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Volume 1, 2003
International Journal for Multiscale Computational Engineering
Developing a Novel Finite Elastic Approach in Strain Gradient Theory for Microstructures
Department of Mechanical Engineering, Islamic Azad University of Kerman Branch, Kerman, Iran
Young Researchers Club, Kerman branch, Islamic Azad University, Kerman, Iran
Size-dependent effects can significantly be indicated in experimental deformation of microstructures. In accordance with statistic behavior of size-dependent parameters, it is predictable that finite deformation and nonlinear forms of equations may obtain more appropriate computational results for microstructures. In this paper, classic couple stress theory is used to explain size dependency in strain gradient theory. Based on results obtained from couple stress in strain gradient theory, the theory is extended in nonlinear form. In this case, a length scale parameter is used in this model as a Lagrangian coefficient and a strain gradient is attested in a classic constitutive equation as a constraint. Finally, a nonlinear form of equation is used for a cylinder in micron order subjected to torsion, and results are compared with a linear model, the model expressed by Yang et al. (Int. J. Solids Struct., 39, pp. 2731-2743, 2002), and the finite element model of bone.
Chong, A. C. M. and Lam, D. C. C.,
Strain gradient plasticity effect in indentation hardness of polymers.
Chong, A. C. M., Yang, F., Lam, D. C. C., and Tong, P.,
Torsion and bending of micron-scaled structures.
Clarke, D. R. and Ma, Q.,
Size dependent hardness of silver single crystals.
Fleck, N. A., Muller, G. M., Ashby, M. F., and Hutchinson, J. W.,
Strain gradient plasticity: Theory and experiment.
Fleck, N. A. and Hutchinson, J. W,
Strain gradient plasticity.
Hori, M. and Nemat-Nasser, S.,
On two micromechanics theories for determining microâ€“macro relations in heterogeneous solids.
Nix, W. D.,
Mechanical properties of thin films.
Ogden, R. W.,
Non-Linear Elastic Deformations.
Papargyri-Beskou, S. and Beskos, D.,
Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates.
Park, S. K. and Gao, X. L.,
Bernoulliâ€“Euler beam model based on a modified couple stress theory.
Peerlings, R. H. J. and Fleck, N. A.,
Computational evaluation of strain gradient elasticity constants.
Poole, W. J., Ashby, M. F., and Fleck, N. A.,
Micro-hardness of annealed and work-hardened copper polycrystals.
Sansour, C. and Skatulla, S.,
A strain gradient generalized continuum approach for modeling elastic scale effects.
Stelmashenko, N. A., Walls, M. G., Brown, L. M., and Milman, Y. V.,
Microindentations onWand Mo oriented single crystals: An STM study.
Steolken, J. S. and Evans, A. G.,
A microbend test method for measuring the plasticity length scale.
Yang, F., Chong, A. C. M., Lam, D. C. C., and Tong, P.,
Couple stress based strain gradient theory for elasticity.