  Modeling contact between deformable solids is a fundamental problem in
computer animation, mechanical design, and robotics. Existing methods based on
$C^0$-discretizations -- piece-wise linear or polynomial surfaces -- suffer
from discontinuities and irregularities in tangential contact forces, which can
significantly affect simulation outcomes and even prevent convergence. To
overcome this limitation, we employ smooth surface representations for both
contacting bodies. Through a series of test cases, we show that our approach
offers advantages over existing methods in terms of accuracy and robustness for
both forward and inverse problems. The contributions of our work include
identifying the limitations of existing methods, examining the advantages of
smooth surface representation, and proposing forward and inverse problems to
analyze contact force irregularities.
