Anthony Petrella (ID: 55DUDE55)
ENME 442: Lab 2 Report
Introduction
Physical wear testing of ultra-high molecular weight polyethylene (UHMWPE) in total joint replacements is
ubiquitous and a necessary part of the design verification & validation process for any new device. The process is
time and resource intensive though, making it challenging to perform multiple design iterations to optimize wear
performance in concert with other design outputs. Computational wear modeling has obvious utility in this context
as it can be conducted with much greater economy than physical testing. Most simulation studies, however, did
not account for the cross-shear associated with multidirectional sliding in the joint, which has been shown to
significantly increase UHMWPE wear measured in vitro. Use past tense throughout the report. Establish some
background in the Introduction that helps explain why you are looking at this problem.
The purpose of this lab exercise, therefore, was to propose a robust cross-shear model applicable to any interface
geometry under any kinematic conditions. State clearly and directly what was the goal of the exercise – you don’t
have to use these exact words, you can be flexible and write what makes sense for your specific case.
Methods
Archard’s law may be written concisely in terms of either wear depth or wear volume as,
𝐻𝑗 = 𝑘̅ ∑𝑛𝑖=1 𝜏𝑖𝑗
(1)
n
W = k̅ ∑N
j=1 ∑i=1 τij A j
(2)
where 𝐻𝑗 is wear depth (mm) at a discrete location on the surface, 𝑊 is wear volume (mm3), 𝑘̅ (mm3/N·mm) is the
experimentally measured apparent wear factor, and 𝐴𝑗 is an element of surface area (mm2). The focus of this study
will be to apply (2) for the purpose of wear computation. Equations should each be numbered on the right hand
margin. After you present the equation make sure to explain each term that appears in the equation for the first
time – if you reuse terms again in later equations, you don’t have to explain them again. You can refer to equations
in the text by reference to the number as illustrated above.
Note that for most of your labs you will be provided with detailed instructions. You do not need to repeat those
instructions here in the methods section. The goal should be to present a concise summary of the basic steps you
performed. If there are any important equations or model parameters that were varied in your study, you should
describe them.
Results
Computed wear volume was found to increase with cross-shear motion in the knee in strong agreement with
experimental results. Contour plots of wear depth on the tibial implant surface are illustrated in Figure 1. A table is
used below to organize figures. This is not required, but it can be a helpful way to organize spacing and layout of
content. The table can be designed in any configuration/arrangement that makes sense for your report. You should
layout the table first and place figures into it, and then you can merge cells at the bottom of the table to create a
single caption. Remove the table borders as the very last step. Note that every figure must have a caption at the
bottom and must be referenced by number in the text BEFORE appearance of the figure. If you have multiple
images in a single figure, make sure to label them (a), (b), (c), etc. and explain each part in the caption.
(a)
(b)
(c)
Figure 1. Contour plots illustrating wear depth on the tibial implant surface. Results are shown for three kinematic conditions:
high (a), intermediate (b), and low (c) cross-shear.
Quantitative analysis of wear volume from each kinematic condition was also performed and a summary is
presented in Table 1. If you use a table to present results, you must include a caption at the top of the table and
the table must be referenced by number in the text of the report before appearance of the table. You are free to
design the borders and/or shading of the table however you choose.
Table 1. Summary of wear volume results.
Wear Volume (mm3)
High Cross-shear
Intermediate Cross-shear
Low Cross-shear
15
12
9
Discussion
The purpose of this study was to develop and validate a generalized model for cross-shear wear. The proposed
model was implemented in ANSYS and successfully used to account for the variations in cross-shear associated
with different kinematic inputs to a total knee replacement. Wear results predicted by the cross-shear wear model
were round to exhibit strong agreement with experimental data. The goal of the discussion is to interpret what
you’ve found and explain what it means in practical terms.