Discussion of stress tensor nonuniqueness with application to nonuniform, particulate systems
The indeterminacy of the mechanical stress tensor has been noted in several developments of expressions for stress in a system of particles. It is generally agreed that physical quantities related to the stress tensor must be insensitive to this nonuniqueness, but there is no definitive prescription for insuring it. Kroener's tensor decomposition theorem is applied to the mechanical stress tensor [sup [sigma]][sub ij] to show that its complete determination requires specification of its incompatibility,'' [epsilon][sub ijk] [epsilon][sub lmn] [sup [partial derivative]][sub j] [sup [partial derivative]][sub m] [sup [sigma]][sub kn], in addition to its divergence, which is obtained from the momentum conservation relation. For a particulate system, stress tensor incompatibility is shown to vanish to recover the correct expression for macroscopically observable traction. This result removes concern about nonuniqueness without requiring equilibrium or arbitrarily-defined force lines.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE; USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 6372003
- Report Number(s):
- LA-UR-93-1968; CONF-9306167-1; ON: DE93014352
- Resource Relation:
- Journal Volume: 309; Conference: 14. international conference on high pressure science and technology and 1993 technical meeting of the topical group on shock compression of condensed matter, Colorado Springs, CO (United States), 28 Jun - 3 Jul 1993
- Country of Publication:
- United States
- Language:
- English
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