Shortcuts in multiple dimensions: the multiaxial racetrack filter

Filtering techniques have been proposed for multiaxial load histories, usually aiming to filter out non-reversals, i.e. sampling points that do not constitute a reversal in any of its stress or strain components. However, the path between two reversals is needed to evaluate the equivalent stress or strain associated with each event. Filtering out too many points in such path would almost certainly result in lower equivalent stresses or strains than expected. To avoid such issues, it is important to consider how a measured multiaxial loading path deviates from its course using some metric, such as the von Mises stress or strain. In this work, a multiaxial version of the racetrack filter is proposed, which is able to perform efficient filtering even for 6D nonproportional histories. In the Multiaxial Racetrack algorithm, the stress or strain history is represented in a 6D space, only requiring from the user a desired scalar filtering amplitude r. For uniaxial histories, the proposed algorithm exactly reproduces the classic racetrack filter. The efficiency of the proposed Multiaxial Racetrack filter is qualitatively verified from a tension-torsion history example, showing the reduction in the number of data points for larger filter amplitudes r. The procedure can efficiently filter out non-damaging events but preserving the overall multiaxial path shape and multiaxial reversion points, which usually do not coincide with the reversion points of individual stress or strain components.