Bifurcation phenomena in the plane tension test

A basic tensile bifurcation problem is studied. Bifurcations from a state of homogeneous inplane tension are investigated for an incompressible rectangular block constrained to undergo plane deformations. The sides of the block are traction-free, and it is elongated by a uniform, shearfree, relative displacement of its ends. For a wide class of incrementally-linear, time-independent materials only two instantaneous moduli enter into the analysis. Symmetric and anti-symmetric bifurcations are examined in each of the characteristic regimes of the governing equations (elliptic, parabolic and hyperbolic). Both diffuse modes and localized shearing modes are considered. Lowest bifurcation stresses are computed for essentially the entire range of possible combinations of material properties and geometry. A number of limiting cases are studied in detail, including those for slender and stubby specimens and for specimens which are rigid in shear. Applications to elastic and elastic/plastic solids are discussed.