On a consistent hourglass stabilization technique to treat large inelastic deformations and thermo‐mechanical coupling in plane strain problems

In linear elasticity, the concept of reduced integration combined with hourglass stabilization can be directly derived from a mixed method, if certain assumptions are made. Such a derivation is much more difficult when the relation between stress and strain is highly non‐linear. Earlier works use the linearized form of a classical multi‐field functional in order to derive the hourglass stabilization analytically. In the present contribution, it is shown how such stabilization techniques can be directly derived at the level of the weak form. Crucial to the new concept is a Taylor expansion of the constitutively dependent quantities with respect to the centre of the element. The approach is suitable for various kinds of inelastic material models and thermo‐mechanical coupling. One of the important features of the new element technology is its computational efficiency which is especially visible when the numerical effort at the element level is very high.