The Effect of Microstructure Size on Bar Cross-Sectional Area Changes in Elastic Tensile Deformation

Abstract

In classical elasticity, the displacement, strain and stress are homogeneous and the analysis of the tensile bar is based on the initial cross-sectional area of the bar specimen which is assumed constant for a restricted small uniform deformation. However, in experimental mechanics, tested specimens often present inhomogeneous strain distribution and it is usually difficult to obtain reliable measurement values in the presence of high strain gradient.
In this paper the analysis of the tensile deformation of the bar within the elastic regime is based on the gradient elasticity theory, which includes higher order strain gradient terms and an internal length scale in the constitutive stress-strain relation. Thus, a relation is established between the macro-scale and micro-scale deformation of the bar which results in inhomogeneous displacement, strain and stress. Hence, unlike in the classical elasticity theory by imposing a displacement controlled deformation, the effect of changes in the microstructure dimension is reflected in the bar cross-sectional area. Thus, it is shown to be non-uniform in contrast to the classical elasticity assumption and to also exhibit size and scale dependence response.
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