Continuum damage models with non-conventional finite element formulations

C.M. Silva , L.M.S.S. Castro

In recent years, some research effort has been devoted to the development of nonconventional finite element models for the analysis of concrete structures. These models use continuum damage mechanics to represent the physically non-linear behavior of this quasi-brittle material. Two alternative approaches proved to be robust and computationally competitive when compared with the classical displacement finite element implementations. The first corresponds to the hybrid-mixed stress model where both the effective stress and the the displacement fields are independently modeled in the domain of each finite element and the displacements are approximated along the static boundary, which is considered to include the interelement edges. The second approach corresponds to a hybrid displacement model. In this case, the displacements in the domain of each element and the tractions along the kinematic boundary are independently approximated. Since it is a displacement model, the inter-element boundaries are now included in the kinematic boundary. In both models, complete sets of orthonormal Legendre polynomials are used to define all approximations required so very effective -refinement procedures can be implemented. This paper illustrates the numerical performance of these two alternative approaches and compares their efficiency and accuracy with the classical finite element models. For this purpose, a set of numerical tests is presented and discussed.

Mots clés: Hybrid and mixed finite element formulations; Non-local damage models; Legendre polynomials

C.M. Silva, L.M.S.S. Castro. Continuum damage models with non-conventional finite element formulations. International Journal of Non-Linear Mechanics, 2010, 45 (2), pp.83. ⟨10.1016/j.ijnonlinmec.2009.09.005⟩. ⟨hal-00607490⟩