ANALYTICAL AND NUMERICAL-STUDIES OF DEFORMATION-BEHAVIOR AT MICROSCOPIC SCALE

The paper presents an overview of the analytical methods as well as fi nite element method employed by the author in a few earlier investigat ions pertaining to modelling and simulation of deformation at microsco pic scale. The following case-studies are considered for illustrations : deformation of a set of powder particles during hot isostatic pressi ng; effective properties of a typical particulate metal matrix composi te and porous material; constitutive behaviour of a material exhibitin g transformation-induced plasticity; shear band formation in polycryst alline material. The paper describes certain generalized techniques fo r constructing the microstructural geometries, assigning material prop erties and imposing boundary conditions. The concept of generating two -phase geometries using a master mesh and the generalized plane strain approach to handle two-dimensional approximations used in the above s tudies are also reviewed. In contrast to the commonly employed unit ce ll models based on certain regular geometries, the present method uses the actually observed microstructural geometries. This method accommo dates more realistic and complex conditions compared to those supporte d by the well-explored analytical methods. Although, only homogeneous and isotropic systems have been discussed in this paper, this method c an be easily extended to inhomogeneous and anisotropic cases as well. In general, the technique is emerging as a suitable numerical tool for designing materials for specific applications.