Both plasticity and fracture behaviour. These behaviour both dissipate stresses and are driven by the loads applied on the material. Although much development effort has improved material models derived from first principles, numerical efficacy keeps empirical descriptions attractive. A key difficulty, however it capturing the path-dependent aspects of behaviour, in particular in the case of strong localisation. Provided empirical descriptions of each behaviour, we propose an unconditionally stable algorithm which guarantees their effects are combined in a thermodynamically admissible way. During a simulation, the algorithm compute the instant irreversible mechanisms are triggered and the appropriate increment of e.g. damage or plasticity. We demonstrate the algorithm using a numerical examples of plastic and plastic-damage behaviour. These examples show how numerical instability can be overcome using the algorithm proposed.