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Plane-Strain Problems for a Class of Gradient Elasticity Models—A Stress Function Approach

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Abstract

The plane strain problem is analyzed in detail for a class of isotropic, compressible, linearly elastic materials with a strain energy density function that depends on both the strain tensor ε and its spatial gradient ∇ε. The appropriate Airy stress-functions and double-stress-functions are identified and the corresponding boundary value problem is formulated. The problem of an annulus loaded by an internal and an external pressure is solved.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Thessaly, Volos, 38334, Greece

    Nikolaos Aravas

  2. The Mechatronics Institute, Center for Research and Technology—Thessaly (CERETETH), 1st Industrial Area, Volos, 38500, Greece

    Nikolaos Aravas

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  1. Nikolaos Aravas
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Correspondence to Nikolaos Aravas.

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The paper is dedicated to the memory of Professor Donald Carlson.

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Aravas, N. Plane-Strain Problems for a Class of Gradient Elasticity Models—A Stress Function Approach. J Elast 104, 45–70 (2011). https://doi.org/10.1007/s10659-011-9308-7

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  • DOI: https://doi.org/10.1007/s10659-011-9308-7

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