  In this paper, we propose an eXtended Virtual Element Method (X-VEM) for
two-dimensional linear elastic fracture. This approach, which is an extension
of the standard Virtual Element Method (VEM), facilitates mesh-independent
modeling of crack discontinuities and elastic crack-tip singularities on
general polygonal meshes. For elastic fracture in the X-VEM, the standard
virtual element space is augmented by additional basis functions that are
constructed by multiplying standard virtual basis functions by suitable
enrichment fields, such as asymptotic mixed-mode crack-tip solutions. The
design of the X-VEM requires an extended projector that maps functions lying in
the extended virtual element space onto a set spanned by linear polynomials and
the enrichment fields. An efficient scheme to compute the mixed-mode stress
intensity factors using the domain form of the interaction integral is
described. The formulation permits integration of weakly singular functions to
be performed over the boundary edges of the element. Numerical experiments are
conducted on benchmark mixed-mode linear elastic fracture problems that
demonstrate the sound accuracy and optimal convergence in energy of the
proposed formulation.
