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This paper reports on an investigation into the relationship between stiffness and applied force of an advanced biological composite structure using four techniques: experimental observation; finite element analysis (FEA); regression learner analysis; and, artificial neural networks (ANNs). The entire hydrated third metacarpal bones (MC3) from 16 thoroughbred horses were loaded in compression in an MTS machine. The stiffness was then determined from the applied force, MC3 displacement, and load exposure time. A variety of mathematical functions were fitted to the sample data points using MATLAB to demonstrate force-dependent stiffness. Two functions were found that exhibited a strong correlation between force and stiffness ( R2  = 0.75). Additionally, a power function was found that demonstrated a stronger correlation between the stiffness and force ( R2  = 0.81) if the exposure time was also incorporated. FEA considered the calculated force-dependent stiffness when assigning material properties. FEA results were compared with experimental data (for verification and validation), and a good agreement was found for the displacement (RMSE = 0.032 mm) and strain (RMSE = 61.85 μ ε ). Machine learning regression models were also employed to predict the stiffness of this complex structure. Applied force, exposure time, MC3 geometry (length and area of cross sections), and age were defined as the independent variables. The regression learner offered excellent reliability ( R2  = 0.98) for the prediction of stiffness. Also, feedforward back-propagation artificial neural networks were employed to improve and generalize the stiffness prediction ability to a wider population. ANN regression analysis showed  R  = 0.992 for training,  R  = 0.99 for testing, and  R  = 0.991 for the all datasets. To confirm its accuracy, the ANN was used to predict stiffness of specific samples that were not used in its training. This offered excellent reliability in predicting real-world data that ANNs have not seen before ( R  = 0.976).

Experimental, regression learner, numerical, and artificial neural network analyses on a complex composite structure subjected to compression loading