Hybrid impotent–incompatible eigenstrain based homogenization
Abstract
We present a constitutive framework for a periodic heterogeneous medium with minimal number of internal variables. The method is based on a variant of the transformation field analysis (TFA) where eigenstrains are discretized using C 0 continuous approximation in matrix dominated mode of deformation, hereafter referred to as impotent eigenstrain mode, whereas in multiphase mode of deformation, the eigenstrains are approximated using the usual C − 1 approximation. The delay in the onset of inelastic response and the eigenstrain induced anisotropy in a microphase, both characteristic to averaging methods, are alleviated by introducing an eigenstrain upwinding scheme and by enhancing constitutive laws of microphases. The proposed formulation has been verified against a direct numerical simulation. The method has been found to be very accurate in predicting an overall material response at a computational cost comparable with the phenomenological modeling of a periodic heterogeneous medium. Copyright © 2013 John Wiley & Sons, Ltd.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- May 28, 2013
- Source ID
- 10.1002/nme.4473
Entities
People
- Jacob Fish
- Vasilina Filonova
- Yuan Zheng
Organizations
- Columbia University
- National Science Foundation
- Office of Naval Research
- Rolls-Royce