Numerical Methods Considering Heat Conduction In Impact Dynamics

The impact dynamics problem can be properly described by the numerical calculation which is based on the strict physical model and mathematical derivation.The numerical method and procedure in impact dynamics are obtained tremendous development.But there are still some issues worth studying in depth,and one of them is the heat conduction.In the usual numerical simulations of impact dynamics,for example penetration and adiabatic shear,the heat conduction was ignored.It was thought that the impact process is pretty short,which result in the tiny influence of heat conduction on the calculation.However,it is not clearly that how much effect the heat conduction would have on the calculation,and which has rarely been studied.High temperature,high pressure and large deformation are involved in the impact dynamics problem,and the energy is usually highly centralized at some places,such as the projectile head and the adiabatic shear band.The heat conduction certainly affects the energy distribution and the material mechanics properties.Therefore,if the heat conduction is considered in the numerical simulation,the result would be more in accord with the physical fact and is more instructive for engineering problem.Based on the study of Finite Element Method(FEM),Smoothed Particle Hydrodynamics(SPH)and FEM-SPH coupled method,the heat conduction is introduced into these methods,and then the numerical methods considering heat conduction are established.The numerical calculations of some typical problems are conducted and the influences of heat conduction on calculations are analyzed.The research includes following contents:First,the FEM method considering heat conduction in the impact dynamics is studied.For the contradiction between impact dynamics FEM method and transient heat transfer FEM method on the temperature calculation,"temperature background grid method" is proposed.Based on the newly built FEM procedure which considers heat conduction,the Taylor impact problem and the adiabatic shear problem are simulated.It is found that the heat conduction has an obvious influence on temperature computation:(1)for the Taylor impact simulation,the adiabatic model overestimate the maximum temperature rise and temperature gradient in the impact process;(2)for the adiabatic shear simulation,the adiabatic model not only overestimate the maximum temperature rise and temperature gradient,but also overestimate the shear band formation time.Second,the SPH method considering heat conduction in the impact dynamics is studied.Based on the kernel estimate and particle approximate theory,the discrete forms of conservation equations for continuum mechanics and transient heat transfer are derived.Then,the heat conduction is introduced in energy equation,and the SPH numerical simulation considering heat conduction for impact dynamics is achieved.With the SPH procedure,the long-rod penetration process and the adiabatic shear in plugging are simulated,and the following conclusions can be reached:(1)the influence of heat conduction on temperature distribution become more obvious with the increases of Fourier number;(2)when the Fourier number increases,the influence of heat transfer on penetration depth is always small,but the influence of heat transfer on the plugging problem becomes more and more obvious.Third,FEM-SPH coupled method considering heat transfer for impact dynamics problem is researched.The most important is that how to conduct the global heat conduction calculation when the FEM elements coexist with SPH particles.On the basis of traditional FEM-SPH coupled method,the SPH heat conduction is introduced,the calculation carried out in two steps:(1)follow the traditional process of FEM-SPH coupled method to compute the mechanical response;(2)the FEM elements are equivalent to virtual SPH particles,which form the heat conduction domain together with the real SPH particles.Based on the newly built FEM-SPH coupled method,the long-rod penetration process and the adiabatic shear in plugging are simulated,which validate the feasibility of heat conduction calculation in FEM-SPH coupled method,and provide a reference for the study of heat conduction in impact dynamics.In conclusion,the heat conduction has certain effect on impact dynamics simulation.Especially in some cases,the heat conduction has significant effect on calculation results.Hence,it is necessary to take into account the heat conduction in the impact numerical simulation.Moreover,consider the heat transfer in the impact numerical simulation makes the calculation results more consistent with the physic facts and provides a valuable reference to the related research.