Study On Elastovisco–Plastic Impact Response Model Of Plate Struck By Sphere

Plate is a type of basic components widely applied in engineering structure,and shows convenience in manufacturing and installation.Impact of plate is a common phenomenon in mechanical engineering,being of research interest for structural protection and dynamic control.The impact of plate involves several complicated mechanical behaviours,such as local elasto–plastic contact behaviour,impact-induced wave propagation and structural dynamic response.For strain rate sensitive materials,such as steels,the rapid plastic deformation causes obvious increase in yield stress,shows remarkable effect on local plastic contact deformation,and further influences the deformation response and impact-induced wave propagation in plate.The impact makes local contact region expand,and belongs to the nonlinear problem with elasto–plastic moving boundary.Hence,the great difficulty is encountered in the modelling and computation.The elasto–plastic impact response between sphere and plate can be analysed by using finite element method(FEM),but a huge effort is required for FE modelling.The contact region and its adjacent regions need to be discretized with dense and regular elements,which should be implemented manually with great care.The densely meshed elements lead to extremely short time step in computation,which is about 10^-9?10^-10 s in general.As a result of the contact nonlinearity,material nonlinearity and strain rate effect,the computational efficiency of FEM is relatively low,and is incapable for parametric study on characterizing plate impact responses.This dissertation develops a new mixed numerical–analytical approach that considers the strain rate effect on local plastic contact deformation and the problems of moving boundary,unilateral constraint and nonlinearity,to investigate accurately and efficiently the characteristics of elastovisco–plastic impact responses between sphere and plate.The main contributions of this dissertation are as the followings.(1)Based on Johnson's spherical expansion model and Stronge's relationship between elasto–plastic contact radius and indentation,an elastovisco–plastic contact model(EVPCM)is developed,which considers the strain rate effect on local plastic contact deformation.Two ways of calculating the effective strain rate in local contact region are presented,based on the uniaxial compression model and Johnson's spherical expansion model,respectively.The strain rate effect in dynamic contact is modelled theoretically.(2)Based on Kirchhoff plate theory and Craig–Bampton component mode synthesis,a dynamic substructure model is developed for the simualtions of the impact-induced wave propagation and dynamic deformation response.(3)An eccentric impact test of steel plate is performed.The exprimental data of the local contact deformation and impact responses are sampled to validate the present model.(4)For the dynamic analysis of elasto–plastic impact between a sphere and a plate at an arbitrary position,a mixed numerical–analytical model(EPIM)that neglects the strain rate effect on local contact deformation is presented.The mixed model is based on the degenerated EVPCM without strain rate effect and dynamic substructure model.The computational efficiency and accuracy of the model have been validated by the available analytical solution,experimental data from eccentric impact test,and FE result,respectively.(5)For the dynamic analysis of elastovisco–plastic impact between a sphere and a plate,a mixed numerical–analytical model(EVPIM)that combines the EVPCM and dynamic substructure model is presented.The computational efficiency and accuracy of the model have been validated by the experimental data from eccentric impact test and FE result,respectively.(6)The strain rate effect on the impact response of a phere and a flexible plate is analyzed by performing elasto–plastic and elastovisco–plastic simulations,based on EPIM and EVPIM,respectively.With different structural flexibilities and impact velocities,the strain rate effects on the coefficient of restitution,maximum contact force,maximum indentation,permanent indentation,impact duration,impact impulse and sphere rebound velocity are investigated,respectively.With different structural flexibility and impact velocities,the strain rate effect on impact is illustrated.It is found that the strain rate effect depends upon either the impact velocity or the ratio of the plate stiffness to contact stiffness.In addition,the characteristics of strain rate effect are different with different impact response parameters.