  In the present work we generalize the curvilinear Virtual Element technology,
introduced for a simple linear scalar problem in a previous work, to generic 2D
solid mechanic problems in small deformations. Such generalization also
includes the development of a novel Virtual Element space for displacements
that contains rigid body motions. Our approach can accept a generic black-box
(elastic or inelastic) constitutive algorithm and, in addition, can make use of
curved edges thus leading to an exact approximation of the geometry. Rigorous
theoretical interpolation properties for the new space on curvilinear elements
are derived. We undergo an extensive numerical test campaign, both on elastic
and inelastic problems, to assess the behavior of the scheme. The results are
very promising and underline the advantages of the curved VEM approach over the
standard one in the presence of curved geometries.
