Curvilinear Virtual Elements for 2D solid mechanics applications

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