Adaptive schemes and mesh refinement strategies are developed to create a hierarchy of computational sub-domains with varying resolution. Such hierarchy allow for differentiation between non-critical and critical regions, and help in increasing the efficiency of computations through preferential `zoom in' regions. Coupling between the scales for regions with periodic microstructure is accomplished through asymptotic homogenization, whereas regions of nonuniformity and non-periodicity are modeled by true microstructural analysis with VCFEM.
An adaptive Voronoi cell finite element model is also developed for micromechanical analysis. Microstructural damage initiation and propagation in the form of debonding and particle cracking are incorporated. Error measures, viz. a traction reciprocity error and an error in the kinematic relation, are formulated as indicators of the quality of VCFEM solutions. Based on a-posteriori evaluation of these error measures, element adaptation is executed by displacement function adaptations and enrichment of stress functions. The complete process improves convergence characteristics of the VCFEM solution. Aspects of parallel computing in the implementation of the codes will be discussed.
Prof. Ghosh is a Fellow of the American Society of Mechanical Engineers and is the Chairman of the Committee of Materials Modeling of the United States Association of Computational Mechanics. He received the National Science Foundation's prestigious Young Investigator Award in 1994. He received the Harrison faculty award for Excellence in Engineering Education in 2001 and the Lumley Research award in 1998 and 1994 from the OSU College of Engineering