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Deformation of beams in the grade consistent theory of microstretch elastic solids

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Abstract

A microstretch continuum is a material with microstructure in which the microelements can stretch and contract independently of their translations and rotations. This paper is concerned with the grade consistent theory of microstretch elastic solids, where the second-order displacement is added to the classical set of independent constitutive variables. We study the equilibrium of a homogeneous and isotropic elastic beam loaded by tractions distributed over its plane ends. First, the problem of bending and extension is investigated. It is shown that the solution of the problem can be expressed in terms of solutions of three plane strain problems. Then, we study the problem of torsion in the framework of the grade consistent theory of microstretch elastic solids. This problem is solved with the help of three torsion functions. The results are used to investigate the torsion of a right circular cylinder.

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  1. “Octav Mayer” Institute of Mathematics, Romanian Academy, Bd. Carol I, nr. 8, 700506, Iaşi, Romania

    D. Ieşan

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  1. D. Ieşan
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Ieşan, D. Deformation of beams in the grade consistent theory of microstretch elastic solids. Acta Mech 231, 1351–1363 (2020). https://doi.org/10.1007/s00707-019-02590-w

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  • DOI: https://doi.org/10.1007/s00707-019-02590-w

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