A displacement-based nonlinear finite element formulation using meshfree-enriched triangular elements for the two-dimensional large deformation analysis of elastomers

In this paper a displacement-based meshfree-enriched finite element method, which was proposed for the linear modeling of near-incompressible elasticity, is generalized for the nonlinear analysis of elastomers. A four-noded triangular element based on the convex meshfree approximation is utilized to discretize the domain. An area-weighted smoothing of deformation gradient is performed on the four-noded triangular elements to provide a locking-free analysis for near-incompressible materials. The L2-orthogonality property of the smoothing operator enables the employed Hu–Washizu–de Veubeke variational to be degenerated to an assumed strain method. Different from the extra displacement fields in the conventional assumed strain methods or bubble-enriched finite element methods, the enriched meshfree nodes carry physical quantities and are not eliminated by a local static condensation procedure. This leads to a displacement-based formulation easily to be implemented in the existing finite element code. Several numerical examples are solved to demonstrate the effectiveness and accuracy of the proposed formulation for the large deformation analysis of elastomers.

► Meshfree-enriched triangular element is incorporated in a nonlinear FEM.
► Smoothed deformation gradient is introduced.
► Displacement-based variational formulation is derived.
► Near-incompressible problems of elastomers are solved.
► Results are volumetric locking-free and pressure oscillation-free.