A Two-Experiment Approach to Scaling in Biomechanics

A new approach to scaled experimentation has recently appeared in the open literature where hitherto unknown similitude rules have been discovered. The impact of this discovery on biomechanics is the focus of this paper, where rules for one and two scaled experiments are assessed. Biomechanical experimentation is beset by problems that can hinder its successful implementation. Availability of resources, repeatability and variability of specimens, ethical compliance and cost are the most prominent. Physical modeling involving synthetic composite materials can be used to advantage and circumvent ethical concerns but is presently impeded by cost and the limited scope of standardized geometries. The increased flexibility of the new approach, combined with the application of substantially cheaper three-dimensional printed materials, is investigated here for bone biomechanical experiments consisting of mechanical tests for the validation of finite element models by means of digital image correlation. The microstructure of the scaled materials is analyzed using a laser confocal microscope followed by the construction and validation of numerical models by means of a Bland-Altman statistical analysis. Good agreement is obtained demonstrated with means under 18 microstrains (μϵ) and limits of agreement below 83 μϵ. Consequently, numerical results for the new similitude approach shows an average percentage error of 3.1% and 4.8% for the optimized results across all values. The two-scaled experiment approach results in a sevenfold improvement for the average difference values of strain when compared to the single-scaled experiment, so demonstrating the potential of the new approach.