Saint-Venant End Effects for Materials With Negative Poisson’s Ratios

Abstract

In this paper we analyze Saint-Venant end effects for materials with negative Poisson ’s ratios. We present an example of slow decay of stress arising from selfequilibrated stress at the end of a circular cylinder of elastic material with a negative Poisson’s ratio. By contrast, a sandwich panel containing rigid face sheets and a compliant core exhibits no anomalous effects for negative Poisson’s ratio, but exhibits slow stress decay for core Poisson’s ratio approaching 0.5. In sandwich panels with stiff but not perfectly rigid face sheets, slow decay of stress is known to occur; a negative Poisson’s ratio results in end stress decay, which is faster than it would be otherwise.

Analytical parametric analysis of the contact problem of human buttocks and negative Poisson's ratio foam cushions

“…Such foams can exhibit negative Poisson's ratio as small as À0.7 for polymer foams, and À0.8 for metal foams. For potential applications, the design considerations (Lakes, 1993) on stress concentrations, Saint Venant's effects (Lakes, 1992), and stress distributions and curvatures in bending problems with negative Poisson's ratio materials have been clearly pointed out. As for seat cushions, the fabrication process has been scaled up to cushion size by Loureiro and Lakes (1997), Lowe and Lakes (2000) experimentally concluded that the contact pressure distribution decreases as sample density decreases for both conventional and re-entrant foams.…”

Minimizing specimen length in elastic testing of end-constrained cancellous bone

“…For an isotropic solid in tension or compression, the decay length is usually equivalent to the maximum cross-sectional dimension; however, the decay length is not determined by macroscopic specimen dimensions alone. Shorter decay lengths occur in thin-walled cylinders (Stephen and Wang, 1992) and piezo-electric materials (Borrelli and Patria, 1999), whereas longer lengths are reported for anisotropic materials (Arridge and Folkes, 1976), composites (Horgan, 1982) and negative Poisson's ratio foams (Lakes, 1992). Since the present study showed that the extensometer can be placed much closer to the loaded ends than would be expected based on the macroscopic specimen diameters, it appears that the very short decay length found in cancellous bone is controlled by a much smaller characteristic dimension, reported here as about four trabecular units.…”

Determination of maximum negative Poisson's ratio for laminated fiber composites

“…Rechtsman et al [5] used a Lennard-Jones potential approach [6] to derive a condition for two-dimensional many-body systems to investigate their auxetic behaviors. Characterizing the mechanical properties of materials with NPR can be done for various goals [7]. Chen and Lakes [8] studied the Saint-Venant effect for those materials to magnify the role of Poisson's ratio in stress concentration at the constraint area.…”