T. Boukharouba et al. (eds.), Damage and Fracture Mechanics: Failure Analysis of Engineering
© Springer Science + Business Media B.V. 2009
Mixed Finite Element for Cracked Interface
S. Bouziane
1
, H. Bouzerd
1
and M. Guenfoud
2
1
Civil Engineering department, University of Skikda, Skikda, Algeria
2
Laboratory of Civil Engineering and Hydraulics, University of Guelma, Guelma, Algeria
Abstract Several disorders observed in an existing work on civil engineering may have their
origin in local phenomena which reveal the weak points of this work. These critical zones are
located, on the one hand in the links between materials or interfaces, on the other hand in
singularly formed areas such as cavities, angles and cracks, seats of strong stress concentrations.
In this paper, the finite element method (mixed formulation) is used for the study of the
interfacial cracks in bimaterials. A special finite element based on the mixed formulation, able to
take into account the continuity of the interface on the coherent part (mechanical and geometrical
continuity), and the discontinuity of this one on the cracked part (edge effect), is used to model at
best this type of interface. This element was developed by H. Bouzerd using a direct formulation:
the shape functions of the displacement and stress fields are built directly starting from the real
configuration of the element in a reference (x, y). In this purpose, this element was reformulated
starting from a reference element in a natural plan (ȟ,Ș). This formulation presents, in addition to
the simplification of calculations, the enormous advantage of modelling the types of cracks and
their orientations. This interface element was associated with the virtual extension–crack to
evaluate the energy release rates using only one meshing by finite elements. Several numerical
examples concerning the interfacial cracks are analysed to assess the validity of this element by
comparing with an available analytical solution or numerical ones obtained from others finite
elements.
Keywords: Mixed Finite Element of Interface, Cracked Interface, Energy Release Rate, Virtual
Crack Extension, Bimaterial, Brittle Fracture.
1. Introduction
Disorders observed in an existing civil engineering structure, have generally their
origin in local phenomena which reveal the weak points of this structure. These
critical zones are located, on the one hand in the links between materials or
interfaces, on the other hand in singularly formed areas such as cavities, angles
and cracks, locations for strong stress concentrations.
In this paper, the mixed finite element method is used for the study of the
interfacial cracks in bimaterials. The mixed variational formulation has several
advantages [2] over the conventional finite element formulations, including direct
evaluation of nodal stresses along with nodal displacements and improved
accuracy of both displacements and stresses.
591
Materials and Structures, 591–600.