A mixed three-eld FE formulation for stress accurate analysis including the incompressible limit

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/displ-acement 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 …nite element methods to formulate stable displacement/stress/pressure …nite elements aimed for the solution of nonlinear problems for both solid and ‡uid …nite element (FE) analyses. The …nal goal is to design a …nite element technology able to tackle simultaneously problems which may involve isochoric behaviour (preserve the original volume) of the strain …eld together with high degree of accuracy of the stress …eld. These two features are crucial in nonlinear solid and ‡uid mechanics, as used in most numerical simulations of industrial manufacturing processes. Numerical benchmarks show that the results obtained compare very favourably with those obtained with the corresponding mixed displacement/pressure formulation.