Journal of Elasticity

, Volume 133, Issue 2, pp 223–252 | Cite as

Finite Third-order Gradient Elasticity and Thermoelasticity

  • Jörg Christian ReiherEmail author
  • Albrecht Bertram


A constitutive format for the third-order gradient elasticity is suggested. It includes both isotropic and anisotropic non-linear behavior under finite deformations. Appropriate invariant stress and strain variables are introduced, which allow for reduced forms of the elastic energy law that identically fulfill the objectivity requirement. After working out the transformation behavior under a change of the reference placement, the symmetry transformations for third-order materials can be introduced. After the mechanical third-order theory, an extension to thermoelasticity is given, and necessary and sufficient conditions are derived from the Clausius-Duhem inequality.


Third-order elasticity Second strain gradient elasticity Finite gradient elasticity 

Mathematics Subject Classification (2000)

74A99 74B20 



Jörg Christian Reiher’s position as a PhD-student has been funded by the German Research Foundation, Graduiertenkolleg 1554: Micro-Macro-Interactions in structured Media and Particle Systems.

Conflict of interest

The authors declare that they have no conflict of interest.


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Authors and Affiliations

  1. 1.Institut für MechanikOtto-von-Guericke-Univ.MagdeburgGermany

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