Peridynamic Damage Simulation Method And Its Application On Crack Propagation Analysis Of PBX Energetic Materials

Peridynamics(PD)is a nonlocal meshless method.It is no longer modelled based on the continuity assumption,and the solids are discretized into a series of material points with mass.It substitutes the governing partial differential equations with integral equations,and the discontinuities spontaneously arise.Therefore,PD method has obvious advantages in studying damage,fracture or instability et al discontinuous problems.In 2000,Silling proposed the original formulation of peridynamics,usually referred to as the bond-based theory.Since the response of a bond is independent of the other bonds,the bond-based PD scheme is limited to constitutive models with a fixed Poisson's ratio.Because bond-based theory does not distinguish between volumetric and distortional deformation,it is not suitable to capture the plastic incompressibility condition.To address these issues,Silling developed state-based peridynamics,including ordinary state-based PD and non-ordinary state-based PD.Since it has a close connection with the classical continuum mechanics,the non-ordinary state-based peridynamics has attracted more and more attention.This paper developed the analytical ability of peridynamics in considering elastic brittle,elasto-plastic and viscoelastic behaviors and be applied to the simulation of crack growth in PBX energetic materials.Peridynamic method supplies a new idea in the simulation of damage and frature of PBX.The main research contents and research findings are shown as:A bond-based peridynamic creep simulation method was established.Under the framework of bond-based PD,the expression of creep compliance under different stresses and the peridynamic creep response functions were deduced by combing the time-stress equivalence principle of nonlinear viscoelastic materials and Burgers viscoelastic model.In this manner,the peridynamic creep simulation method which can be applied to nonlinear viscoelastic materials was established.The creep behavior of PBX9502 was then simulated,which indicates a good conformity with the experimental results.The developed method can be applied to analyze creep behavior of nonlinear viscoelastic materials under different temperatures and different stresses.A new high efficient zero-energy modes control method was proposed,and the zero-energy modes control in explicit solution of non-ordinary state-based peridynamics was acheieved.Considering the nonuniform deformation state as a deformation vector in the linearized bond-based peridynamic theory,and combing the formulation of the strain energy density in the linearized bond-based peridynamic theory,the strain energy density incorporated by the nonuniform deformation state can be obtained.The force state incorporated by the nonuniform deformation is derived through minimum potential principle.The stabilized force state is arrived at by adding the nonuniform force state to the peridynamic force state.A stabilized non-ordinary state-based peridynamic model was proposed and implemented explicitly.It was applied to the analysis of quasi-static problems,including the elastic properties and damage process of the plate with a circular hole,the double cantilever beam,the three point bend specimen,and the plate with a rectangular hole.It was also used to simulate the crack growth of the diagonally loaded square plate under mode I,mode II and different mixed modes loading conditions.The dynamic fracture of a brittle material was also analyzed.The numerical results indicate that the proposed model is effective for controlling zero-energy modes in non-ordinary state-based peridynamics.In comparison with existing zero-energy modes control methods,the parameters have definite physical meaning and the complicated process of adjusting parameter is avoided.Hence,the computational efficiency and accuracy are evidently improved.Damage was incorporated through the influence function.In the foundation of considering the influence of damage on the force state,the effects of damage on the approximate deformation gradient and the shape tensor are also calculated.Therefore,the problem of stress un-releasing in damaged region was overcome.The damage incorporation method was applied to the simulation of damage and failure behaviors of polymer bonded explosives in Brazilian disc experiment.It shows that the results of the modified method are in better correspondence with the experiment.An implicit solution method of the stabilized non-ordinary state-based peridynamic model was established.The implicit discretization formulation of the stabilized non-ordinary state-based peridynamic model was derived.A bilinear damage model based on the influence function was also developed.Then,an implicit solution method was presented.The model was implemented implicitly through the secant stiffness method,in which the zero-energy modes was controlled utilizing the control method proposed above.The proposed method was applied to study the crack propagataion of the model I double cantilever beam,the wedge-splitting test specimen and the three point bend specimen.The numerical results indicate that the proposed model can simulate the crack growth path,the crack-tip stress concentration during crack propagation,the failure force and softening stage of the reaction force-displacement curve.A PD plastic-damage simuation method was established and be applied to the simulation of uniaxial stress-strain curves of PBX.Considering the nonsymmetry of tensile and compressive behaviors and the obvious plastic characteristic under compressive state of PBX,the plastic-damage model proposed by Lubliner and Lee was introduced into non-ordinary state-based peridynamics.The constitutive model can be defined through the plastic model,and the damage criterion can be defined by the damage model combing with the influence function in PD.Thus,the peridynamic plastic-damage simulation method which can be applied to study the concrete,soil and polymer bonded explosives mechanical behaviors under complicated stress state was established.The proposed model was applied to PBX.The numerical results show that the proposed model can simulate the linear elastic properties,plastic hardening,and the softening stage of the uniaxial stress-strain curves.