Impact Modeling by Manifold Approach in Explicit Transient Dynamics

Abstract eng:
In this paper we study numerically different methods to impose contact constraints in explicit dynamics. The traditional methods, the penalty method and the more recent forward increment Lagrange multiplier method, are compared, in their performance and accuracy, to a direct elimination method based on the theory of manifolds. The idea of the method is that when a contact constraint is active the solution lies on the boundary of the contact manifold generated by contact constraints. Then the contact problem can be solved with the elimination of additional degrees of freedom. This elimination technique can be viewed as a parameterization of the contact manifold. We show numerically that in the case of a rigid impactor, the elimination method is highly more efficient than the forward Lagrange multiplier method since the latter leads to a coupled system of equations for solving the Lagrange multipliers while both methods produce similar results. In the present work the elimination method is also developed for the impact problem of deformable bodies and the performance of the different methods are compared in numerical simulations of the longitudinal impact of thick bars. The modified Euler method is employed in solving the equations of motion in time.

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