Fitting an Anisotropic Yield Surface Using the Generalized Method of Cells

  • K. ActonEmail author
  • L. Graham-Brady
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 168)


Homogenization of a composite material by the generalized method of cells can be used for determining effective elastic properties, and it can also be extended into an incremental, plastic analysis [1]. The stress–strain curve of a given GMC-modeled composite extended into the inelastic range may be complex. The composite level curve often exhibits multiple distinct yield points as different subcells undergo yield. Also, the stress–strain curve for a given material may be different when the material is loaded in different directions. The objective of this work is to gather information at the microstructural level, as described by GMC, to generate a meso-scale effective representation of the elastic and plastic behavior of the material. A meso-scale representation is useful in addressing the computational difficulties of multi-scale modeling. Meso-scale constitutive property fields can also be used as a basis for simulation of sample realizations of the microstructure. The meso-scale models are developed using GMC in conjunction with a moving window averaging procedure. The GMC homogenization results for each unit cell, or “window” in the moving window analysis, are used to generate an approximation of the anisotropic yield surface that can be implemented into a macro-scale finite element analysis. In order to develop accurate models, a single inclusion benchmark analysis is performed where the meso-scale model results are compared against the solution developed by Mendelson [9].


Window Size Yield Surface Initial Yield Effective Elastic Property Hill Criterion 
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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Civil EngineeringJohns Hopkins UniversityBaltimoreUSA

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