Causality constraint for fractures with linear slip weakening

We consider the problem of dynamic fracture growth characterized by linear slip-weakening properties. If the problem is attacked by standard linear sp ectral methods, we show that the elastic wave radiation from the slip in th e weakening zone has noncausal terms. The nonphysical behavior is specifica lly attributable to the application of a weak causality constraint in stand ard linear spectral analysis to a problem with an active boundary condition . We give the correct analytic solution, derived from linear spectral analy sis applied to a boundary integral procedure.