An explicit Lagrange constraint method for finite element analysis of frictionless 3D contact/impact problems

An effective contact algorithm is essential for modeling complicated contact/impact problems. Unlike the penalty method, the Lagrange multiplier method can generate more precise results while not adversely affecting stability; however, its formulation in explicit contact treatment is singular. In order to overcome this deficiency, a new Lagrange constraint method with different constraints under initial impact and persistent contact is proposed. In this method, the coupled contact system equilibrium equations with non-diagonal coefficient matrix are uncoupled via Gauss-seidel iteration strategy. Particularly, this implicit contact treatment can be compatible with explicit time integration scheme. To reduce oscillations, the displacement constraint is imposed under initial impact, while the combined constraints of velocity, acceleration and displacement are enforced under persistent contact. Numerical example validates this method.