the numerical solutions of these equations by computer,which provides the possibility of numerical simulation of cracks.Nowadays,people mainly use the finite element method,the mesh-less method and the extended finite element method(XFEM)to numerically simulate the crack.Recently,a new numerical method for simulating cracks has been developed: the phase field method.The phase field method is mainly applied to the study of brittle and quasi-brittle materials.The main advantages of the phase field method are: 1.It only needs to divide the grid once,and does not need to process the grid during the simulation of the crack;2.The number of grids is not sensitive;3.No special treatment of cracks is required.Therefore,the phase field method will be used to numerically simulate the fracture of brittle materials.In order to verify the applicability of the phase field method in isotropic brittle materials and the accuracy of the newly constructed projection operator in this paper,the main work done in this paper is as follows:The main content of the first part of this paper is: According to the characteristics of the phase field method,the energy method is used to derive the partial differential equations of the damage field and the displacement field from the principle of energy minimum.According to the partial differential equations of the damage field and the displacement field,the partial differential equations of the damage field and the displacement field are used.The finite element method finds the weak forms of the two fields and interpolates them.Then the method of solving the fourth-order tensor projection operator appearing in both fields is discussed.A new algorithm with more concise expressions and no need to discuss the root of the feature root is given.The new algorithm has the advantage of being easier to understand and easier to program.The main content of the second part of this article is: According to the discussion of the first part,in addition to the Matlab program.Firstly,the applicability of the damage field in the case of the existence of the damage field is verified.The accuracy of the crack density function to the crack is calculated,and the influence of the parameter l introduced in the damage field on the crack in the numerical simulation process is discussed.The effect of grid density on the damage field.Next,this paper discusses the numerical simulation of cracks in the case of damage and displacement fields.Firstly,the accuracy of the new algorithm proposed in the first part is verified.Then,the parameters introduced in the phase field method,the mesh density,the initial crack length,the crack initial position and other parameters and conditions are analyzed in the numerical simulation process.Finally,the numerical simulation results of the crack in the phase field method under different models and different loads are given.