Vol. 4, No. 1, 2016

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Gradient materials with internal constraints

Albrecht Bertram and Rainer Glüge

Vol. 4 (2016), No. 1, 1–15

The concept of internal constraints is extended to gradient materials. Here, interesting constraints can be introduced, such as pseudorigid ones. The stresses and the hyperstresses will be given by constitutive equations only up to reactive parts, which do no work during any compatible motion of the body. For the inclusion of thermodynamical effects, the theory is generalized to the case of thermomechanical constraints. Here one obtains reactive parts of the stresses, heat flux, entropy, and energy, which do not contribute to the dissipation. Some critical remarks on the classical concept of internal constraints are finally given. A method to introduce internal constraints in a natural way is described to overcome some conceptual deficiencies of the classical concept.

internal constraints, gradient materials, pseudorigidity
Mathematical Subject Classification 2010
Primary: 74A30
Received: 16 July 2015
Revised: 26 September 2015
Accepted: 8 November 2015
Published: 29 February 2016

Communicated by Francesco dell'Isola
Albrecht Bertram
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2
D-39106 Magdeburg
Rainer Glüge
Otto-von-Guericke-Universität Magdeburg
University of Magdeburg
Universitätsplatz 2
D-39106 Magdeburg