Multiscale Study On Micro-macro Nonlinear Analysis Of Heterogeneous Materials

All materials have a variety of length scale characteristics,including natural materials in the presence of rock,salt geological,biological tissues and engineered materials such as fiber reinforced composite materials,metal alloy materials,concrete.When the length scale is small enough,materials exhibit heterogeneous attributes.From the viewpoint of engineering application,the desired engineering materials are consructed by the components specific performance of heterogeneous materials.In fact,the micro-scale materials properties have a decisive influence on the macro-scale materials.Therefore,research on the relationship between the macro and micro scale has become an urgent study direction.Considering computer memory and computing time,it is very difficult to to solve the problem for heterogeneous materials using conventional numerical methods(e.g.finite element method),and finite element mesh is needed to refine heterogeneous material mesoscopic level.The multi-scale analysis method provides a new idea for solving this kind of problem,and it has become a hot research topic in recent years.In view of the existing problems for the research on multi-scale analysis method,in this paper a general periodic boundary conditions the finite element method is proposed,which solved the problem of symmetric mesh generation for complex structure RVE.The homogenization method comes true for RVE,and the mechanical properties of the particles reinforced composites with holes were studied by this method.In the ABAQUS finite element software platform,the coupled nonlinear multi-scale method was achieved by programming,which provided a powerful tool for the study of heterogeneous materials.Based on the coupled nonlinear multi-scale method,the damage multi-scale analysis was realized.The main work of this paper was summarized as the following aspects.(1)In order to reduce the difficulty of symmetric mesh generation for complex structure model,the constraint equations of general periodic displacement boundary conditions were derived by interpolation processing of periodic boundary conditions constraint equations.General periodic boundary conditions were implemented for RVE through Python scripts programming,and the processing efficiency improved.The correctness of applying general periodic boundary conditions was proved by 3D four-directional braided composites RVE model.(2)In the case of void defects,the mechanical properties of particles reinforced composites with holes were studied by RVE homogenization.The two-dimensional RVE model with particles/voids was constructed by FORTRAN programming,and the homogenization method is realized by the second development using a number of user subroutines.Homogenization procedure provides a necessary preparation for the coupled nonlinear multi-scale analysis.(3)Based on ABAQUS software,the application of asymptotic homogenization theory,the coupled nonlinear multi-scale method was implemented by programming.Firstly,multi-scale analysis formulas and finite element expansions derived from asymptotic homogenization theory.Secondly,the finite element implementation process of the linear elastic problem multi-scale analysis is presented,and the method was applied to the identification of the macro equivalent elastic parameters for particle reinforced composites and composites with void defects.Finally,the finite element implementation process of nonlinear multi-scale analysis was presented,and the method was applied to the particle reinforced composite.The influence of plasticity evolution in micro-scale model in terms of reinforced particle materials on macro mechanical properties was studied.The coupled nonlinear multi-scale analysis method provides a powerful tool for the study of heterogeneous materials.(4)A progressive damage model was embedded in the nonlinear multi-scale program framework,which can be implemented by multi-scale analysis,and the effectiveness of this method was verified by an example.This work can provide a basic program framework for the damage analysis of heterogeneous materials.