Thin Hyperelastic sheets of compressible material: Field equations, airy stress function and an application in fracture mechanics

The equations of the equilibrium theory of thin hyperelastic sheets under plane stress condition and the associated Airy stress function are deduced for a compressible Mooney-Rivlin material. Such an analysis is then employed to formulate a nonlinear fracture mechanics problem. By means of an asymptotic procedure, the deformation and stress singular fields in proximity of the crack-tip are computed.