Microstructure-Informed Achilles Tendon Modelling: Absolute Nodal Coordinate Formulation Approaches

  • Ghasemkhani, Amir (The University of Manchester)
  • Harish, Ajay B (The University of Manchester)
  • Matikainen, Marko K (LUT University)
  • Mandal, Parthasarathi (The University of Manchester)
  • Shearer, Tom (The University of Manchester)

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The Achilles tendon connects the calf muscles (gastrocnemius and soleus) to the heel bone (calcaneus) and plays a vital role in human locomotion[1]. Computational modelling of the Achilles tendon provides valuable insight into its mechanical behaviour under various loading conditions. The tendon exhibits a nonlinear tensile response arising from its hierarchical collagen architecture and the progressive recruitment of initially slack fibrils. We implement and compare two transversely isotropic hyperelastic models for Achilles tendon within an Absolute Nodal Coordinate Formulation (ANCF) finite-element framework[2-4]: the Gasser–Ogden–Holzapfel (GOH) model[5] and a microstructurally motivated Fibre Length Distribution (FLD) model[6] explicitly represents fibril recruitment through a triangular distribution of critical stretches. The primary aim is to investigate how tendon microstructure, represented through fibril length distributions, effects the overall mechanical behaviour of human Achilles tendon. An MRI-derived geometry of a human Achilles tendon is used with constitutive data obtained from experiments. We observed that the FLD model can capture more precisely the initial toe region in human Achilles tendon. In addition, varying the fibre length distribution within the FLD–ANCF framework revealed that shorter fibrils are recruited earlier and result in a stiffer overall response, while longer fibrils delay recruitment and lead to a more compliant behavior. These findings emphasize the influence of fibril length distribution as a key, physically interpretable microstructural determinant of Achilles tendon mechanics. REFERENCES [1] P. Szaro, G. Witkowski, R. Śmigielski, P. Krajewski, and B. Ciszek, “Fascicles of the adult human Achilles tendon–an anatomical study,” Annals of Anatomy-Anatomischer Anzeiger, vol. 191, no. 6, pp. 586-593, 2009. [2] A. A. Shabana, “Definition of the slopes and the finite element absolute nodal coordinate formulation,” Multibody System Dynamics, vol. 1, no. 3, pp. 339-348, 1997. [3] E. Grossi, and A. A. Shabana, “Analysis of high-frequency ANCF modes: Navier–Stokes physical damping and implicit numerical integration,” Acta Mechanica, vol. 230, no. 7, pp. 2581-2605, 2019. [4] H. Ebel, M. K. Matikainen, V.-V. Hurskainen, and A. Mikkola, “Higher-order beam elements based on the absolute nodal coordinate formulation for three-dimensional elasticity,” Nonlinear Dynamics, vol. 88, no. 2, pp. 1075-1091, 2017. [5] T. C. Gasser, R. W.