  We present a Virtual Element Method (VEM) for possibly nonlinear elastic and
inelastic problems, mainly focusing on a small deformation regime. The
numerical scheme is based on a low-order approximation of the displacement
field, as well as a suitable treatment of the displacement gradient. The
proposed method allows for general polygonal and polyhedral meshes, it is
efficient in terms of number of applications of the constitutive law, and it
can make use of any standard black-box constitutive law algorithm. Some
theoretical results have been developed for the elastic case. Several numerical
results within the 2D setting are presented, and a brief discussion on the
extension to large deformation problems is included.
