Multiscale Methods For Nonlinear Analysis Of Composite Materials
材料非线性微-宏观分析的多尺度方法研究

A composite material is called spatially periodic if it is possible to be decomposed into elementary components or cells of periodicity. The characteristic size of the single cell of periodicity is assumed much smaller than the geometrical dimensions of the structure which is therefore composed of a large number of cells. The great achievements have been obtained from the research of homogenization algorithm based on the elastic assumption. Because the failure process of material is generally related to the nonlinear analysis of the materials, the research work on the multi-scale analysis of the nonlinear behaviors of the materials is more significant for engineering applications. However, due to the difficulties of the solving of nonlinear problems, the research work will be more complex and more difficult than those performed for the elastic homogenization analysis. The numerical approach in the paper differs somewhat from those proposed in previous studies. For micro-macro analysis of periodic material composed of elastic granules with contact characteristics, this paper adopts the method which was developed by the first author. The basic principle of the method is based on the numerical constitutive model. The important features of developed algorithm are that during the process of establishing macroscopic constitutive law the stick-disengage-slip behaviors in the granular contact interfaces are taken into account. Different from the pure contact problem, the stick relationship considers initial stick cohesion between the granules when the sticking state is destroyed (the material will thus proceed a damaged state). For the micro-macroscopic analysis of multi-phase elastic-plastic materials, according to transformation field theory, a consistent algorithm for elastic-plastic material analysis on micro-macroscopic is proposed. The basic theories for the establishing of the numerical method are introduced first in the paper, and then the numerical technique is described in detail. Finally, the numerical example is presented to demonstrate the validity and efficiency of the two algorithms.