Prediction of load-displacement curve in a complex structure using artificial neural networks: A study on a long bone

Abstract

Long bones are composite materials possessing nonhomogeneous and anisotropic properties. They repair themselves (self-repairing) and adapt to changing mechanical demands by altering their shape and mechanical properties (self-adapting). Such exceptional features make long bones intriguing materials to comprehend properly. This also expands our knowledge of engineering materials and motivates researchers to employ novel techniques where conventional approaches may present limitations. This paper delves into the use of artificial neural network (ANN) expert systems to predict load-displacement curves of a long bone. Thirteen hydrated third metacarpal (MC3) bones from thoroughbred horses aged from twelve hours to three years were loaded in compression in an MTS machine. Strain readings from one three-gauge rosette and three distinct single-element gauges at different locations on the MC3 midshaft, displacement, load, load exposure time, horse age and bone side (left or right limb) were recorded for each bone. This information shaped ANNs input variables. Two in-series feedforward back-propagation ANNs were employed where the experimental recordings except for load were fed into the first ANN to predict load. Then, the predicted load along with the rest of experimental recordings were fed into the second ANN to predict displacement. Cyclic load-displacement and stiffness predicted by ANNs were plotted versus experimental counterparts. ANNs regression analyses showed R > 0.95 for training and testing datasets. To confirm their accuracy, ANNs were used to predict responses of specific bone samples that were not used in ANNs training. The ANNs trained using 17,718 experimental data points from twelve bones predicted the load (R = 0.997, RMSE = 2.44 kN), displacement (R = 0.948, RMSE = 0.321 mm), and stiffness (R = 0.982, RMSE = 1.197 kN/mm) of the thirteenth bone. The encouraging outcomes exhibit the exceptional ability of artificial neural networks in capturing the mechanical characteristics of complex structures.