Numerical Simulation On Fuse Mechanism And Melting Surface Of Random Fuse Model

The fracture of materials,especially the fracture of non-uniform disordered materials,is of great significance both in theory and in engineering applications.The numerical simulation of the microscopic kinetics of fracture of heterogeneous materials will help to understand the macroscopic and microscopic mechanisms of material fracture.Based on the numerical simulation and analysis of the random fuse model,a series of valuable results have been obtained,which provides a very effective way to explore the fracture mechanism and fracture law of heterogeneous materials.Practice has proved that the random fuse model is a very important and effective theoretical model for numerical simulation of non-uniform material fracture.In this paper,the numerical simulation of the two-dimensional honeycomb structure and the triangular structure of the random fuse model is carried out according to the classical scale theory and the extreme value statistical theory.The main work of the thesis includes two aspects:Firstly,Study on the scale property of the surface roughness and the extreme value of the longitudinal height of the melted surface by the random fuse model of the two-dimensional honeycomb structure.It is found that under different substrate sizes and long-term interaction,the roughness of the fracture surface has obvious scale behavior,which satisfies the scale law proposed by Family-Viseck.The global roughness exponent is?=0.911±0.005,and the local roughness exponent is?=_loc0.808±0.003.The significant difference indicates that the fracture profile has a singular scale.In addition,through the statistical analysis of the extreme values of the longitudinal height of the fracture section,it is found that the relative maximum and minimum height distribution of the fracture surface show a good scale law,and it satisfies the Asym2Sig-type distribution function;Secondly,simulation of the fracture process of random triangular fuse model with incomplete structure?pre-fracture structure?,the variation of survival rate with voltage is an important research content of random fuse model.It is found that the fracture surface can be described by the Duxbury-Leath-Beale?DLB?distribution or the Weibull distribution under different incomplete structures.In the simulation calculation process of this paper,the coefficient matrix is constructed by using the node analysis method,and the cholesky decomposition is performed on the coefficient matrix,and then the Sherman-Morrison-Woodbury algorithm is used to quickly invert the coefficient matrix,which greatly optimizes the calculation process and calculation effectiveness.The work in this paper shows that the random fuse model is not only suitable for the simulation of the fracture dynamics process of heterogeneous materials,but also for the analysis of the dynamic properties of fracture surfaces.The work of this paper is a useful attempt.In theory,this will expand the application of random fuse models.