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A Review on Recent Advances in Micro and Nano Scale Beam Theories and the Relevant Areas of Applied Solid Mechanics
The present paper reports a review on several aspects associated with advancement in beam theories to predict size dependent mechanical behavior of micro and nano scale beam. Inherent geometric nonlinearity of large deflection couples with complicated material behavior of micro and nano sized beams, and makes such small scale beam problem very complicated. Hence, proper modeling of constitutive behavior and solution of nonlinear partial differential equation are the two major components in analysis of micro and nano beam. Developments in the two areas from classical to modern higher order approaches are critically reviewed in the paper. Several constitutive relations used to model material behavior of small scale beam and the frequently used analysis methods in association with computational solution schemes to solve nonlinear system governing equation are identified and presented in the paper. Increasing trend of using miniature devices and non-metallic materials leads towards several class of micro and nano beam problems according to application. The problems are not only limited to common beam problem like bending, vibration, static and dynamic stability, but also includes several interdisciplinary areas like fracture mechanics, bio-mechanics, molecular dynamics, material science, etc. Hence in addition to material modeling and analysis methods, type of problem encountered in literature and application areas together with experimental works on micro and nano sized beam like structures are also addressed in the review paper.
Micro/Nano Beam, Size Dependent Deformation, Geometric Nonlinearity, Higher Order Continuum Mechanics, Constitutive Relation, Couple Stress Theory, Strain Gradient Theory, Nonlocal Theory.
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