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Mixture unified gradient theory: a consistent approach for mechanics of nanobars

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Abstract

The mixture unified gradient theory of elasticity is invoked for the meticulous assessment of peculiar size-dependent behavior of materials with nano-structural features. The size-dependency of the strain gradient theory and the stress gradient theory is consistently integrated with the classical continuum theory within a variational elasticity framework. The boundary-value problem associated with the dynamics of the nano-scale elastic bar is determined and enriched with the proper form of the extra non-standard boundary conditions. The constitutive model of the resultant fields is cast as differential relations in view of the stationarity of the proposed functional. The efficacy of the established generalized continuum theory in the accurate description of the size-effects at the ultra-small scale is put into evidence via electrostatic and elastodynamic analysis of nanobars. The nanoscopic characteristics of the wave dispersion are analytically addressed and appropriately compared with the counterpart experimental measurements. The elastostatic size-dependent behavior of nanobars is rigorously examined by applying an efficacious solution approach. Size-dependent elastostatic response of nanobars with kinematic constraints of interest in nano-mechanics are analytically determined and graphically illustrated. A promising approach to tackling the statics and dynamics of structural bar-type modules of advanced nano-systems is introduced.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    S. Ali Faghidian

  2. Faculty of Mechanical Engineering, Bialystok University of Technology, Białystok, Poland

    Krzysztof Kamil Żur

  3. Institute of Structural Mechanics, Bauhaus-Universität Weimar, Marienstr. 15, 99423, Weimar, Germany

    Timon Rabczuk

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  1. S. Ali Faghidian
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Faghidian, S.A., Żur, K.K. & Rabczuk, T. Mixture unified gradient theory: a consistent approach for mechanics of nanobars. Appl. Phys. A 128, 996 (2022). https://doi.org/10.1007/s00339-022-06130-7

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