Study On The Theory And Application Of Extended Voronoi Cell Finite Element Method

Fracture of materials is a common phenomenon in many important industries,such as aerospace,automobile,military production,nuclear energy,electronic industry and so on.Studying the propagation law of cracks in structures under external loads is critical to the safety assessment of materials and the design of new materials.Numerical simulation in the research of crack propagation problem has always been a research hotspot in the field of mechanics and material science.How to correctly analyze and simulate the multi-crack propagation of real materials has also been one of the significant topics in this field,and it is of great significance to the development of modern industry.With the development of computer technology,various computational mechanics methods have emerged,especially the Voronoi cell finite element method(VCFEM),which has become one of the most effective methods to study the mechanical properties of materials containing heterogeneity such as particles and holes.However,the traditional VCFEM is difficult to solve the simulation for the whole process of large-scale crack propagation through materials.To effectively model the whole process of crack propagation,an extended Voronoi cell finite element method(X-VCFEM)for large-scale crack propagation problem is proposed in this study and a corresponding computational program is developed.The whole process of large-scale crack propagation,intersection and penetration in homogeneous and particle reinforced composites is simulated by the proposed method.It provides a new method to study the crack evolution process of materials.The main contributions can be listed as follows:(1)An extended Voronoi cell finite element method(X-VCFEM)for modelling the propagation of multiple cracks in homogeneous materials containing cracks is proposed,in which a new X-VC element to describe the central crack and the side crack of homogeneous materials is proposed by establishing a functional,which is suitable to formulate the traction free conditions along the crack surfaces.In order to accurately capture crack-tip stress concentrations,the analytic functions of singular stress field in the vicinity of crack tips are introduced in the stress functions in X-VCFEM.The element stress field function consists of two parts: polynomial stress function and singular stress field function.The former is used to characterize far-field stresses,while the latter is used to capture the singularity of the crack tip.A corresponding fortran program is developed to solve the new element,and the stress field of homogeneous material containing cracks is obtained.Based on the stress field,the crack tip stress intensity factor is solved by the least square method.The stress distribution and crack tip stress intensity factors are compared with the results calculated by commercial finite element software ABAQUS model with fine mesh.The results are consistent and the accuracy of the proposed new element considering cracks are verified.At the same accuracy,the present method have the advantage of mechanics computation of crack materials that element meshing is simpler and computation is faster for real materials,in which multiple cracks are randomly distributed.(2)A remeshing strategy that a node at a last incremental crack tip in the crack advance process is replaced by a node pairs to realize the gradual crack propagation is proposed.The direction of the crack propagation is adaptively determined in terms of the maximum energy release rate near the crack tip.In the process of crack propagation,the division of element integral regions after remeshing is improved.A Fortran program for remeshing is realized to simulate the crack propagation,coalescence and penetration in homogeneous materials containing a large number of randomly distributed cracks with arbitrary length and direction.(3)An extended Voronoi cell finite element method(X-VCFEM)for dealing with the interfacial and matrix damage of composite materials containing a large number of inclusions and cracks is proposed,in which a new X-VC element to describe the interfacial cracking and matrix cracking of particle reinforced composites is proposed by establishing a functional,which is suitable to formulate both the traction reciprocity conditions on the bonded inclusion-matrix interfaces and the traction free conditions along the crack surfaces.In order to accurately capture crack-tip stress concentrations,the analytic functions of singular stress field in the vicinity of crack tips are introduced in the assumed stress hybrid formulation which also includes the polynomial functions and the reciprocal functions.The polynomial stress functions are used to describe the far field stresses,the reciprocal stress functions are used to reflect the influence of the interface shape corresponding to the stress field,and the singular stress field analytic functions are used to capture the singularity of the crack tip.A Fortran program is developed to solve the new element,and the stress field of particle reinforced composites containing cracks is obtained.Based on the stress field,the matrix crack tip stress intensity factor is solved by the least square method.The stress distribution and crack tip stress intensity factors are compared with the results calculated by commercial finite element software ABAQUS model with fine mesh.The results are consistent and the accuracy of the proposed new element considering inclusions,matrixinclusion interfacial cracks and matrix cracks are verified.(4)A remeshing algorithm is proposed for the simulation of the whole process of crack propagation: interfacial cracks initiation and propagation,interfacial cracks transformation into matrix,further propagation and penetration of matrix cracks in particulate reinforced composites.In the process of crack propagation,the division of element integral regions after remeshing is improved.The direction of the crack propagation in matrix is determined by the maximum energy release rate and the interface crack propagation along the interface or into the matrix is assessed on the base of a series of criteria relating to the critical normal stress and the critical hoop stress.A complete finite element program is developed to simulate the whole process of crack damage evolution of particle reinforced composites with a large number of randomly distributed inclusions.The interaction between interface cracks and matrix cracks and the failure mechanism of particle reinforced composites have been analyzed.In present dissertation,an extended Voronoi cell finite element method has been proposed to study the mechanical properties and crack evolution process of homogeneous materials and particle reinforced composites under mechanical loadings.The corresponding calculation techniques have been put forward,and the mechanism of material crack evolution has been analyzed and discussed.