A Stochastic Transformation Field Theory for Heterogeneous Materials
Publication: Journal of Engineering Mechanics
Volume 132, Issue 11
Abstract
The formulation of a stochastic transformation field analysis framework is presented. The theory introduces the statistics of the underlying material microstructure through the incorporation of probability density functions (PDFs) for the mechanical and transformation field concentration tensors for the phases. Thus, this approach represents a departure from the practice in current micromechanical stochastic theories of considering PDFs for the distributions in the spatial arrangements in the microstructure. General equations governing the behavior of the concentration tensors in the presence of arbitrary variations in these tensors as well as other fields (such as the stress, strain, and eigenfields) are developed. The resulting framework is subsequently specialized to two-phase composite materials. It is shown in this case that the amount of stochastic information required by the theory can be substantially reduced. In particular, only stochastic information about the mechanical concentration tensors is required. An example illustrating the application of the theory to the prediction of the behavior of a two-phase, viscoplastic, continuous fiber composite is given.
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Acknowledgments
The writer would like to acknowledge several fruitful discussions with Dr. Rick Rauenzahn, Dr. Frank Harlow, Dr. Sarah Baxter, and Dr. Curt Bronkhorst. The writer would like to thank Dr. Cheng Liu for the use of his experimental data for the composite system. Finally, the writer would like to acknowledge the support of this work by the ASC program of the Los Alamos National Laboratory.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 132 • Issue 11 • November 2006
Pages: 1224 - 1240
Copyright
© 2006 ASCE.
History
Received: May 16, 2005
Accepted: Dec 20, 2005
Published online: Nov 1, 2006
Published in print: Nov 2006
Notes
Note. Associate Editor: Yunping Xi
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