Zeroth-order finite similitude and scaling of complex geometries in biomechanical experimentation

Abstract

Scaled experimentation provides an alternative approach to full-scale biomechanical (and biological) testing but is known to suffer from scale effects, where the underlying system behaviour changes with scale. This phenomenon is arguably the overriding principal obstacle to the many advantages that scaled experimentation provides. These include reduced costs, materials and time, along with the eschewal of ethical compliance concerns with the application of substitute artificial materials as opposed to the use of hazardous biological agents. This paper examines the role scale effects play in biomechanical experimentation involving strain measurement and introduces a formulation that overtly captures scale dependencies arising from geometrical change. The basic idea underpinning the new scaling approach is the concept of space scaling, where a biomechanical experiment is scaled by the metaphysical mechanism of space contraction. The scaling approach is verified and validated with finite-element (FE) models and actual physical-trial experimentation using digital image correlation software applied to synthetic composite bone. The experimental design aspect of the approach allows for the selection of three-dimensional printing materials for trial-space analysis in a complex pelvis geometry. This aspect takes advantage of recent advancements in additive manufacturing technologies with the objective of countering behavioural distorting scale effects. Analysis is carried out using a laser confocal microscope to compare the trial and physical space materials and subsequently measured using surface roughness parameters. FE models were constructed for the left hemipelvis and results show similar strain patterns (average percentage error less than 10%) for two of the three trial-space material combinations. A Bland–Altman statistical analysis shows a good agreement between the FE models and physical experimentation and a good agreement between the physical-trial experimentation, providing good supporting evidence of the applicability of the new scaling approach in a wider range of experiments.