The breaking of geometric similarity

Abstract

Scaled experimentation plays an important role in prototype and process development but is recognised to be severely constrained by the need for similitude, founded on the concepts of geometric, kinematic and kinetic similarity.This paper examines the possibility of breaking the requirement for geometric similarity by introducing the law of finite similitude for anisotropic scaling, which applies to continuum mechanics on anisotropically-scaled spaces. The law confirms that similarity solutions on skewed spaces always exist separately for quasistatic deformational and thermal-continuum problems. Thermomechanical and continuum dynamic problems however are shown to suffer from the inclusion of a (non-physical) non-orthogonal metric arising from the skewed coordinate system associated with anisotropic-space scaling. Even in this case however, an important subclass of problems is shown to be physically realisable involving a dominant component of velocity (displacement), where geometric similarity can again be broken yet retain good accuracy. The ability to skew artefacts yet achieve similitude is recognised to be a particularly important outcome as it allows for example one experimental model to be used to predict the behaviour of multiple skewed models.To showcase and highlight the significance of the new concept various scaled numerical models with anisotropic scaling with different geometrical scaling ratios in different directions is considered. The applicability of the theory is tested on a number of case studies providing strong supporting evidence for the validity and applicability of the new theory.