Ta. Laursen et V. Chawla, DESIGN OF ENERGY CONSERVING ALGORITHMS FOR FRICTIONLESS DYNAMIC CONTACT PROBLEMS, International journal for numerical methods in engineering, 40(5), 1997, pp. 863-886
This paper proposes a formulation of dynamic contact problems which en
ables exact algorithmic conservation of linear momentum, angular momen
tum, and energy in finite element simulations. It is seen that a Lagra
nge multiplier enforcement of an appropriate contact rate constraint p
roduces these conservation properties. A related method is presented i
n which a penalty regularization of the aforementioned rate constraint
is utilized. This penalty method sacrifices the energy conservation p
roperty, but is dissipative under all conditions of changing contact s
o that the global algorithm remains stable. Notably, it is also shown
that augmented Lagrangian iteration utilizing this penalty kernel repr
oduces the energy conserving (i.e. Lagrange multiplier) solution to an
y desired degree of accuracy. The result is a robust, stable method ev
en in the context of large deformations, as is shown by some represent
ative numerical examples. in particular, the ability of the formulatio
n to produce accurate results where more traditional integration schem
es fail is emphasized by the numerical simulations.