The quasilinear wave equation for antiplane shearing of nonlinearly elastic bodies

We formulate an efficient numerical algorithm based on finite-difference ap proximations and inspired by algorithms from gas dynamics to treat the quas ilinear wave equation w(11) = [alpha (w(x)(2) + w(y)(2))w(x)](x) + [alpha (w(x)(2) + w(y)(2))w(y) ](y). governing antiplane motions of incompressible, isotropic nonlinearly elasti c bodies in two-dimensions. In particular, we are concerned with the treatm ent of focusing and shocks for bodies whose material response differs marke dly from that of linear elasticity. We carefully validate our method by com paring our results with those of the axisymmetric version of this equation in polar coordinates. (C) 2001 Academic Press.