Efficiency of algorithms for shear stress amplitude calculation in critical plane class fatigue criteria

Fatigue criteria that belong to the critical plane class necessitate unambiguous definitions of the amplitude and mean value of the shear stress acting on a material plane. This is achieved through the construction of the minimum circle circumscribing the path described by the tip of the shear stress vector on each plane. By definition, the centre and the radius of this circle provide the mean shear stress and the shear stress amplitude, respectively. The search of the minimum enclosing circle is an optimisation problem for which efficient numerical solution schemes are required. Several algorithms exist for similar situations; however these are not necessarily related to the fatigue strength of metals. In this paper some algorithms are studied to assess their computational efficiency within the engineering framework of the application of fatigue criteria of the critical plane type.