Vol. 3, No. 3, 2015

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On the constitutive equations of viscoelastic micropolar plates and shells of differential type

Holm Altenbach and Victor A. Eremeyev

Vol. 3 (2015), No. 3, 273–283
DOI: 10.2140/memocs.2015.3.273

Within the framework of the micropolar theory of continuum we discuss the constitutive equations of viscoelastic micropolar thin-walled structures, i.e. viscoelastic micropolar plates and shells. Starting from the linear viscoelastic micropolar continuum and using the correspondence principle of the linear viscoelasticity we extend the procedure of reduction of three-dimensional equilibrium equations of elastic shell-like solids to the case of viscoelastic behavior. We restricted ourselves by constitutive equations of differential type. In other words, we consider both 2D and 3D constitutive equations which are linear dependencies between certain set of time derivatives of stress and strain measures.

micropolar plate, Cosserat continuum, viscoelasticity, through-the-thickness integration, constitutive equations
Mathematical Subject Classification 2010
Primary: 74A35
Secondary: 74K20, 74K25, 74D05, 74A20
Received: 14 April 2015
Revised: 12 August 2015
Accepted: 8 October 2015
Published: 11 October 2015

Communicated by Francesco dell'Isola
Holm Altenbach
Chair of Engineering Mechanics
Institute of Mechanics, Faculty of Mechanical Engineering
Universitätsplatz 1
39106 Magdeburg
Victor A. Eremeyev
Department of Applied Mechanics and Robotics
Rzeszow University of Technology
al. Powstańców Warszawy, 8
35-959, Rzeszów