On the spectral analysis of residual stress in finite elasticity

M. H.B.M. Shariff, R. Bustamante, J. Merodio

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


In the literature, residual stress problems are generally formulated using classical invariants despite most of them having an unclear physical meaning and not having experimental advantages. In this article, we give an alternative formulation for residual stress problems using a set of spectral invariants. These invariants have a clear physical meaning which may facilitate the design of a residual stress experiment. For the case of an energy function that depends on the right Cauchy tensor and the residual stress tensor, we show that only nine of the classical invariants are independent, not 10 as commonly assumed. Details of the spectral formulation are given and several boundary value problems are illustrated.

Original languageBritish English
Pages (from-to)656-680
Number of pages25
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Issue number3
StatePublished - 2017


  • Invariants
  • Residual stresses
  • Spectral invariants


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