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Frequency-dependent tensile and compressive effective moduli of elastic solids with distributed penny-shaped microcracks

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Abstract

This paper develops micromechanics models to estimate the tensile and compressive elastic moduli of elastic solids containing randomly distributed penny-shaped microcracks. The crack faces are open under tension and closed under compression. When the crack faces are closed, they may slide against one another following Coulomb’s law of dry friction. The micromechanics models provide analytical expressions of the tensile and compressive moduli for both static and dynamic cases. It is found that the tensile and compressive moduli are different. Further, under dynamic loading, both compressive and tensile moduli are frequency dependent. As a by-product, the micromechanics models also predict wave attenuation in the dynamic case. Numerical simulations using the finite element method are conducted to validate the micromechanics models.

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Authors and Affiliations

  1. School of Civil Engineering, Southwest Jiaotong University, Chengdu, 610031, China

    Youxuan Zhao & Yanjun Qiu

  2. Department of Civil and Environmental Engineering, Department of Mechanical Engineering, Northwestern University, Evanston, IL, 60208, USA

    Youxuan Zhao & Jianmin Qu

  3. College of Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0360, USA

    Laurence J. Jacobs

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  1. Youxuan Zhao
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  2. Yanjun Qiu
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  3. Laurence J. Jacobs
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  4. Jianmin Qu
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Correspondence to Jianmin Qu.

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Zhao, Y., Qiu, Y., Jacobs, L.J. et al. Frequency-dependent tensile and compressive effective moduli of elastic solids with distributed penny-shaped microcracks. Acta Mech 227, 399–419 (2016). https://doi.org/10.1007/s00707-015-1450-z

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  • DOI: https://doi.org/10.1007/s00707-015-1450-z

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