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When the cantilever beam thickness is scaled down to micron, the dimension of material and the intrinsic length scale affect the mechanical behavior of the beam. The purpose of this paper is analyzing the bending of cantilever micro-beam and presenting an exact relation for the beam deflection using Chen-Wang gradient plasticity theory. To this end, the Euler-Bernoulli beam theory is utilized to model a micro-beam and three cases including elastic, rigid-plastic and elasto-plastic beams are considered. Clear relations for elastic and plastic strains are given. For all mentioned cases, the beam deflection is determined for different intrinsic lengths and the obtained results are compared with each other and the data obtained from experimental tests and some explanations are presented. The results obtained from classical theory are also shown in the results section to prove that classical theories don’t have the capability to predict behavior of micron-size structures precisely. Numerical results clarify the dependence of responses to the range of dimensions and intrinsic lengths. The comparison between present results and those observed from experimental tests authenticate the reliability of utilized gradient theory.

Keywords: Strain Gradient Plasticity, Micro Cantilever Beam, Bending, Intrinsic Length Scale, Chen-Wang Theory

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