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An Efficient Implementation of the GMC Micromechanics Model for Multi-Phased Materials with Complex MicrostructuresAn efficient implementation of the generalized method of cells micromechanics model is presented that allows analysis of periodic unidirectional composites characterized by repeating unit cells containing thousands of subcells. The original formulation, given in terms of Hill's strain concentration matrices that relate average subcell strains to the macroscopic strains, is reformulated in terms of the interfacial subcell tractions as the basic unknowns. This is accomplished by expressing the displacement continuity equations in terms of the stresses and then imposing the traction continuity conditions directly. The result is a mixed formulation wherein the unknown interfacial subcell traction components are related to the macroscopic strain components. Because the stress field throughout the repeating unit cell is piece-wise uniform, the imposition of traction continuity conditions directly in the displacement continuity equations, expressed in terms of stresses, substantially reduces the number of unknown subcell traction (and stress) components, and thus the size of the system of equations that must be solved. Further reduction in the size of the system of continuity equations is obtained by separating the normal and shear traction equations in those instances where the individual subcells are, at most, orthotropic. The reformulated version facilitates detailed analysis of the impact of the fiber cross-section geometry and arrangement on the response of multi-phased unidirectional composites with and without evolving damage. Comparison of execution times obtained with the original and reformulated versions of the generalized method of cells demonstrates the new version's efficiency.
Document ID
19970026616
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Pindera, Marek-Jerzy (Virginia Univ. Charlottesville, VA United States)
Bednarcyk, Brett A. (Virginia Univ. Charlottesville, VA United States)
Date Acquired
September 6, 2013
Publication Date
May 1, 1997
Subject Category
Composite Materials
Report/Patent Number
NASA-CR-202350
E-10770
NAS 1.26:202350
Accession Number
97N25865
Funding Number(s)
PROJECT: RTOP 523-21-13
CONTRACT_GRANT: NAS3-1319
CONTRACT_GRANT: NAG3-1377
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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