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A new modified couple stress theory for anisotropic elasticity and microscale laminated Kirchhoff plate model

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Abstract

A new modified couple stress theory for anisotropic elasticity is proposed. This theory contains three material length scale parameters. Differing from the modified couple stress theory, the couple stress constitutive relationships are introduced for anisotropic elasticity, in which the curvature (rotation gradient) tensor is asymmetric and the couple stress moment tensor is symmetric. However, under isotropic case, this theory can be identical to modified couple stress theory proposed by Yang et al. (Int J Solids Struct 39:2731–2743, 2002). The differences and relations of standard, modified and new modified couple stress theories are given herein. A detailed variational formulation is provided for this theory by using the principle of minimum total potential energy. Based on the new modified couple stress theory, composite laminated Kirchhoff plate models are developed in which new anisotropic constitutive relationships are defined. The First model contains two material length scale parameters, one related to fiber and the other related to matrix. The curvature tensor in this model is asymmetric; however, the couple stress moment tensor is symmetric. Under isotropic case, this theory can be identical to the modified couple stress theory proposed by Yang et al. (Int J Solids Struct 39:2731–2743, 2002). The present model can be viewed as a simplified couple stress theory in engineering mechanics. Moreover, a more simplified model of couple stress theory including only one material length scale parameter for modeling the cross-ply laminated Kirchhoff plate is suggested. Numerical results show that the proposed laminated Kirchhoff plate model can capture the scale effects of microstructures.

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Authors and Affiliations

  1. Key Laboratory of Liaoning Province for Composite Structural Analysis of Aerocraft & Simulation, Shenyang Aerospace University, Shenyang, 110136, LN, People’s Republic of China

    Wanji Chen & Xiaopeng Li

Authors
  1. Wanji Chen
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  2. Xiaopeng Li
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Correspondence to Wanji Chen.

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Contract/grant sponsor: National Natural Sciences Foundation of China(No. 11072156).

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Chen, W., Li, X. A new modified couple stress theory for anisotropic elasticity and microscale laminated Kirchhoff plate model. Arch Appl Mech 84, 323–341 (2014). https://doi.org/10.1007/s00419-013-0802-1

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  • DOI: https://doi.org/10.1007/s00419-013-0802-1

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