Multiscale Methods For Nonlinear Analysis Of Composite Materials

A composite material is called spatially periodic if itis possible to be decomposed into elementary components or cells ofperiodicity. The characteristic size of the single cell of periodicity isassumed much smaller than the geometrical dimensions of the structure whichis therefore composed of a large number of cells. The great achievementshave been obtained from the research of homogenization algorithm based onthe elastic assumption. Because the failure process of material is generallyrelated to the nonlinear analysis of the materials, the research work on themulti-scale analysis of the nonlinear behaviors of the materials is moresignificant for engineering applications. However, due to the difficultiesof the solving of nonlinear problems, the research work will be more complexand more difficult than those performed for the elastic homogenizationanalysis. The numerical approach in the paper differs somewhat from thoseproposed in previous studies. For micro-macro analysis of periodic materialcomposed of elastic granules with contact characteristics, this paper adoptsthe method which was developed by the first author. The basic principle ofthe method is based on the numerical constitutive model. The importantfeatures of developed algorithm are that during the process of establishingmacroscopic constitutive law the stick-disengage-slip behaviors in thegranular contact interfaces are taken into account. Different from the purecontact problem, the stick relationship considers initial stick cohesionbetween the granules when the sticking state is destroyed (the material willthus proceed a damaged state). For the micro-macroscopic analysis ofmulti-phase elastic-plastic materials, according to transformation fieldtheory, a consistent algorithm for elastic-plastic material analysis onmicro-macroscopic is proposed. The basic theories for the establishing ofthe numerical method are introduced first in the paper, and then thenumerical technique is described in detail. Finally, the numerical exampleis presented to demonstrate the validity and efficiency of the twoalgorithms.