A Stabilization‐Free Virtual Element Method for 2D Thermo‐Mechanical Contact Problems

The virtual element method (VEM) has gained increasing attention in recent years due to its flexibility with respect to element shapes. The applications of VEM to thermo‐mechanical contact problems remains largely unexplored. In this work, the stabilization‐free virtual element method (SFVEM) is applied to two dimensional thermo‐mechanical contact problems for the first time. Compared with the conventional VEM, the SFVEM modifies the virtual element space to enable the calculation of the higher‐order projection of the gradient, thereby eliminating the need for stabilization terms in the stiffness matrix. This feature significantly simplifies the implementation and analysis of nonlinear thermo‐mechanical contact problems and avoids the influence of artificial stabilization parameters on the numerical results. To accurately capture the coupled thermo‐mechanical interactions at contact interfaces (governed by heat conduction and mechanical pressure), a node‐to‐segment discretization strategy is employed to handle non‐conforming meshes. A staggered solution strategy is further employed to solve the resulting nonlinear coupled system. Several numerical examples are presented to demonstrate the accuracy and convergence of the proposed method in thermal contact problems. The results confirm that the stabilization‐free VEM achieves high accuracy in both temperature and stress fields, provides a computational framework for the simulation of complex thermal contact problems without the use of traditional stabilization techniques.