Foot Model for Investigating Foot Biomechanics and Footwear Design - Computational Biomechanics of the Musculoskeletal System - page 9

tetrahedral elements. For the sake of geometrical simplification, truss elements were chosen to
model the ligaments. Truss elements are typically designated to model slender, line-like structures
that can only transmit force along the axis or the center line of the element. Truss elements cannot
resist loading perpendicular to their axis. The distance between the two connecting nodes defines
the length of each truss element and the cross-sectional area is specified by the user. As the liga-
ments were assumed to sustain tensile force only, the No-Compression option in ABAQUS was used
to modify the elastic behavior of the material so that compressive stress could not be generated. In
the current FE model, a total number of 98 tension-only truss elements were used to represent the
ligaments and the plantar fascia.
To simulate the surface interactions among the bony structures, ABAQUS's automated surface-
to-surface contact algorithm was used. A pair of contacting surfaces consisted of a master and a
slave surface. Because of the lubricating nature of the articulating surfaces, the contact behavior
between the articulating surfaces can be considered as frictionless. The overall joint stiffness against
shear loading was assumed to be governed by the surrounding ligamentous and encapsulated soft
tissue structures together with the contacting stiffness between the adjacent contoured articulating
surfaces. Frictionless surface-to-surface contact behavior was defined between the contacting bony
structures. Contact stiffness resembling the softened contact behavior of the cartilaginous layers
(Athanasiou et al. 1998) was prescribed between each pair of contact surfaces to simulate the cover-
ing layers of articular cartilage.
To simulate a barefoot stance, a horizontal plate consisting of an upper concrete layer and a rigid
bottom layer was used to establish the foot-ground interface. The horizontal ground support was
meshed with hexahedral elements. The same contact modeling algorithm was used to establish the
contact simulation of the foot-ground interface with an additional frictional property assigned to
model the frictional contact behavior at the foot-support interface. During the contact phase, sliding
was allowed only when the shear stress exceeded the critical shear stress value. During the sliding
phase, if the shear stress was reduced and lower than the critical shear stress value, sliding stopped.
It was assumed that the static and kinetic coefficients of friction were the same in this model. The
coefficient of friction between the foot and ground was taken as 0.6 (Zhang and Mak 1999).
The geometry of the foot orthosis was obtained from the shape of the subject's bare foot. The
three-dimensional foot shape of the subject was obtained from surface digitization via a three-
dimensional laser scanner (INFOOT Laser Scanner, I-Ware Laboratory Co. Ltd.). The foot shape
was obtained under three different weight-bearing conditions: single-limb standing (full-weight-
bearing), double-limb standing (semi-weight-bearing), and upright sitting (non-weight-bearing).
Algorithms were established in MATLAB ® software (Mathworks, Inc.) to create surface models for
the insole and midsole from the digitized foot surface for each scanning position. The surface mod-
els were transferred to SolidWorks software (SolidWorks Corporation, Massachusetts) for creation
of solid models of variable thicknesses.
The solid model of the foot orthosis was then imported into ABAQUS for meshing. In order to
enhance the accuracy of the FE analysis, the foot orthosis was properly partitioned for meshing with
hexahedral elements. The FE mesh of the foot orthosis (Figure 1.4) is composed of an insole layer,
a midsole layer, and an outsole layer. The same frictional contact modeling approach was used to
establish the contact simulation of the foot-insole interface.
1.2.2 m aterial p ropertieS
A number of material property models can be used, from the simplest linear elasticity to nonlinear
elasticity and even viscoelasticity. The material properties used in this model are listed in Table 1.2.
To reduce the complexity and the size of the problem, except for the encapsulated soft tissue, all
tissues, including bony, ligamentous, and cartilaginous structures and ground supports, were ideal-
ized as homogeneous, isotropic, and linearly elastic. The linearly elastic properties can be defined
by providing any two constants: Young's modulus E , shear modulus G , and Poisson's ratio v .