Augmented Lagrangian bonding block model for contact problems

A novel bonding block model is proposed for elastic contact simulations. The original model problem is expressed as the minimization problem with the penalty item of gluing spring strain energies, and Lagrangian multipliers are introduced to represent gluing spring forces. In this way, the total potential energy as the objective function becomes an augmented Lagrangian function. To solve this model, a new algorithm is presented by implementing augmented Lagrangian iterations to obtain the optimal solution in every time step. A numerical example is conducted to verify the accuracy and effectiveness of the presented model and algorithm.