![]() Lord in Macmillan's Chemical and Physical Data, Macmillan, London, UK, 1992. Krieger, Malabar FL, second edition, 1983. Sokolnikoff, Mathematical theory of elasticity. the resonant ultrasound studies in, provide cross-checking comparison of multiple vibration mode frequencies confirms the modulus and Poisson's ratio follow linear isotropic elasticity. In a large compilation of properties of polycrystalline materials, most have Poisson's ratio in the vicinity of 1/3. Poisson's ratio of the elements are, unless otherwise cited, via Web Elements, which adduce references. Poisson's ratio in various materials: table of Poisson's ratio Objects constrained at the surface can have a Poisson's ratio outside the above range and be stable. ![]() ![]() Physically the reason is that for the material to be stable, the stiffnesses must be positive the bulk and shear stiffnesses are interrelated by formulae which incorporate Poisson's ratio. The theory of isotropic linear elasticity allows Poisson's ratios in the range from -1 to 1/2 for an object with free surfaces with no constraint. also further details.įurther interrelations among elastic constants for isotropic solids are as follows. Stress is force per unit area, with the direction of both the force and the area specified. The elastic moduli are measures of stiffness. Poisson's ratio is related to elastic moduli K (also called B), the bulk modulus G as the shear modulus and E, Young's modulus, by the following (for isotropic solids, those for which properties are independent of direction). Poisson's ratio: relation to elastic moduli in isotropic solids Negative Poisson's ratio in designed materials and in some anisotropic materials is by now well known. Stretching of yellow honeycomb by vertical forces, shown on the right, illustrates the concept. In the structural view, the reason for the usual positive Poisson's ratio is that inter-atomic bonds realign with deformation. The reason why, in the continuum view, is that most materials resist a change in volume as determined by the bulk modulus K (also called B) more than they resist a change in shape, as determined by the shear modulus G. Virtually all common materials, such as the blue rubber band on the right, become narrower in cross section when they are stretched. Strain e is defined in elementary form as the change in length divided by the original length. If your browser does not interpret Symbol font properly, Greek nu, n may instead look like a boldįace Latin n. Poisson's ratio, also called Poisson ratio or the Poisson coefficient, or coefficient de Poisson, is usually represented as a lower case Greek nu, n. The definition of Poisson's ratio contains a minus sign so that normal materials have a positive ratio. Tensile deformation is considered positive and compressive deformation is considered negative. Poisson's ratio is the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force.
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