Closed form solution for the finite anti-plane shear field for a class of hyperelastic incompressible brittle solids

International audienceThe equilibrium solution of a damaged zone in finite elasticity is given for a class of hyper-elastic materials which does not suffer tension when a critical stretching value is reached. The study is made for a a crack in anti-plane shear loading conditions. The prescribed loading is that of linearised elasto-statics conditions at infinity. The geometry of the damaged zone is found and the stationary propagation is discussed when the inertia terms can be neglected