NTFA inspired model order reduction including contact and friction
Résumé
Key Words: Model reduction, NTFA, Creep, Contact, Friction.
Dealing with dimensional stability in nuclear industry often leads to consider irradiation
creeping as well as contact and friction. However, large detailed models require extended
memory and computational time. On the opposite, simplified finite element models provide the
useful first order response of the structure [1]. To obtain better precision, while keeping a
reasonable computing cost, then leads us to model reduction techniques.
We propose a model reduction methodology largely inspired by the homogenisation technique
called NTFA [2], specially designed for non-linear materials. A first level of model order
reduction is achieved by representing all the useful fields by shape modes, either arbitrary or
obtained by an a posteriori POD or NMF analysis [3,4]. Then, the stress fields induced by each
unique transformation mode can be superposed using the linearity of the elastic operator. A
second reduction level arises from the derivation of a modal evolution law for plasticity or
creep. This projection step usually requires a coupling hypothesis between the thermodynamic
forces associated to each internal variable mode. Concerning the contact conditions, we propose
to reduce them through the building of Lagrange multiplier modes [5] and a specifically built
basis of opening modes. Once this reduced contact problem is solved, it enables to formulate a
regularised modal friction criterion to be applied onto a orthogonal basis of sliding modes. A
classical implicit integration scheme is then applied and two simple example are given, which
show the drastic shortening obtained with this reduction method.