Couple Stress Theory in Functionally Graded Microbeams
Summary
Couple stress theory extends classical continuum mechanics by incorporating a material length scale parameter that captures size-dependent stiffening in micro- and nano-structures. In functionally graded microbeams, material properties vary through the thickness—often following a power-law distribution—so that strength, stiffness and thermal response can be tailored. Classical beam theories neglect microscale effects and thus underestimate bending rigidity, buckling loads and natural frequencies when beam dimensions approach the internal material length. By introducing additional stress measures associated with material microstructure, couple stress formulations yield enriched governing equations, typically derived via Hamilton’s principle. These equations describe how gradient profiles and scale parameters jointly influence static bending, postbuckling behaviour, free vibration characteristics and dynamic stability. Both analytical approaches—such as modified third-order beam theories—and numerical implementations—including finite element models—have demonstrated enhanced accuracy in predicting the interplay between gradation and size effects, thereby guiding the design of advanced microelectromechanical systems.
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Couple Stress Theory in Functionally Graded Microbeams publication trend
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Technical terms
Couple Stress Theory: A continuum mechanics extension introducing additional stress measures and a length scale parameter to account for size-dependent mechanical behaviour in small-scale structures.
Functionally Graded Material (FGM): A composite whose material properties change continuously over volume—commonly through thickness—to optimise performance under thermal or mechanical loading.
Material Length Scale Parameter: A constitutive constant in couple stress theory quantifying the influence of microstructural size on the deformation and stiffness of beams at the microscale.
Power-law Distribution: A mathematical function describing how material properties vary spatially in an FGM, typically following the form property ∝ (coordinate)n for a chosen exponent n.
Microbeam: A beam with one or more dimensions on the order of micrometres, where classical continuum models fail to capture observed stiffening and size effects.
References
- Modified couple stress-based third-order theory for nonlinear analysis of functionally graded beams. Latin American Journal of Solids and Structures (2014).
- Application of Modified Couple-Stress Theory to Nonlinear Vibration Analysis of Nanobeam with Different Boundary Conditions. Journal of Vibration Engineering & Technologies (2024).
- Bimodular Microbeams Based on the Elastic Foundation: Free Vibration. Journal of Physics Conference Series (2023).
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