If the double contraction of a stress tensor such as T and rate of a Lagrangean strain tensor such as E, i.e. T : E˙, produces the stress power then these stress and strain tensors are called a conjugate pair. The applications of the conjugate stress and strain measures are in the development of the basic relations in nonlinear continuum mechanics analysis such as modeling of constitutive equations of elastic-plastic materials. In this paper relations for stress tensors conjugate to an arbitrary Lagrangean strain measure of Hill’s class are obtained. The results of this paper are more compact and simpler in compare with those available in the literature. The results are valid for the three dimensional Euclidean inner product space and the case of distinct eigenvalues of the right stretch tensor U.
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ASME 8th Biennial Conference on Engineering Systems Design and Analysis
July 4–7, 2006
Torino, Italy
ISBN:
0-7918-4248-7
PROCEEDINGS PAPER
Compact Basis Free Relations for Stress Tensors Conjugate to Hill’s Strain Measures
Reza Naghdabadi,
Reza Naghdabadi
Sharif University of Technology, Tehran, Iran
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Mohsen Asghari,
Mohsen Asghari
Sharif University of Technology, Tehran, Iran
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Kamyar Ghavam
Kamyar Ghavam
Sharif University of Technology, Tehran, Iran
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Reza Naghdabadi
Sharif University of Technology, Tehran, Iran
Mohsen Asghari
Sharif University of Technology, Tehran, Iran
Kamyar Ghavam
Sharif University of Technology, Tehran, Iran
Paper No:
ESDA2006-95367, pp. 405-409; 5 pages
Published Online:
September 5, 2008
Citation
Naghdabadi, R, Asghari, M, & Ghavam, K. "Compact Basis Free Relations for Stress Tensors Conjugate to Hill’s Strain Measures." Proceedings of the ASME 8th Biennial Conference on Engineering Systems Design and Analysis. Volume 1: Advanced Energy Systems, Advanced Materials, Aerospace, Automation and Robotics, Noise Control and Acoustics, and Systems Engineering. Torino, Italy. July 4–7, 2006. pp. 405-409. ASME. https://doi.org/10.1115/ESDA2006-95367
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