  Wear on total knee replacements (TKRs) is an important criterion for their
performance characteristics. Numerical simulations of such wear has seen
increasing attention over the last years. They have the potential to be much
faster and less expensive than the in vitro tests in use today. While it is
unlikely that in silico tests will replace actual physical tests in the
foreseeable future, a judicious combination of both approaches can help making
both implant design and pre-clinical testing quicker and more cost-effective.
  The challenge today for the design of simulation methods is to obtain results
that convey quantitative information, and to do so quickly and reliably. This
involves the choice of mathematical models as well as the numerical tools used
to solve them. The correctness of the choice can only be validated by comparing
with experimental results.
  In this paper we present finite element simulations of the wear in TKRs
during the gait cycle standardized in the ISO 14243-1 document, used for
compliance testing in several countries. As the ISO 14243-1 standard is
precisely defined and publicly available, it can serve as an excellent
benchmark for comparison of wear simulation methods. Our novel contact
algorithm works without Lagrange multipliers and penalty methods, achieving
unparalleled stability and efficiency. We compare our simulation results with
the experimental data from physical tests using two different actual TKRs, each
test being performed three times. We can closely predict the total mass loss
due to wear after five million gait cycles. We also observe a good match
between the wear patterns seen in experiments and our simulation results.
