Abstract：The resolution of forward and inverse contact analysis of finite-sized inhomogeneous media is pivotal to high-throughput characterization of materials. This paper begins with the forward problem, detailing the foundational theory of the symplectic analysis, the strategy for determining contact areas, and the extended formulations for more complicated situations. Two classes of neural operators for solving the inverse problems in 2D and 3D cases are then introduced. A range of challenges to the research of contact analysis of finite-sized inhomogeneous materials are summarized and discussed in the end.
2026, Vol. 47 
