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2021, Volume 15, Issue 2

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Frontiers of Structural and Civil Engineering >> 2021, Volume 15, Issue 2 doi: 10.1007/s11709-021-0707-y

Size effects in two-dimensional layered materials modeled by couple stress elasticity

. Applied Mechanics and Structures Research Unit, Department of Civil Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand.. Department of Civil Engineering, University of Thessaly, Pedion Areos, Volos GR-38334, Greece.. Faculty of Civil Engineering, Ho Chi Minh City University of Technology and Education, Ho Chi Minh 721400, Vietnam.. Department of Civil Engineering, Faculty of Engineering, Prince of Songkla University, Songkla 90110, Thailand

Received: 2021-03-26 Accepted: 2021-04-30 Available online: 2021-04-30
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Abstract

In the present study, the effect of material microstructure on the mechanical response of a two-dimensional elastic layer perfectly bonded to a substrate is examined under surface loadings. In the current model, the substrate is treated as an elastic half plane as opposed to a rigid base, and this enables its applications in practical cases when the modulus of the layer (e.g., the coating material) and substrate (e.g., the coated surface) are comparable. The material microstructure is modeled using the generalized continuum theory of couple stress elasticity. The boundary value problems are formulated in terms of the displacement field and solved in an analytical manner via the Fourier transform and stiffness matrix method. The results demonstrate the capability of the present continuum theory to efficiently model the size-dependency of the response of the material when the external and internal length scales are comparable. Furthermore, the results indicated that the material mismatch and substrate stiffness play a crucial role in the predicted elastic field. Specifically, the study also addresses significant discrepancy of the response for the case of a layer resting on a rigid substrate.

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