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On the strain-energy density in linear elasticity

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Summary

Standard results from matrix theory are used to derive optimal upper and lower bounds for the strain-energy density in terms of the norm of the stress tensor in two and three dimensions. The approach also yields directly necessary and sufficient conditions for positive-definiteness.

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References

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Author notes

  1. C. O. Horgan

    Present address: School of Mathematics and Physics, University of East Anglia, Norwich, England

Authors and Affiliations

  1. Department of Engineering Mechanics, The University of Michigan, Ann Arbor, Michigan, USA

    C. O. Horgan

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  1. C. O. Horgan
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Horgan, C.O. On the strain-energy density in linear elasticity. J Eng Math 7, 231–234 (1973). https://doi.org/10.1007/BF01535284

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  • DOI: https://doi.org/10.1007/BF01535284

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