Heterogeneous materials characterized by a complex microstructure with multiple phases or constituents with different mechanical properties are frequently used in aerospace engineering applications. Modelling the crack propagation in such materials is highly important to predict the durability of many aerospace engineering structures. Numerical simulations involving an explicit description of microcracks and all heterogeneities can be cumbersome due to the need to build very detailed finite element models to accurately reproduce the structure's damage. Adaptive mesh refinement (AMR)\cite{zhu1988adaptive} is a mesh adaptation technique used in numerical simulations to dynamically refine or coarsen the discretization of the problem domain to achieve a desired level of accuracy with minimal computational resources. The Virtual Element Method (VEM)\cite{BdV2013,BdV2015} is a recent numerical method used to solve partial differential equations (PDEs) by employing a domain discretization in general polytopal elements. Due to this feature, VEM has already been used to model complex microstructure behaviour\cite{LoCascio2020CS,LoCascio2021IJMS}. In this work, VEM's flexibility in the choice of elements' geometry is exploited in developing a procedure which combines AMR and a Continuous damage mechanics (CDM) approach to efficiently model crack propagation in heterogeneous material. Several numerical examples of crack propagation in complex microstructure are presented to show the procedure's potential.