Stabilized finite element formulation for elastic–plastic finite deformations

This paper presents a stabilized finite element formulation for nearly incompressible finite deformations in hyperelastic–plastic solids, such as metals. An updated Lagrangian finite element formulation is developed where mesh dependent terms are added to enhance the stability of the mixed finite element formulation. This formulation circumvents the restriction on the displacement and pressure fields due to the Babu?ka–Brezzi condition and provides freedom in choosing interpolation functions in the incompressible or nearly incompressible limit, typical in metal forming applications. Moreover, it facilitates the use of low order simplex elements (i.e. P1/P1), reducing the degrees of freedom required for the solution in the incompressible limit when stable elements are necessary. Linearization of the weak form is derived for implementation into a finite element code. Numerical experiments with P1/P1 elements show that the method is effective in incompressible conditions and can be advantageous in metal forming analysis.