7. Conclusions and discussion
• The implementation of an implicit MRCT element into FEAP has been verified. It is a general formulation for higher order continuum theory and can accommodate several other types of formulations. It can accommodate multiple scales, as shown in the works by Liu and coworkers. • The merit of the implicit MRCT element compared to the explicit version is that no dynamic vibrations show up when modeling quasistatic problems. • The element shows second order convergence in the equilibrium iterations verifying the formulation of the element tangent matrix.• The element can be used to obtain mesh independent results in the case of deformation localization when choosing an appropriate length scale associated with the microdomain. The mesh needs to be refined to fully resolve the length scale. • The length scale of the microdomain should be related to the physics of the problem at hand. However, it can also be used as a numerical regularization parameter to obtain mesh independent results. It is not obvious how to calibrate the constitutive behavior of the microdomain. One can note from the evaluations above that the used properties must be related to the chosen length scale. In future work, the implicit MRCT element will be applied to the problem of fracturing of high strength steels where the constitutive behavior need to be addressed more in detail.
