A nonlinear history-dependent cohesive zone (CZ) model of quasi-static crack propagation in
linear elastic and viscoelastic materials is presented. The viscoelasticity is described by a linear
Volterra integral operator in time. The normal stress on the CZ satisfies the history-dependent yield
condition, given by a nonlinear Abel-type integral operator. The crack starts propagating, breaking
the CZ, when the crack tip opening reaches a prescribed critical value. A numerical algorithm for
computing the evolution of the crack and CZ in time is discussed along with some numerical
results
