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An analytical investigation of elastic–plastic behaviors of 3D warp and woof auxetic structures

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Abstract

The present paper was conducted to calculate Young's modulus and Negative Poisson's ratio (NPR) of a warp and woof (WAW) 3D auxetic structure in three perpendicular directions using an analytical method under uniaxial loading and considering the elastic–plastic behavior of materials. Due to the periodic pattern of the auxetic structure, a unit cell was chosen as a representative volume element (RVE) and its mechanical properties were assessed by developing analytical formulations in the elastic region. To this end, the principle of virtual work along with the concept of lumped plasticity (plastic hinges) were utilized. For validating the proposed analytical model, the 3D finite element (FE) simulations were used. Fairly good correlations were found between the present analytical results and the results of FE simulations. Subsequently, the effects of parameters, such as the initial re-entrant (IRE) angle, the cell thickness, and the auxetic cell aspect ratio on the mechanical properties were investigated. The obtained results revealed that with the increase in the IRE angle, NPR increases in the vertical direction and decreases in two other horizontal directions; it also increases the cell stiffness in three perpendicular directions. The thickness of cell walls does not alter NPR, yet relatively increases the cell stiffness. Furthermore, it was found that the cell aspect ratio has an important role in the mechanical properties of WAW auxetic structures.

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Acknowledgments

This paper was supported by the Iran National Science Foundation: INSF under the research grant No. 99002114.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Hakim Sabzevari University, 9617976487, Sabzevar, Iran

    Mohammad Shoja-Senobar & Ehsan Etemadi

  2. Department of Civil Engineering, Hakim Sabzevari University, 9617976487, Sabzevar, Iran

    M. Lezgy-Nazargah

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  1. Mohammad Shoja-Senobar
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  2. Ehsan Etemadi
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  3. M. Lezgy-Nazargah
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Correspondence to Ehsan Etemadi.

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Shoja-Senobar, M., Etemadi, E. & Lezgy-Nazargah, M. An analytical investigation of elastic–plastic behaviors of 3D warp and woof auxetic structures. Int J Mech Mater Des 17, 545–561 (2021). https://doi.org/10.1007/s10999-021-09546-w

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  • DOI: https://doi.org/10.1007/s10999-021-09546-w

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