Numerical Simulations Research On The Damage And Fracture Behaviors Of Concrete Based On Peridynamic Theory

With the development of society,the requirements for the design level of concrete structure become higher and higher.It is necessary to predict the performance of structures during earthquakes accurately,and which relies on numerical analysis.In addition,the structural optimization design,reinforcement,reliability analysis or safety evaluation also depend on the selection of concrete constitutive model and numerical analysis method.In order to ensure the safety,economy and applicability of concrete structures,it is very important to analyze the damage and failure mechanism of concrete and its behaviour under complex loading conditions.The existing numerical methods and theoretical models are still difficult to predict the response of concrete structures accurately.As a new non-local meshfree theory,Peridynamics has circumvented the solution of spatial differential equation based on continuity assumption in traditional method,and absorbed the advantages of molecular dynamics,so it has unique advantages in analyzing discontinual problem.This paper is mainly based on the bond-based peridynamics and the nonordinary state-based peridynamics,the corresponding numerical analysis program is developed to study and solve the numerical simulation problem in the damage and fracture behavior of concrete.The main research contents and results of this paper are as follows:(1)Basic parameters of Peridynamics are derived by equal the elastic potential energy density in peridynamics and the strain energy density from traditional continuum mechanics theory,and the dispersion equation is derived through discretization and euler transformation.By changing the peridynamics parameters in the dispersion equation,the influence of the parameters,such as the particle spacing,the size of the horizon,the number of nodes in horizon,and the time step,on the calculation accuracy of the algorithm are evaluated.(2)The corresponding numerical analysis program,using the bond-based peridynamics model,is made for simulating the concrete cantilever beam under lateral loading.By comparing the results with the analytical solution and finite element results,the calculation accuracy of the improved bond-based peridynamics concrete model is verified.The effects of different horizon size on the displacement field and the lateral deformation of cantilever beam are also analyzed.An extended bond-based peridynamic approach with the bond force softening is proposed and used to study the problem of anchor bolt pull out in concrete.The reliability and applicability of the proposed method are verified by comparison with experimental results,and the results obtained by traditional finite element method and meshless galerkin method.(3)Based on the nonordinary state-based peridynamics theory and the concrete Druker-Prager elastoplastic constitutive model,the algorithm process suitable for the analysis of the concrete structure is proposed,and the corresponding program used for analyzing three-dimensional quasi-static problem is made,the convergence studies are carried out by varying the particle spacing through the analysis of three dimensional cantilever beam example,the results show that the calculation accuracy can be improved by reducing the particle spacing,while if the particle spacing is less than a certain value(0.02 mm in this paper),the analysis time will be increased,and the calculation efficiency may be reduced.(4)The whole progressive failure process of the 3D anchor system are investigated with the approach proposed in this paper.Numerical analysis results indicate that the obtained peak pullout load shows good agreement with the current design formula,and the crack branching of anchoring system also agreed well with the experimental investigations.Including the failure process and the final failure mode.It can be concluded that the proposed method can distinguish the cone-shaped failure mode and the cone-split mixed failure mode more effectively compared to the traditional finite element method,and it has good applicability in analyzing the failure mechanism of anchor bolt pull out in concrete.(5)The random aggregate model of mesoscopic concrete is developed based on matlab,and the proposed nonordinary state-based peridynamics concrete model is applied to simulate the tensile failure process of two-dimensional concrete specimens.It is found that the particle spacing has a certain impact on the stress displacement curve and crack pattern.The results show that the crack path can be predicted more accurately when the particle spacing is greater than or equal to 0.5mm,and the crack pattern is fine enough when the particle spacing is less than or equal to 0.33 mm under the tensile loading conditions considered in this paper.In addition,the method proposed in this paper can effectively reflect the influence of aggregate volume fraction and porosity on the tensile strength of concrete specimens,and the phenomenon of multiple crack initiation,propagation,connection and bifurcation in the crack pattern obtained is also consistent with the observed test phenomenon.