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Constitutive equations for porous plane-strain gradient elasticity obtained by homogenization

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Abstract

This paper addresses the problem of plane-strain gradient elasticity models derived by higher-order homogenization. A microstructure that consists of cylindrical voids surrounded by a linear elastic matrix material is considered. Both plane-stress and plane-strain conditions are assumed and the homogenization is performed by means of a cylindrical representative volume element (RVE) subjected to quadratic boundary displacements. The constitutive equations for the equivalent medium at the macroscale are obtained analytically by means of the Airy’s stress function in conjunction with Fourier series. Furthermore, a failure criterion based on the maximum hoop stress on the void surface is formulated. A mixed finite-element formulation has been implemented into the commercial finite-element program Abaqus. Using the constitutive relations derived, numerical simulations were performed in order to compute the stress concentration at a hole with varying parameters of the constitutive equations. The results predicted by the model are discussed in comparison with the results of the theory of simple materials.

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Authors and Affiliations

  1. Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, 09596, Freiberg, Germany

    Lutz Zybell, Uwe Mühlich & Meinhard Kuna

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  1. Lutz Zybell
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  2. Uwe Mühlich
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  3. Meinhard Kuna
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Correspondence to Uwe Mühlich.

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Zybell, L., Mühlich, U. & Kuna, M. Constitutive equations for porous plane-strain gradient elasticity obtained by homogenization. Arch Appl Mech 79, 359–375 (2009). https://doi.org/10.1007/s00419-008-0238-1

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  • DOI: https://doi.org/10.1007/s00419-008-0238-1

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