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Size-dependent nonlinear response of thin elastic films with nano-scale thickness. (English) Zbl 1098.74640
Summary: The paper aims at modeling the size-dependent geometrically nonlinear response of thin elastic films with nano-scale thickness based on a continuum approach. The film is assumed elastically isotropic, and the Kirchhoff’s hypothesis is adopted to approximate the deformation kinematics. By using Hamilton’s principle, we derive the governing equations and associated boundary conditions for the films incorporating nonlinearity in von Karman’s sense. The model is then applied to analyze the bending, buckling and vibration of simply supported micro- and nano-films in plane strains. Differing from the results predicted by the conventional plate theory neglecting surface effect, the proposed model and solutions involve intrinsic length scales. Consequently, the new model leads to the conclusion that the static and dynamic responses of micro- and nano-film are scaling dependent. The significance of surface effect is more profound for smaller scales.

MSC:
74K35 Thin films
74G60 Bifurcation and buckling
74H45 Vibrations in dynamical problems in solid mechanics
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