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3). In the same idea, the definition of the virtual mean interface resultant stress is not obvious in the case of material nonlinearities (e.g. plasticity or damage). In Chapter 2, we will develop a new non-invasive coupling strategy based on the non-symmetric variant of the Nitsche methodology, which will result in a flexible and efficient tool to perform global/local isogeometric simulations.

NOTE.– It may be finally noted that with the Nitsche technique, the average operator in equation [1.44] can be defined more generally. Any convex combination can actually be chosen without violating the consistency of the formulation (Hansbo 2005; Bazilevs et al. 2012). As a result, we can use:

      [1.47]

      In particular, when there is an important contrast between the two materials to be coupled, it could be interesting to adjust the convex combination to counterbalance the material gap and therefore preclude the emergence of undesirable mesh locking phenomena (Sanders et al. 2012). Such treatment has been performed in the non-invasive algorithm proposed in Chapter 2, to properly introduce a stiff inclusion within a soft B-spline patch (see Bouclier and Passieux (2018)).

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