DOI: 10.1016/J.CMA.2023.116555

Abstract:  In this paper, a novel higher stabilization-free virtual element method isproposed for compressible hyper-elastic materials in 2D. Different from the mosttraditional virtual element formulation, the method does not need any stabilization.The main idea is to modify the virtual element space to allow the computation ofa higher-order polynomial Lz projection of the gradient. Based on that the stifnessmatrix can be obtained directly which greatly simplifies the analysis process, es-pecially for nonlinear problems. Hyper-elastic materials are considered and somebenchmark nonlinear problems are solved to verify the capability and accuracy ofthe stabilization-free virtual element method.