Serendipity virtual element formulation for nonlinear elasticity. (15th October 2019) - De Bellis, M.L.; Wriggers, P.; Hudobivnik, B.
Highlights: The novel Serendipity Virtual Elements are exploited to solve nonlinear elasticity problems in 2D. Second order polynomials are adopted for the projection part. Different stabilization approaches are proposed and compared. Numerical simulations reproducing classical benchmarks provide encouraging results. Abstract: In this paper, the novel concept of Serendipity Virtual Elements is extended to the case of compressible hyper-elastic materials in 2D. Second order polynomials are adopted for the projection involved in the consistency part, while different stabilization techniques are proposed and critically compared with each other. Various numerical examples, involving very severe loading conditions, indicate that the proposed elements are very accurate and robust with respect to distortion. Furthermore the proposed virtual elements are inherently able to capture higher order deformation modes, such as bending states.