First-order perturbation expansion progressive homogenization method for statistical prediction of elastic constitutive matrix of random distributed composite materials

Abstract

The invention discloses a first-order perturbation expansion progressive homogenization method for statistical prediction of an elastic constitutive matrix of random distributed composite materials. The method comprises the steps that (1), according to an actual material domain, the source and range of random variables are determined, and a probability model is established; (2), the random variables are introduced by a material elastic constitutive flexibility matrix based on a first-order perturbation hypothesis, and a stiffness matrix is obtained by inversion; (3), a microscopic representative unit subdomain is intercepted in a macroscopic material structure system, and a functional scale effect relationship on a microscopic representative volume unit is hypothesized based on a progressive homogenization method to derive a virtual work principle equation and establish the equivalence relation between a macro elastic matrix and a finite element equation of a representative volume unitmaterial domain; (4), the equivalence relation between probability and statistical characteristics of the macroscopic elastic matrix and the finite element equation of the representative volume unitmaterial domain is solved; (5), probability and statistical characteristics of elastic engineering constanTS are derived from the macroscopic elastic matrix.

Description

technical field [0001] The invention relates to a statistical first-order perturbation expansion progressive homogenization method for predicting the elastic constitutive matrix of a randomly distributed composite material, which is suitable for the prediction of the macroscopic elastic constitutive matrix of a composite material structure with random material properties. Background technique [0002] With the advancement of science and technology, composite materials have attracted more and more attention due to their high strength, high stiffness, high temperature resistance and corrosion resistance. Therefore its performance calculation becomes more and more important. Multiphase composites are often encountered in composite calculations. Randomly distributed composite material is an important form of composite material, which has been widely used in civil engineering and industrial products. According to the random distribution characteristics of fillers, it can be div...

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Problems solved by technology

Yu and Cui have proposed a statistical second-order dual-scale analysis method, given computer simulation and fast finite element analysis of random particle distribution regions, which can be used to predict uniform random distribution composite materials with various complex microstructures The elastic displacement field and heat conduction performance of the structure, but due to the randomness of the physical properties of the material, there are very few studies on the randomness of the structural mechanical properties

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