Scaling and High-Order Finite Similitude in Biomechanical Experiments

  • Raul Ochoa Cabrero

Student thesis: Phd


Biomechanical experimentation encounters many obstacles that have to be addressed to produce reliable results that guarantee the study under scrutiny is applicable in a realistic setting; especially when considering a clinical application. This work is principally concern with demonstrating the applicability of a new scaling methodology termed finite similitude and whether it is able to provide means for scaled-experimental design that approximate the full-scale behaviour. The approach utilises the notion of space scaling and assumes length-scale invariance in the conservation laws. Single-trial experimentation shows success in approximating simple bone geometries with axes of symmetry, nevertheless, scale effects and length-scale dependencies are absent which are undoubtedly present in experimental reality. Consequently, this work attempts to gauge whether the approach is successful in complex geometries and introduces the concept of high-order similitude which approximates the full-scale behaviour by multiple trial experiments. The experimentation analysed consists of validation of FE models by means of synthetic composite bone and DIC equipment; the assessment of one and two scaled experiments in a complex pelvis geometry is undertaken. The approach allows the use of cheap polymer materials manufactured in rapid prototyping technology for the single-trial and multiple-trial experimentation. A microscope analysis confirms the applicability of the selected materials. Preliminary element models are constructed to assess the material selection and projected efficacy, subsequently, the actual physical-trial experimentation is undertaken. A Bland-Altman statistical analysis shows a good agreement between the proposed trial material and synthetic composite bone material; they also demonstrate a good agreement with the finite element models validating the numerical results. The results provide good supporting evidence of the applicability of the finite similitude approach in a wide range of geometries with the high-order implementation constituting a sevenfold decrease in error values.
Date of Award31 Dec 2022
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorKeith Davey (Supervisor), Rooholamin Darvizeh (Supervisor) & Rob Lindsay (Supervisor)


  • Finite Similitude
  • Biomechanics
  • Scaled Experimentation
  • Scaling Theory
  • Multi-scale Experiments

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