The classical flexure problem of nonlinear 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 nondimensional 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 , 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 , where is the nonlinear 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 nonlinear elasticity are connected to those of Landau in weakly (fourth-order) nonlinear elasticity.
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November 2010
Research Papers
Onset of Nonlinearity in the Elastic Bending of Blocks
M. Destrade
,
M. Destrade
School of Electrical, Electronic, and Mechanical Engineering,
michel.destrade@ucd.ie
University College Dublin
, Belfield, Dublin 4, Ireland
Search for other works by this author on:
M. D. Gilchrist
,
M. D. Gilchrist
School of Electrical, Electronic, and Mechanical Engineering,
University College Dublin
, Belfield, Dublin 4, Ireland
Search for other works by this author on:
J. G. Murphy
J. G. Murphy
Department of Mechanical Engineering,
Dublin City University
, Glasnevin, Dublin 9, Ireland
Search for other works by this author on:
M. Destrade
School of Electrical, Electronic, and Mechanical Engineering,
University College Dublin
, Belfield, Dublin 4, Irelandmichel.destrade@ucd.ie
M. D. Gilchrist
School of Electrical, Electronic, and Mechanical Engineering,
University College Dublin
, Belfield, Dublin 4, Ireland
J. G. Murphy
Department of Mechanical Engineering,
Dublin City University
, Glasnevin, Dublin 9, IrelandJ. Appl. Mech. Nov 2010, 77(6): 061015 (6 pages)
Published Online: September 1, 2010
Article history
Received:
March 6, 2009
Revised:
January 21, 2010
Online:
September 1, 2010
Published:
September 1, 2010
Citation
Destrade, M., Gilchrist, M. D., and Murphy, J. G. (September 1, 2010). "Onset of Nonlinearity in the Elastic Bending of Blocks." ASME. J. Appl. Mech. November 2010; 77(6): 061015. https://doi.org/10.1115/1.4001282
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Cited By
Discussion: “Creep of Metals at High Temperature in Bending” (Davis, E. A., 1938, ASME J. Appl. Mech., 5, pp. A29–A31)
J. Appl. Mech (December 1938)
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