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Compact Basis Free Relations for Stress Tensors Conjugate to Hill’s Strain Measures

[+] Author Affiliations
Reza Naghdabadi, Mohsen Asghari, Kamyar Ghavam

Sharif University of Technology, Tehran, Iran

Paper No. ESDA2006-95367, pp. 405-409; 5 pages
doi:10.1115/ESDA2006-95367
From:
  • 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
  • ISBN: 0-7918-4248-7 | eISBN: 0-7918-3779-3
  • Copyright © 2006 by ASME

abstract

If the double contraction of a stress tensor such as T and rate of a Lagrangean strain tensor such as E , i.e. T : Ė , 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 .

Copyright © 2006 by ASME
Topics: Stress tensors

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