Smoothed finite element methods (S-FEMs) with polynomial pressure projection (P3) for incompressible solids

In this paper, we apply a polynomial pressure projection (P3) formulation in the smoothed finite element methods (S-FEMs) to stabilize the pressure solutions for nearly-incompressible and incompressible solids. The P3 technique, using equal-order approximation, is implemented in the cell-based S-FEM (CS), edge-based S-FEM (ES) and node-based S-FEM (NS) all using simplest triangular element. The proposed P3-S-FEMs (P3-CS, P3-ES, P3-NS) are supposed to address issues of volumetric locking and pressure oscillation using equal-order displacement-pressure approximations. Numerical examples are employed to verify and check performances of the proposed methods, demonstrating that all the P3-S-FEMs are fully volumetric locking free. Except for P3-NS, P3-CS and P3-ES are without pressure oscillation. Another founding of P3-S-FEMs is that P3 technique can further soft the whole system besides S-FEMs. The excellent properties of these S-FEMs for compressible materials are still maintained by P3-S-FEMs, such as the insensitiveness to mesh distortion. The unique upper bound property of NS-FEM is also inherited by P3-NS. In the performance studies, P3-ES stands out on accuracy, convergence and efficiency among three proposed methods.