Closed-form solution for Mode I crack acceleration

Two-dimensional semi-infinite crack growth in an otherwise unbounded elastic linear continuum body is considered under the assumption of the idealisation of infinitesimally small scale yielding. The purpose is to model and solve analytically under a closed-form solution by means of a direct method the problem of Mode I crack growth at nonconstant velocity for all the range of velocities up to the dilatational wave velocity. As a result, the transonic regime is implicitly taken into account. As many times previously mentioned in the literature, it is then verified that only Mode I sub-Rayleigh crack propagation is physically possible