  This paper introduces a deep learning method for solving an elliptic
hemivariational inequality (HVI). In this method, an expectation minimization
problem is first formulated based on the variational principle of underlying
HVI, which is solved by stochastic optimization algorithms using three
different training strategies for updating network parameters. The method is
applied to solve two practical problems in contact mechanics, one of which is a
frictional bilateral contact problem and the other of which is a frictionless
normal compliance contact problem. Numerical results show that the deep
learning method is efficient in solving HVIs and the adaptive mesh-free
multigrid algorithm can provide the most accurate solution among the three
learning methods.
