PLANE-STRAIN INCREMENTAL RESPONSE AND SENSITIVITY OF STRETCHED PLATES

A family of rate boundary value problems for initially stretched plate s is investigated, under the plane strain constraint. The governing st rain-rate compatibility equation is solved, in terms of Fourier series , for normal and shear traction rates applied to the longitudinal face s. Specific examples are provided for the Blatz-Ko material, including a mapping of bifurcation stretches in the elliptic range. The perturb ed fields induced by the incremental loads are highly sensitive to ini tial stretch. Near bifurcation stretches in tension and in compression , there is large amplification of traction rates, strain rates and vel ocities whenever the applied load is in resonance with the correspondi ng bifurcation mode. The plate appears to be increasingly sensitive to small perturbations as bifurcation is approached. Numerical illustrat ions of that sensitivity are supported by asymptotic expansions.