International Journal for Multiscale Computational Engineering

Developing a Novel Finite Elastic Approach in Strain Gradient Theory for Microstructures

ABSTRAKT

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.

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