Quasistatic crack growth in finite elasticity

We present a variational model for quasistatic evolutions of brittle cracks in hyperelastic bodies, in the context of finite elasticity.All existence results on this subject that can be found in the mathematical literature were obtained using energy densities with polynomial growth. This is not compatible with the standard assumption in finite elasticity that the strain energy diverges as the determinant of the deformation gradient tends to zero. On the contrary, we consider a wide class of energy densities satisfying this property