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Unified Basis-Free Relation Between Two Stress Tensors Conjugate to Arbitrary Hill’s Strain Measures

[+] Author Affiliations
Mohsen Asghari, Reza Naghdabadi

Sharif University of Technology, Tehran, Iran

Paper No. PVP2006-ICPVT-11-93687, pp. 743-747; 5 pages
doi:10.1115/PVP2006-ICPVT-11-93687
From:
  • ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference
  • Volume 3: Design and Analysis
  • Vancouver, BC, Canada, July 23–27, 2006
  • Conference Sponsors: Pressure Vessels and Piping Division
  • ISBN: 0-7918-4754-3 | eISBN: 0-7918-3782-3
  • Copyright © 2006 by ASME

abstract

The concept of energy conjugacy for stress and strain measures states that a stress tensor T is conjugate to a strain measure E if T: Ė provides the rate of change of the internal energy per unit reference volume of the body in an adiabatic process. The applications of the conjugate stress and strain measures are in the development of the basic relations in nonlinear analysis of solids. In this paper using eigenprojection method, unified explicit basis-free relation between two arbitrary stress tensors T (f) and T (g) , respectively conjugate to two measures of Hill’s strains is determined. The result is valid for arbitrary dimension of the Euclidean inner product space and for all cases of distinct and repeated eigenvalues of the right stretch tensor U .

Copyright © 2006 by ASME
Topics: Stress tensors

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