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Stability of strain gradient elastic bars in tension

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An Erratum to this article was published on 21 March 2008

Abstract

Equilibrium of a bar under uniaxial tension is considered as optimization problem of the total potential energy. Uniaxial deformations are considered for a material with linear constitutive law of strain second gradient elasticity. Applying tension on an elastic bar, necking is shown up in high strains. That means the axial strain forms two homogeneously deformed sections in the ends of the bars and a section in the middle with high variable strain. The interactions of the intrinsic (material) lengths with the non linear strain displacement relations develop critical states of bifurcation with continuous Fourier’s spectrum. Critical conditions and post-critical deformations are defined with the help of multiple scales perturbation method.

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Authors and Affiliations

  1. Mechanics Division, School of Applied Sciences, National Technical University of Athens, Zografou Campus, Athens, 157 73, Greece

    D. G. Bakogianni & K. A. Lazopoulos

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  1. D. G. Bakogianni
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  2. K. A. Lazopoulos
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Correspondence to K. A. Lazopoulos.

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An erratum to this article can be found at http://dx.doi.org/10.1007/s11590-008-0081-x

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Bakogianni, D.G., Lazopoulos, K.A. Stability of strain gradient elastic bars in tension. Optimization Letters 1, 407–420 (2007). https://doi.org/10.1007/s11590-006-0039-9

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