Hybrid and Mixed Finite Element Formulations for Softening Materials

The conforming displacement elements are nowadays dominant in standard finite element applications. Nevertheless, they present some known limitations, particulary in what concerns accuracy and safety in stress estimates. With computational development and the motivation to model increasingly more complex structural problems, several alternative numerical techniques have been proposed to substitute or complement the tradicional displacement formulation, e.g. the boundary elements, meshless models and hybrid and mixed formulations. The hybrid and mixed finite element formulations adopted in this work [

2

] are developed from first-principles of Mechanics, namely, equilibrium, compatibility and constitutive relations. Recently, these formulations have been tested with continuum damage models in order to correctly simulate the behavior of softening materials such as concrete [

3

], [

5

], [

6

], [

4

]. The most promising formulations are the hybrid-mixed stress formulation, with an independent approximation of the effective stress field instead of an approximation of the stress filed [

6

], and the hybrid displacement formulation [

4

].

The objective of this communication is to compare the numerical performance of these two alternative numerical techniques with each other and also with the usually adopted displacement finite element formulation. A simple isotropic integral nonlocal damage model is adopted [

1

] and all the approximation functions of the hybrid-mixed formulations are chosen as complete sets of orthogonal Legendre polynomials. A set of benchmark tests are presented and discussed. It is shown that the alternative techniques may be competitive, namely in terms of stress estimates and computational effort.