Contact Dynamics with Lagrange Multipliers
The efficient modeling of dynamical contact problems with friction is still a callenge in non-linear implicit structural analysis. We employ a mixed formulation in space with the displacement as primal variable and the contact stress as dual variable. For the discretization of the latter we use a discrete Lagrange multiplier space with biorthogonal basis functions. For the treatment of the nonlinear frictional contact conditions semi-smooth Newton methods are applied. To avoid oscillations in the Lagrange multiplier during the solution of dynamical contact problems with mass, we locally under-integrate the mass matrix. We also show the applicability of the mixed formulation to a velocity driven rigid-plastic problem.
Key words: Coulomb friction, semi-smooth Newton methods, non-oscillating Lagrange multiplier, energy conservating time integration.
KeywordsLagrange Multiplier Contact Problem Contact Condition Dual Variable Frictional Contact
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