New, higher-order, elasticity-based micromechanics model

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The formulation for a new homogenization theory is presented. The theory utilizes a higher-order, elasticity-based cell analysis of a periodic array of unit cells. The unit cell is discretized into subregions or subcells. The displacement field within each subcell is approximated by an (truncated) eigenfunction function expansion of up to fifth order. The governing equations are developed by satisfying the pointwise governing equations of geometrically linear continuum mechanics exactly up through the given order of the subcell displacement fields. The specified governing equations are valid for any type of constitutive model used to describe the behavior of the material in ... continued below

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10 p.

Creation Information

Williams, T. O. (Todd O.) January 1, 2003.

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Description

The formulation for a new homogenization theory is presented. The theory utilizes a higher-order, elasticity-based cell analysis of a periodic array of unit cells. The unit cell is discretized into subregions or subcells. The displacement field within each subcell is approximated by an (truncated) eigenfunction function expansion of up to fifth order. The governing equations are developed by satisfying the pointwise governing equations of geometrically linear continuum mechanics exactly up through the given order of the subcell displacement fields. The specified governing equations are valid for any type of constitutive model used to describe the behavior of the material in a subcell. The fifth order theory is subsequently reduced to a third order theory. The appropriate reduction of the fifth and third order theories to the first order theory (which corresponds to a variant of the original method of cells (MOC) (Aboudi, 1991) theory) is outlined. The 3D ECM theory correctly reduces to the 2D ECM theory microstructures and the exact 1D theory for bilaminated structures. Comparison of the predicted bulk and local responses with published results indicates that the theory accurately predicts both types of responses. Furthermore, it is shown that the higher order fields introduced coupling effects between the local fields that can result in substantial changes in the predicted bulk inelastic response of a composite.

Physical Description

10 p.

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  • Submitted to: 14th International Conference Composite Materials (ICCM14) sponsored by ASC/SME, 14-18 Jul 2003 in San Diego, CA

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  • Report No.: LA-UR-03-2220
  • Grant Number: none
  • Office of Scientific & Technical Information Report Number: 976586
  • Archival Resource Key: ark:/67531/metadc934827

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  • January 1, 2003

Added to The UNT Digital Library

  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 12, 2016, 4:20 p.m.

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Williams, T. O. (Todd O.). New, higher-order, elasticity-based micromechanics model, article, January 1, 2003; United States. (digital.library.unt.edu/ark:/67531/metadc934827/: accessed September 25, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.