Regenerative Surface Effect Of Bond-based Peridynamics And Its Influence On The Failure Behavior Of Brittle Materials

The failure process of brittle materials is a typical discontinuous medium problem.Traditional continuum mechanics theory based on displacement differential equations often has difficulties such as singularity when solving these discontinuous problems.The emerging Peridynamics(PD)method uses the displacement space integral equation to describe the mechanical behavior of brittle materials,avoids solving the derivation of displacement and results are without singularity.The governing equation of PD method is derived by assuming that the horizon of the material point is complete.When the horizon of the material point is not complete,the nature of the material point inside the object and the nature of the material point on the boundary of the object are different,this is so-called surface effect.Many scholars have studied the surface effect in PD method,but when the damage occurs,the surface effect caused by the newly generated boundary of the object has not been paid enough attention.This paper firstly describes the error caused by the PD method without considering the surface effect,and then introduces the commonly used PD surface effect processing method.On this basis,the surface effect processing method of the newly generated boundary is studied,and finally the two-dimensional non-fracture and fracture examples are simulated by these methods.Comparing these simulation results,a method suitable for dealing with the surface effect of newly generated boundaries is proposed.The main research work and results of the thesis are as follows:1.The PD method is used to simulate the mechanical behavior of one-dimensional rod,two-dimensional plane plate and three-dimensional rectangular block under tension.The results show that the simulation results based on PD method are quite different from the analytical solution when the surface effect is not considered.It shows that in the PD method,as long as it is a boundary,a more serious surface effect will occur.2.The commonly used surface effect processing methods are introduced:direction correction method and micro-modulus numerical value correction method.On this basis,a surface effect processing method that simultaneously corrects the direction and the micro-modulus numerical value is proposed.The effectiveness of the three methods in dealing with surface effect is verified by plane plate example.3.Defining the boundary where the object already exists is the original boundary,and the newly generated boundary in the destruction process of object is the regenerative boundary.On this basis,it is clear that there is regenerative surface effect in PD method.4.Using the direction correction method,the micro-modulus numerical value correction method,the direction and the micro-modulus numerical value simultaneous correction method to respectively simulate the two-dimensional non-fracture examples,and the simulation results are respectively compared with the analytical solution and the finite element solution.The results show that it is completely feasible to only consider the direction correction when dealing with the original surface effect.The following five methods are used to simulate the two-dimensional fracture example:the direction correction method in which the micro-modulus is constant and the regenerative surface effect is not considered,the direction correction method in which the micro-modulus is constant and the regenerative surface effect is considered,the direction correction method in which the micro-modulus is discrete form and the regenerative surface effect is considered,the micro-modulus numerical value correction method in which the micro-modulus is discrete form and the regenerative surface effect is considered,the direction and micro-modulus numerical value simultaneous correction method in which the micro-modulus is discrete form and the regenerative surface effect is considered.The simulation results are compared with the experimental results.The results show that when dealing with the regenerative surface effect,it is necessary to consider both direction correction and micro-modulus numerical value correction.5.The examples of two parallel isometric crack propagation and three parallel isometric crack propagation and four parallel isometric crack propagation and random distribution pre-crack propagation are simulated by the direction and the micro-modulus numerical value simultaneous correction method in which the regenerative surface effect is considered,and the simulation results are compared with the simulation results of the prototype microelastic brittleness model without considering the regenerative surface effect.The results show that the regenerative surface effect affects the failure path of brittle materials and the appearance of zigzag cracks.