×

On conservation laws in viscoelastostatics. (English) Zbl 0581.73042

(Author’s summary.) Noether’s theorem on variational principles in which the associated functionals are invariant under a group of infinitesimal transformations is used to establish conservation laws associated with linear viscoelastostatics. One of them may be regarded as a viscoelastic generalization of Rice’s J-integral in elasticity. In addition, those conservation laws are discussed briefly in physics.
Reviewer: G.A.C.Graham

MSC:

74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
74S30 Other numerical methods in solid mechanics (MSC2010)
74B99 Elastic materials
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Knowles, J. K., Sternberg, E.: On a class of conservation laws in linearized and finite elasticity. Archive for Rational Mechanics and Analysis44, 187-211 (1972). · Zbl 0232.73017 · doi:10.1007/BF00250778
[2] Fletcher, D. C.: Conservation laws in linear elastodynamics. Archive for Rational Mechanics and Analysis60, 329-353 (1976). · Zbl 0353.73024 · doi:10.1007/BF00248884
[3] Noether, E.: Invariante Variationsprobleme. Göttinger Nachrichten, Mathematischphysikalische Klasse2, 235-257 (1918). · JFM 46.0770.01
[4] Rice, J. R.: A path independent integral and approximate analysis of strain concentrations by notches and cracks. Journal of Applied Mechanics35, 379-386 (1968).
[5] Gurtin, M. E.: Variational principles of elastodynamics. Archive for Rational Mechanics and Analysis16, 34-50 (1964). · Zbl 0124.40001 · doi:10.1007/BF00248489
[6] Budiansky, B., Rice, J. R.: Conservation laws and energy-release rates. Journal of Applied Mechanics40, 201-203 (1973). · Zbl 0261.73059 · doi:10.1115/1.3422926
[7] Gurtin, M. E., Sternberg, E.: On the linear theory of viscoelasticity. Archive for Rational Mechanics and Analysis11, 291-356 (1963). · Zbl 0107.41007 · doi:10.1007/BF00253942
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.