Type

Journal Article

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Subjects
Topics
non linear incompressible elasticity experimental data incompressible elasticity non linear shear coe cient flexure non linearity second order first order

#### Onset of non-linearity in the elastic bending of blocks (2013)

Abstract The classical flexure problem of non-linear incompressible elasticity is revisited assuming that the bending angle suffered by the block is specified instead of the usual applied moment. The general moment-bending angle relationship is then obtained and is shown to be dependent on only one non-dimensional parameter: the product of the aspect ratio of the block and the bending angle. A Maclaurin series expansion in this parameter is then found. The first-order term is proportional to $\mu$, the shear modulus of linear elasticity; the second-order term is identically zero, because the moment is an odd function of the angle; and the third-order term is proportional to $\mu(4\beta -1)$, where $\beta$ is the non-linear shear coefficient, involving third-order and fourth-order elasticity constants. It follows that bending experiments provide an alternative way of estimating this coefficient, and the results of one such experiment are presented. In passing, the coefficients of Rivlin's expansion in exact non-linear elasticity are connected to those of Landau in weakly (fourth-order) non-linear elasticity.
Collections Ireland -> National University of Ireland Galway -> Mathematics
Ireland -> National University of Ireland Galway -> School of Mathematics, Statistics and Applied Mathematics
Ireland -> National University of Ireland Galway -> Mathematics (Scholarly Articles)
Ireland -> National University of Ireland Galway -> College of Science