Computationally efficient model to predict the deformations of a cellular foot orthotic

Background: Foot orthotics (FOs) are frequently prescribed to provide comfortable walking for patients. Finite element (FE) simulation and 3D printing pave the way to analyse, optimize and fabricate functionally graded lattice FOs where the local stiffness can vary to meet the therapeutic needs of each individual patient. Explicit FE modelling of lattice FOs with converged 3D solid elements is computationally prohibitive. This paper presents a more computationally efficient FE model of cellular FOs.

Method: The presented FE model features shell elements whose mechanical properties were computed from the numerical homogenization technique. To verify the results, the predictions of the homogenized models were compared to the explicit model's predictions when the FO was under a static pressure distribution of a foot. To validate the results, the predictions were also compared with experimental measurements when the FO was under a vertical displacement at the medial longitudinal arch.

Results: The verification procedure showed that the homogenized model was 46 times faster than the explicit model, while their relative difference was less than 8% to predict the local minimum of out-of-plane displacement. The validation procedure showed that both models predicted the same contact force with a relative difference of less than 1%. The predicted force-displacement curves were also within a 90% confidence interval of the experimental measurements having a relative difference smaller than 10%. In this case, using the homogenized model reduced the computational time from 22 h to 22 min.

Conclusion: The presented homogenized model can be therefore employed to speed up the FE simulation to predict the deformations of the cellular FOs.