Abstract

In previous works, the authors have presented the stabilized mixed displacement/pressure formulation to deal with the incompressibility constraint. More recently, the authors have derived stable mixed stress/displacement formulations using linear/linear interpolations to enhance stress accuracy in both linear and non-linear problems. In both cases, the Variational Multi Scale (VMS) stabilization technique and, in particular, the Orthogonal Subgrid Scale (OSS) method allows the use of linear/linear interpolations for triangular and tetrahedral elements bypassing the strictness of the inf–sup condition on the choice of the interpolation spaces. These stabilization procedures lead to discrete problems which are fully stable, free of volumetric locking or stress oscillations.

This work exploits the concept of mixed finite element methods to formulate stable displacement/stress/pressure finite elements aimed for the solution of nonlinear problems for both solid and fluid finite element (FE) analyses. The final goal is to design a finite element technology able to tackle simultaneously problems which may involve isochoric behavior (preserve the original volume) of the strain field together with high degree of accuracy of the stress field. These two features are crucial in nonlinear solid and fluid mechanics, as used in most numerical simulations of industrial manufacturing processes.

Numerical benchmarks show that the results obtained compare very favorably with those obtained with the corresponding mixed displacement/pressure formulation.