Research On Multi-scale Analysis Method For Porous Materials Considering Stochastic Parameters

Porous materials are widely used in civil engineering,mechanical engineering,aerospace engineering,and other fields due to their high specific stiffness and specific strength.The analysis of porous materials is time-consuming when using single-scale methods.However,the asymptotic homogenization method models the porous material in two scale,which can effectively improve the computational efficiency.Besides,due to the effect of various uncertain factors,the stochastic model of porous materials is more in line with the actual situation.In this paper,the asymptotic homogenization method and stochastic analysis theory are combined to study the multi-scale analysis method of porous materials with stochastic parameters.The main research work of this paper is as follows:(1)The research progress of porous materials is summarized,and different methods and achievements of those research are introduced to point out the deficiencie.A systematic review of multiscale analysis methods(including asymptotic homogenization methods)was conducted and the advantages and disadvantages of each method were pointed out.The commonly used stochastic analysis methods and stochastic multiscale analysis methods are introduced,and the advantages and problems of the methods are explained.(2)The establishment and solving process of differential equations for asymptotic homogenization method are introduced.Numerical examples are used to verify the accuracy and efficiency of the method.In addition,the difference of several boundary conditions for mesoscopic models is also compared to find one with both high accuracy and good efficiency.Through the study of geometric and material parameters,the influence of each parameter was analyzed,providing the basis for the selection of stochastic parameters.(3)Combining response surface Monte Carlo method with asymptotic homogenization method,a response surface Monte Carlo-asymptotic homogenization method for porous materials containing stochastic parameters is proposed,taking into account two different inputs parametric models,namely stochastic field models and stochastic variable models.The calculation accuracy and efficiency of the response surface Monte Carlo-asymptotic homogenization method are verified by numerical examples,and the distribution type,variation coefficient of random variables and distribution type,correlation structure,correlation length and coefficient of variation of stochastic fields are analyzed.The impact of stochastic analysis results was analyzed and the influence of these factors was obtained.The work in this dissertation shows that the asymptotic homogenization with the boundary condition for the meso-scale model selected in this research can analyze porous materials efficiently and accurately.In addition,a response surface Monte Carlo-asymptotic homogenization method is proposed based on the selected mesoscopic boundary conditions.The method has good calculation accuracy and high computational efficiency.It is suitable for multi-scale analysis of porous materials with stochastic parameters.