  The virtual element method (VEM) allows discretization of the problem domain
with polygons in 2D. The polygons can have an arbitrary number of sides and can
be concave or convex. These features, among others, are attractive for meshing
complex geometries. VEM applied to linear elasticity problems is now well
established. Nonlinear problems involving plasticity and hyperelasticity have
also been explored by researchers using VEM. Clearly, techniques for extending
the method to nonlinear problems are attractive. In this work a novel first
order consistent virtual element method is applied within a static
co-rotational framework. To the author's knowledge this has not appeared before
in the literature with virtual elements. The formulation allows for large
displacements and large rotations in a small strain setting. For some problems
avoiding the complexity of finite strains, and alternative stress measures, is
warranted. Furthermore, small strain plasticity is easily incorporated. The
basic method, VEM specific implementation details for co-rotation, and
representative benchmark problems are illustrated. Consequently, this research
demonstrates that the co-rotational VEM formulation successfully solves certain
classes of nonlinear solid mechanics problems. The work concludes with a
discussion of results for the current formulation and future research
directions.
