  The phase-field model for fracture, despite its popularity and ease of
implementation comes with its set of computational challenges. They are the
non-convex energy functional, variational inequality due to fracture
irreversibility, the need for extremely fine meshes to resolve the fracture. In
this manuscript, the focus is on the numerical treatment of variational
inequality. In this context, the popular history-variable approach suffers from
variationally inconsistency and non-quantifiable nature of the error
introduced. A better alternative, the penalisation approach, has the potential
to render the stiffness matrix ill-conditioned. In order to circumvent both
aforementioned issues, a micromorphic approach towards phase-field fracture
modelling is proposed in this manuscript. Within this approach, a micromorphic
extension of the energy functional is carried out. This transforms the
phase-field into a local variable, while introducing a micromorphic variable
that regularises the fracture problem. This reduction the regularity
requirements for the phase-field enables an easier implementation of the
fracture irreversibility constraint through simple 'max' operation, with system
level precision. Numerical experiments carried out on benchmark brittle and
quasi-brittle problems demonstrate the applicability and efficacy of the
proposed model for a wide range of fracture problems.
