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Modeling size-dependent thermo-mechanical behaviors of shape memory polymer Bernoulli-Euler microbeam

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Abstract

The objective of this paper is to model the size-dependent thermo-mechanical behaviors of a shape memory polymer (SMP) microbeam. Size-dependent constitutive equations, which can capture the size effect of the SMP, are proposed based on the modified couple stress theory (MCST). The deformation energy expression of the SMP microbeam is obtained by employing the proposed size-dependent constitutive equation and Bernoulli-Euler beam theory. An SMP microbeam model, which includes the formulations of deflection, strain, curvature, stress and couple stress, is developed by using the principle of minimum potential energy and the separation of variables together. The size-dependent thermo-mechanical and shape memory behaviors of the SMP microbeam and the influence of the Poisson ratio are numerically investigated according to the developed SMP microbeam model. Results show that the size effects of the SMP microbeam are significant when the dimensionless height is small enough. However, they are too slight to be necessarily considered when the dimensionless height is large enough. The bending flexibility and stress level of the SMP microbeam rise with the increasing dimensionless height, while the couple stress level declines with the increasing dimensionless height. The larger the dimensionless height is, the more obvious the viscous property and shape memory effect of the SMP microbeam are. The Poisson ratio has obvious influence on the size-dependent behaviors of the SMP microbeam. The paper provides a theoretical basis and a quantitatively analyzing tool for the design and analysis of SMP micro-structures in the field of biological medicine, microelectronic devices and micro-electro-mechanical system (MEMS) self-assembling.

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Authors and Affiliations

  1. College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao, Shandong Province, 266580, China

    Bo Zhou, Xueyao Zheng, Zetian Kang & Shifeng Xue

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  1. Bo Zhou
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  2. Xueyao Zheng
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  3. Zetian Kang
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  4. Shifeng Xue
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Correspondence to Bo Zhou.

Additional information

Citation: ZHOU, B., ZHENG, X. Y., KANG, Z. T., and XUE, S. F. Modeling size-dependent thermomechanical behaviors of shape memory polymer Bernoulli-Euler microbeam. Applied Mathematics and Mechanics (English Edition), 40(11), 1531–1546 (2019) https://doi.org/10.1007/s10483-019-2540-5

Project supported by the National Key Research and Development Program of China (No. 2017YFC0307604), the Talent Foundation of China University of Petroleum (No. Y1215042), and the Graduate Innovation Program of China University of Petroleum (East China) (No. YCX2019084)

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Zhou, B., Zheng, X., Kang, Z. et al. Modeling size-dependent thermo-mechanical behaviors of shape memory polymer Bernoulli-Euler microbeam. Appl. Math. Mech.-Engl. Ed. 40, 1531–1546 (2019). https://doi.org/10.1007/s10483-019-2540-5

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  • DOI: https://doi.org/10.1007/s10483-019-2540-5

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Chinese Library Classification

2010 Mathematics Subject Classification

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