Generalized Interpolation Material Point Method For Coupled Thermo-elasto-plasticity

The heat transfer and coupled thermomechanics are widely existed in scientific research and engineering practice.It has a variety of applications in the fields of material design,aviation equipment protection,and natural disaster prediction.The research on the coupled thermomechanical model and algorithm is an interdisciplinary research field of mechanics,mathematics,physics,and material science.It is also the basic problem that needs to be emphatically solved in the research and development of major equipment.Therefore,the establishment of multi-physics model and the development of efficient numerical algorithm with an emphasis on the study of coupled thermo-elasto-plasitic dynamics and the exploration of coupled thermomechanical behavior have important significance for material design and optimization,and the assessment for structural safety.As a particle-based meshless method,the generalized interpolation material point method(GIMP)has certain advantages in numerical simulation of multi-physics and damage problems.It has become one of the most popular methods and has been used in many engineering applications.Based on the theoretical basis of the GIMP method,this dissertation aims to develop the numerical models for coupled thermo-elasto-plasticity taking the coupling effects between the temperature and deformation into consideration.The GIMP methods for steady state and transient heat transfer are proposed firstly.Then the GIMP methods for weakly coupled and fully coupled thermo-elasto-plasticity are developed,including the axisymmetrical formulations.Finally,the Cosserat-based thermomechanical GIMP method for simulating the thermal-induced stain localization is further proposed.The dissertation mainly includes the following parts:Firstly,a GIMP-based discretization method is proposed for simulating transient heat transfer processes based on the weak formulation of heat conduction equation,with a focus on the boundary treatment.The solution scheme for the proposed method is then designed using an explicit time integral method.Several representative examples are presented to demonstrate and verify the proposed procedure as compared with analytical or other numerical solutions.The convergence study for thermal analysis shows that the proposed solution procedure converges with the decrease of cell size and the increase of particles per cell(PPC)number.To improve the accuracy of the method in dealing with the prescribed temperature boundaries,the multi-grid discretization technique is developed to refine the boundary cells.Numerical results show that the multi-grid technique can not only reduce the oscillation of the temperature in the original method,but also accumulate smaller errors.Secondly,an implicit GIMP discretization method is proposed for simulating steady-state heat transfer problems.The heat conduction coefficient matrix is derived based on the weak formulation of the heat conduction equation in the framework of GIMP method.A Newton-Raphson incremental procedure is designed to solve the balanced equation.Numerical examples are performed to verify the proposed method and the results show very good agreement of the proposed implicit GIMP method and analytical solutions,which demonstrate the accuracy and efficiency of the proposed procedure.The convergence study also reveal that the accuracy of the implicit method converges with increasing cell numbers and PPC numbers.Thirdly,a generalized interpolation material point method for simulating weakly coupled thermomechanical processes(WCTGIMP)is developed based on the weak formulations of heat conduction equation and momentum equation.The coupling term between the thermal and mechanical field variables is connected via the thermal strain imposed as the thermal load in the mechanical analysis.Numerical examples sow that the results of the proposed method are consistent with the analytical solutions and the FEM results.The proposed unified GIMP method is further employed for simulating the material failure evolution with the use of a bifurcation-based decohesion model.The results of the representative examples demonstrate the validity and potential of the proposed procedure in simulating multi-physics phenomena.Fourthly,based on the conservation laws of mass,momentum and energy,the generalized interpolation material point(GIMP)method is further developed for fully coupled thermomechanical problems,with applications to model-based simulation of failure evolution.The fully coupled thermomechanical GIMP method(FCTGIMP)considers the effects of both the temperature on deformation and the deformation on temperature.The discrete governing equations are formulated for both thermomechanical motion and heat conduction.A staggered solution scheme is designed to solve the coupled governing equations with an explicit time integration.Representative examples with analytical solutions are presented to verify the proposed FCTGIMP for coupled thermomechanical analyses.The FCTGIMP is then used for model-based simulation of vibration-induced thermoplasticity,and of failure evolution in a snowy slope under the heat convection condition to demonstrate the potential of the proposed procedure in engineering applications.Fifthly,an axisymmetric formulation of the generalized interpolation material point method for fully coupled thermomechanical analysis(AxiCTGIMP)is developed for evaluating the transient responses,where both the thermoelastic and thermoplastic effects are taken into account.The GIMP discretization in space for the coupled governing equations is described in details.A truncation approach is performed to eliminate the singularity of the original shape function in axisymmetric coordinates.A staggered solution scheme is designed to split the coupled system into the parts related to the temperature and displacement fields,respectively,which are then solved individually with explicit time integration.The AxiCTGIMP is then verified and validated with two benchmark examples:the thick-walled cylinder and the Taylor-bar impact test.The simulation results show good agreements with available analytical solutions,experimental data and other numerical results.In addition,the results indicate that the proposed solution procedure is more accurate than the original MPM while it is much more efficient than the fully three-dimensional simulation.Finally,the Cosserat continuum theory is introduced into the implicit formulation of coupled thermomecanical GIMP method as a regularization mechanism for the thermal induced strain localization phenomena.The stiffness matrix in the GIMP discretization is derived based on the weak formulation of the momentum equation in Cosserat model.A staggered incremental procedure is implemented for the solution of the discrete coupled governing equations of the heat conduction and the equation of motion in Cosserat continuum.The proposed method is firstly verified by the patch tests and the bending of cantilever beam demonstrates the characteristics of the Cosserat model.The effect of the intrinsic length scale on the shear band is investigated in the strain localization analysis in a square plate.The thermal-induced strain localization problem is then computed numerically and the results indicate that the width of the shear band is independent on the background cell size.Appendix A introduces the computational program of CTGIMP for simulating coupled thermomechanical responses of solids based on the above numerical methods.The pre-process and post-process modules with Graphical User Interface are designed using MATLAB scripts.The computational module coded in FORTRAN 90 with OpenMP parallelization strategy is developed for simulating steady state and transient heat transfer,the structure dynamics and the coupled thermo-elasto-plasticity.