Well-posedness and numerical performances of the strain gap method

A mixed method of approximation is discussed starting from a suitably modified expression of the Hu-Washizu variational principle in which the independent fields are displacements, stresses and strain gaps defined as the difference between compatible strains and strain fields. The well-posedness of the discrete problem is discussed and necessary and sufficient conditions are provided. The analysis of the mixed method reveals that the discrete problem can be split into a reduced problem and in a stress recovery. Accordingly, the discrete stress solution is univocally determined once an interpolating stress subspace is chosen. The enhanced assumed strain method by Simo and Rifai is based on an orthogonality condition between stresses and enhanced strains and coincides with the reduced problem. It is shown that the mixed method is stable and converges. Computational issues in the context of the finite element method are discussed in detail and numerical performances and comparisons are carried out.