Developing a three-dimensional numerical foot model and identifying the loading condition for designing a stable sole for running shoes

This study presents methods to develop a three-dimensional numerical foot model and to identify the loading condition that is used to design a stable sole for running shoes. In a previous study, the authors proposed a method to optimize the shape of the sole to increase stability while maintaining the cushioning property. In the problem formulation, the loading condition was given as a boundary force distributed on the top surface of the sole. The aim of this study is to replace the loading condition with the force and moment at the origin of the ankle joint coordinate (AJC) system by modeling a foot with a finite element model. A finite element model of a foot is constructed using X-ray CT image data, and consists of bony structures, soft tissue, and plantar fascia. The plantar fascia is set at the bottom of the bony structures. The force and moment used in the finite element analysis are identified by inverse dynamic analysis using an experimental measurement in the practical operation of the ground reaction force (GRF) when the GRF in the direction of the foot length becomes minimum. In the finite element analysis, the finite deformation containing the contact condition between the bottom surface of the foot and the ground representing a sole made of resin is considered. For an index of the shoe stability, we define a heel eversion angle (HEA) by the rotational angle of the heel with respect to an axis in the foot length direction and evaluate it by finite element analysis. The validity of the finite element foot model as well as the force and moment obtained in this study are confirmed based on the agreement in the HEA results between the experiment and finite element analysis.