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Developing a three-dimensional numerical foot model and
identifying the loading condition for designing a stable sole for
running shoes
Mai NONOGAWA et al
The Japan Society of Mechanical Engineers
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.
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