Waves From Suddenly Punched Hole in Finitely Stretched Elastic Sheet

Abstract

The method of characteristics is used to obtain numerical solutions for the plane stress problem of propagation of unloading waves from a suddenly punched circular hole in an elastic sheet subjected to finite, isotropic, tensile, biaxial strain. It is shown that, for instantaneous punching of a sheet of Mooney-Rivlin material, a shock is formed initially. Also an expression is obtained for the time when a shock forms if there is a linear reduction with time, from the initial value to zero, of the nominal tensile stress at the hole boundary. Numerical results are presented for the Mooney-Rivlin material and these results are compared with those obtained from the linear theory of elasticity, significant differences being found for stretches greater than about 1.05.