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TECHNICAL PAPERS: Soft Tissue

Static Indentation of Anisotropic Biomaterials Using Axially Asymmetric Indenters—a Computational Study

[+] Author and Article Information
Jeffrey E. Bischoff

Department of Mechanical Engineering, University of South Carolina, 300 South Main, Columbia, SC 29208 Telephone: 803.777.0084 Fax: 803.777.0106e-mail: bischoff@engr.sc.edu

J Biomech Eng 126(4), 498-505 (Sep 27, 2004) (8 pages) doi:10.1115/1.1785808 History: Received January 28, 2004; Revised April 07, 2004; Online September 27, 2004
Copyright © 2004 by ASME
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References

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Figures

Grahic Jump Location
Two representative axially asymmetric indenter geometries with associated dimensional variables: (left) Rectangular solid geometry with cross-section dimensions lx and ly used to indent linear anisotropic materials (e.g. bone); (right) Semi-ellipsoid geometry with major axes Rx,Ry, and Rz used to indent nonlinear anisotropic materials (e.g. myocardium). The latter geometry is also used to validate the computational model by setting Rx=Ry and hence making the computational model axisymmetric
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Schematic definition of θ, used to characterize the direction of the in-plane material axes a and b relative to the reference axes x and y . When θ=0° or θ=90° the model is symmetric about the x and y axes and the model domain is reduced; for all other values of θ a full model domain must be used. For all simulations, material axis c and reference axis z are aligned. Also shown are cross-sectional silhouettes (to scale) of the rectangular tip and the four ellipsoidal tips used (ellipsoid dimensions are given in Table 1)
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Linear elasticity theory and computational simulation predictions for axisymmetric indentation. The series representation of the compressible eight chain model is used with material parameters N=2,n=1016/mm3, and κ=1000 kPa, corresponding to small strain Lame constants λ=1030 kPa and μ=65.7 kPa
Grahic Jump Location
Load at an indenter displacement of 0.01 mm from indentation of a linear anisotropic material whose material axes are oriented at various angles relative to the indenter geometry. When θ=0 deg the indenter is aligned with the stiff material direction a ; when θ=90 deg the indenter is aligned with the compliant material direction b
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Load versus displacement results from indentation of a linear anisotropic material for various values of Ebb; in all simulations Eaa=21 GPa. When θ=0 deg the indenter is aligned with the stiff material direction a ; when θ=90 deg the indenter is aligned with the compliant material direction b
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Load versus displacement results from indentation of a nonlinear anisotropic material using ellipsoidal indenters with various aspect ratios. Indenter dimensions are given in Table 1. When the long axis of the indenter is aligned with the stiff material direction (θ=0 deg) the resulting data are denoted ‘Aligned’; when the long axis of the indenter is orthogonal to the stiff material direction (θ=90 deg) the resulting data are denoted ‘Rotated’. Material parameters for these simulations are as follows: a=1.5,b=1.0,c=1.2,n=1012/mm3, and κ=1000 kPa
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Load versus displacement data demonstrating the effect of prestretch along material axis b on the tissue response for indenters in the ‘Aligned’ and ‘Rotated’ configurations. All simulations were performed using indenter ‘C’ geometry; material parameters are as in Fig. 6
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Load versus displacement data demonstrating the influence of prestretch along material axis a for indenters in the ‘Aligned’ and ‘Rotated’ configurations. Indenter geometry and material parameters are as in Fig. 6
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Contour plots of the normal in-plane logarithmic strains accompanying indentation of bone. (a) Logarithmic strain e22 for indentation in the ‘Aligned’ configuration. (b) Logarithmic strain e11 for indentation in the ‘Rotated’ configuration

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