The Multiscale Coupling Model And Algorithms For Thermo-Mechanical Behaviours Of Metal Crystalline Materials

It has been realized that the properties of materials at macro scale depend to a great degree on the structures and properties at atomic scale.In order to obtain more accurate prediction of physical and mechanical properties of materials,we should at first study the atomic structures and the connections of physical quantities among different scales.Further,the effective and efficient multiscale coupling model that connect models at different scales and suitable for multi physical processes should be constructed.As we have already known,because of the essential difference of continuous and discrete physical properties between the continuum and atomic models,it is a very complex task to build the effective multiscale coupling model and has been one of the most challenging topics in intersection between mathematics,mechanics and material science.In this thesis,we focus on the thermodynamic and kinetic properties of metal crystalline materials based on the analysis of atomic motion,and develop the multiscale coupling model and algorithms for thermo-mechanical behaviours of metals.The main achievements of this paper are as follows:In the first part,based on the detailed analysis of the atomic motion,we built an coupled atomic-continuum model of free energy that includes both the thermo-mechanical mechanism and non-harmonic effects.The motion equation of atoms is firstly decomposed into structural deformation and thermal vibration.The thermal vibration equation is built on structural deformation positions at each transient time,which includes the non-harmonic effects by considering the high-order(up to the fourth order)Taylor expansion terms of interatomic potentials.Further,based on the thermo-mechanical coupling mechanism,both the thermal and mechanical aspects of structural deformation are investigated.Finally,the coupled atomistic-continuum model of free energy is obtained as a function of the structural deformation positions and thermal vibration frequencies,which combines the expressions of free energy both in continuum and atomic models.In the second part,based on the model of free energy above,the multiscale atomic-continuum coupling model for the thermo-mechanical properties of metallic crystalline materials is established.Firstly,a parameter ? =-? ln ?/? ln T is newly introduced to illustrate how the thermal vibration frequencies ? vary with the temperature T,which reveals the non-harmonic effects included in free energy.It is worth to note that the parameter ? shows a linear correlation of the temperature and is of great importance in thermodynamic properties,especially at high temperatures.Then by means of the improved free energy and parameters ?,a set of thermodynamic properties,including internal energy,entropy,heat capacity and thermal expansion coefficient,are derived from the free energy.Further,the thermoelastic constitutive relation is constructed at finite deformation for cubic crystal materials.Finally,numerical results of the thermodynamic properties,thermoelastic stress-strain relations and elastic constants for eight face-centered cubic metals Cu,Al,Au,Ag,Ni,Pd,Pt and Pb,from 0 K to the melting points at 0 ～ 50 Gpa,are provided by comparing with the experimental data to demonstrate the usability of the present models.In the third part,the multiscale coupling model that combine the molecular dynamics(MD)and peridynamics(PD)models for the kinetic properties of metal crystalline materials is constructed,based on the multiscale atomic-continuum coupling model above.The ”bottom-up”micro elastic modulus in peridynamic theory is firstly obtained by establishing the relationship between the interatomic potential energy in MD model and the strain energy in PD model.Then the region is decomposed into the atomic region,the continuum region and the overlapping region.The MD and PD model are respectively adopted to the atomic and continuum region,while a linear complementary weight function is applied to combine the energies of MD and PD model in the overlapping region.Furthermore,in order to ensure the smooth transition of energy in the interface between these two models,the Lagrange multiplier is also introduced in the overlapping region.Finally,the 1-dimensional case is implemented to verify this multiscale coupling model and the effects of several factors,such as the complementary weight function,the length of the coupling region,the time step and the size of the near-field neighborhood,on the whole coupling model are studied.