A new hybrid-mixed stress model for the analysis of concrete structures using damage mechanics

This paper presents a new hybrid-mixed stress finite element model for the static analysis of concrete structures. A non-linear behaviour at the material level is assumed and to model the material's quasi-brittle behaviour damage mechanics is considered. In this model, the stress, the strain and the displacement fields are independently approximated in the domain of each element. The displacements along the static boundary, which is considered to include inter-element boundaries, are also directly approximated. Complete sets of orthonormal Legendre polynomials are used to define all approximation bases required by the finite element model. The adoption of these functions enables the use of analytical closed form solutions for the computation of all linear structural operators and leads to the development of very effective p-refinement procedures. A simple isotropic damage model is adopted and to control strain localization problems a non-local integral formulation is considered. The model being discussed is applied to the solution of two-dimensional structures. To validate the model, to illustrate its potential and to assess its accuracy and numerical efficiency, several numerical examples are discussed and comparisons are made with solutions provided by experimental tests and with other numerical results obtained using conventional finite elements.