Mathematical and numerical study of detachment with frictional contact and adhesion in a two-mass system

Abstract This work presents mathematical and numerical analyses of a two mass-spring-damper system with frictional resistance and interfacial adhesion. The proposed model extends an existing detachment model to a more realistic setting and leads to modified steady states and adhesion-dependent detachment behavior. The motion of two masses, governed by Coulomb's law of dry friction and bonding fields, is described by a highly nonlinear system of ordinary differential equations. We prove the convergence of approximations in both the continuous and discrete cases, as well as the uniqueness of solutions. To handle the inherent non-smoothness of friction and adhesion and the associated nonlinearity, stable numerical schemes are constructed using appropriate regularization and the Newton-Raphson method. Numerical simulations illustrate the onset and propagation of detachment processes and support the theoretical predictions, providing new insights into the system.