Noncoaxiality between Two Tensors with Application to Stress Rate Decomposition and Fabric Anisotropy Variable
Publication: Journal of Engineering Mechanics
Volume 146, Issue 3
Abstract
The coaxial and totally noncoaxial parts of a tensor in regard to another reference tensor are derived in closed analytical form based on representation theorems of tensor-valued isotropic functions. In the process a new interpretation is obtained for a singular case of representation theorems. As a first application, the coaxial and noncoaxial parts of a stress rate tensor in regard to the stress tensor are analytically expressed, and the findings applied to the following two cases: analytically express the part of a stress rate tensor that induces change of stress principal axes at fixed principal stress values, and change of stress principal values at fixed stress principal axes such that the stress orbit on the stress -plane is circular. A second application refers to enhancing the definition of the fabric anisotropy variable , a quantity of cardinal importance for anisotropic critical state theory in granular mechanics, so that the orthogonal coaxial and noncoaxial parts of the fabric tensor in regard to the plastic strain rate direction participate in the definition of .
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Data Availability Statement
No data, models, or code were generated or used during the study.
Acknowledgments
Y. F. Dafalias acknowledges partial support by the European Research Council under the European Union’s Seventh Framework program (FP7/2007-2013)/ERC IDEAS Advanced Grant Agreement 290963 (SOMEF), the European Regional Development Fund under Grant No. CZ.02.1.01/0.0/0.0/15_003/0000493 – CeNDYNMAT, Czech Republic, and the US Army Research Laboratory and US Army Research Office under Grant No. W911NF-19-1-0040.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 3 • March 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Feb 22, 2019
Accepted: Aug 19, 2019
Published online: Jan 10, 2020
Published in print: Mar 1, 2020
Discussion open until: Jun 10, 2020
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