  In this paper, a recently developed Higher Order Microplane (HOM) model for
softening and localization, is implemented within a isogeometric finite element
framework. The HOM model was derived directly from a three dimensional discrete
particle model and it was shown to be associated with a high order continuum
characterized by independent rotation and displacement fields. Furthermore, the
HOM model possesses two characteristic lengths: the first associated with the
spacing of flaws in the material internal structure and related to the gradient
character of the continuum; and the second associated with the size of these
flaws and related to the micro-polar character of the continuum. The
displacement-based finite element implementation of this type of continua
requires $C^1$ continuity both within the elements and at the element
boundaries. This motivated the implementation of the concept of isogeometric
analysis which ensures a higher degree of smoothness and continuity. NURBS
based isogeometric elements were implemented in a 3D setting, with both
displacement and rotational degrees of freedom at each control point. The
performed numerical analyses demonstrate the effectiveness of the proposed HOM
model implementation to ensure optimal convergence in both elastic and
softening regime. Furthermore, the proposed approach allows the natural
formulation of a localization limiter able to prevent strain localization and
spurious mesh sensitivity known to be pathological issues for typical local
strain-softening constitutive equations.
