Multiscale Model And Algorithm For Elasto-Plastic Analysis Of Composite Materials

The multiscale analysis method has undoubtedly been a useful tool in the region of computational mechanics with the development of Micro-Mechanics. The investigation of multiscale analysis method of composite material proceeding with three length scales, i.e. macro, meso and micro, has promoted the development of computation solid mechanics.The finite element method has been used widely in analysis for linear and non-linear mechanical problems of composite materials. However, mechanical problems of composite bodied with a very fine periodic structure cannot be analyzed by known computational techniques with the use of direct discretization of the body because of too large computation cost of such analysis. Therefore, some methods of substitution for a real heterogeneous material with the homogeneous one, macroscopically equivalent, are used. Such a substitution procedure is known as the homogenization method, can speedup modeling, reduce the cost of computation, and achieve the computational simulation of mechanical behavior of composite material subjected to various kinds of loading. Main idea of the method is to substitute primary heterogeneous material by a specific kind of homogenous one, which needs guarantee that they have the equivalent strain energy. Early mutiscale methods represent the direct averaging of strain and stress fields of the represent volume element(Average Field Method), such as Mori-Tanaka's effective field method , self-consistent , generalized self-consistent method differential method and so on. But some of them are limited to solve such problems as linear or certain non-linear problems for effective characters of heterogeneous materials.A unified macro- and micro-mechanics constitutive model is built in this thesis for the homogenization analysis of periodic elastic-plastic composite materials. Based on the TFA (Transformation Field Analysis), the present paper constructs a basic theory and algorithm for multiscale computation of the elastic-plastic structures constructed by composite materials. According to the algorithm developed, the problem can be generalized to effective computation of stress integration at Gauss points in the elements. On the basis of the unit cells, modeling approach and algorithm of elastic-plastic analysis of composite materials established based on von-Mises yield law for the basic materials are represented. The finite element model for non-linear analysis of composite materials is thus established and the problem is changed to the solution process of traditional non-linear numerical problems.Numerical examples are computed and the results show the validity and efficiency of the theory and finite element program developed for multiscale analysis.