The Elastic-plastic Theory Based On Peridynamics

Peridynamics is a new non-local theory that has emerged in recent years.Different from the traditional continuum mechan ics theory,the kinematics equation is constructed based on the differential equation,but the kinematics equation is constructed based on the integral equation.It is because of this characteristic that when dealing with discontinuities such as damage and fracture,Peridynamics does not have a derivative that does not exist at the fracture compared to traditional continuous-mechanical mechanics because of its theoretical advantage.At the same time,it is precisely because each material point in the Peridynamics needs to interact with other material points in a certain range to form an integral domain,which in turn makes Peridynamics computationally inefficient and the boundary effect is obvious Cannot form a complete integral domain),and difficult to app ly loads.On the other hand,because the Peridynamics theory is relatively late compared to other doctrines,it is not sufficient for modeling various types of materials.Therefore,the research focus of this paper is on the Peridynamics modeling of plastic materials.In addition,we consider that the efficiency problem of Peridynamics will be more obvious in dealing with plasticity problems,so we propose an adaptive coupling method.The main work can be summarized as follows.(1)Bond-based Peridynamics has the problem of Poisson's ratio limitation in dealing with conventional problems.In recent years,many scholars have proposed various solutions to improve the Poisson-ratio limitation of bond-based Peridynamics.We refer to one of the schemes in this article,and based on the nature of the bond,we further improved this method,making the improved method closer to the results of continuum mechanical calculations.When the two are coupled,the coupling boundary The transition is smoother and there is no a brupt displacement compared to before the improvement.Then we combined the bond-group near-field dynamic plasticity theory proposed by Professor Ladányi,and proposed a bond-based Peridynamics plasticity theory without Poisson's ratio limitation,and the material's tensile force and displacement successfully exhibited bilinear behavior.(2)Because the bond-based Peridynamics is based on the bond to consider the plasticity of the material,but the properties of the material are equivalent to the material point,so we consider using the state-based Peridynamics to further consider the plasticity of the material.A plastic model based on the Peridynamics of the state base is presented.The model can successfully simulate ideal plasticity and plastic hardening,including linear and nonlinear hardening problems.And by comparing with the plastic model of continuum mechanics,the expressions of yield function,flow criterion and equivalent plastic stress are established.Based on the bond energy fracture criterion,the crack propagation problem of plastic materials is successfully simulated.(3)When we deal with plasticity,the efficiency problem of Peridynamics is particularly significant when we deal with plasticity.The most common solution to the efficiency problem in Peridynamics is to couple it with a continuum mechanical scheme,but the conventional coupling method needs to know the crack direction in advance.So we proposed an adaptive coupling scheme based on the dual coupling scheme proposed by others.When we use this scheme to deal with the fracture problem,the Peridynamics region in the material always changes dynamically before the crack growth,and the expansion of the Peridynamics region can also be consistent with the crack growth trend.Greatly improved the efficiency of problem handling.