Contact‐impact by the pinball algorithm with penalty and Lagrangian methods

Contact‐impact algorithms, which are sometimes called slideline algorithms, are a computationally time‐consuming part of many explicit simulations of non‐linear problems because they involve many branches, so they are not amenable to vectorization, which is essential for speed on supercomputers. The pinball algorithm is a simplified slideline algorithm which is readily vectorized. Its major idea is to embed pinballs in surface elements and to enforce the impenetrability condition only to pinballs. It can be implemented in either a Lagrange multiplier or penalty method. It is shown that, in any Lagrange multiplier method, no iterations are needed to define the contact surface. Examples of solutions and running times are given.