A mixed-enhanced strain method: Part I: Geometrically linear problems

A general formulation of an assumed strain method in the context of mixed finite elements is presented. A mixed strain field is presented to which an enhancement is added resulting in a formulation which produces coarse mesh accuracy in bending dominated problems and locking-free response in the near incompressible limit. The structure of the mixed fields present permits a consistent variational stress recovery. Also, the construction of the formulation is such that the mixed parameters may be obtained explicitly and the resulting finite element arrays obtain full rank using standard order quadrature. In this paper our attention is restricted to the area of geometrically linear problems in solid mechanics. Specifically, we investigate the proposed formulation in the setting of nearly incompressible elasticity, physically nonlinear plasticity and thin shell structures. Representative simulations show favorable performance of the formulation.