Poisson’s Ratio

Definition

Poisson’s ratio is the name given to a ratio of lateral strain to axial strain. Its recognition as a property of materials is attributed to Siméon-Denis Poisson (1781–1840), a French mathematician and student of Laplace. Uniaxial extension of a solid rod causes it not only to elongate a small amount but also to become more slender or to undergo a reduction in diameter. Conversely, uniaxial compression of a solid rod or rock core sample causes it to shorten a small amount, but also to expand in diameter or become thicker. Therefore, principal stress in only one direction (uniaxial extension or compression) produces strain in all three directions. Hooke’s law explained the proportional change in length of a spring to the application of a load. Generalized Hooke’s law (Pariseau, 2012) recognizes that strain (ε_x = Δl/l_o) is proportional to the applied stress (σ_x), and the constant of proportionality for an isotropic material being stressed and strained in the elastic range of...