Keywords: interface elements, kinematic inconsistency, finite elements analysis.

Interface elements have been used in many engineering problems since late sixties. The two-dimensional element proposed by Goodman et al. [1] in 1968 is often referred to as the first application of an interface element. Its formulation was derived by interpolating displacement fields in two faces separated by a null thickness, and strains were obtained from relative movements of the faces. Since then, several interface elements were proposed, many of which were based in the same idea of the original approach. Membrane and solid elements with minor or no modifications and a small thickness were also used [2,3]. A third approach was to use linkage elements, in which opposite nodes were connected by discrete springs.

According to Kaliakin and Li [4], although the Goodman's element has a robust normal response, it possesses a deficiency of the tangential behavior, which was named kinematic inconsistency. In a recent work [5], it was proved that kinematic inconsistency also occurs in the triangular three-dimensional version of this element. It was also shown that this is a natural behavior of rectangular membrane elements with one side much smaller then the other.

Ghaboussi et al. [6] and Beer [7] used an approach similar to the adopted by Goodman et al. [2], but the displacement field at the faces was taken from surrounding elements. For a two-dimension analysis, if the surrounding elements are bilinear quadrilateral solids, then this approach will be equivalent to the original model of Goodman. In a three-dimensional analysis, if the surrounding elements are linear tetrahedral, then the resulting interface element will be the triangular version of the Goodman's element. Thus, kinematic inconsistency may appear in many interface models, such as those based in thin membrane and solid elements and the many variations of the original approach of Goodman et al.

In this paper, we study the quadrilateral version of the interface element of Goodman et al. This element was considered by Schellekens and De Borst [8], who considered different numerical integration schemes to avoid stress oscillations. Here, the stiffness matrix of this element is explicitly integrated, and it is shown that kinematic inconsistency is also present. We also show that kinematic inconsistency may be responsible for shear stress oscillation, and new kinematic consistent interface elements are presented. These new elements are very simple, and involve no additional costs to the analysis.

1

R.E. Goodman, R.L.Taylor, T.L. Brekke. "A model for the mechanics of jointed rock", ASCE J. Soil Mech. Fdns. Div 1968; 99: 637-659.

2

O.C. Zienkiewicz, B. Best, C. Dullage, K.C. Stagg, "Analysis of non-linear problems in rock mechanics with particular reference to jointed rock systems", Proc 2nd Int Conf of the Society of Rock Mechanics, Belgrade 1970: 8-14.

3

C.S. Desai, M.M. Zaman, J.G. Lightner, H.J. Siriwardame, "Thin layer element for interface and joints", Int J Num Anal Meth Geomech 1984; 8: 19-43. doi:10.1002/nag.1610080103

4

V.N. Kaliakin, J. Li, "Insight into deficiencies associated with commonly used zero-thickness interface elements", Computers and Geotechnics 1995; 17: 225- 252. doi:10.1016/0266-352X(95)93870-O

5

A.L.G.A Coutinho, M.A.D. Martins, R.M. Sydenstricker, J.L.D. Alves, L. Landau, "Simple zero thickness kinematic consisten interface elements", Computers and Geotechnics , submitted for publication in 2002.

6

J. Ghaboussi, E.L. Wilson, J. Isenberg, "Finite element for rock joints and interfaces", ASCE J Soil Mech Found Div 1973; 99: 833-848.

7

G. Beer, "An isoparametric joint/interface element for finite element analysis", Int J Num Meth Eng 1985; 21: 585-600. doi:10.1002/nme.1620210402

8

J.C.J. Schellekens, R. De Borst, "On the numerical integration of interface elements", Int J Num Meth Eng 1993; 36: 43-66 . doi:10.1002/nme.1620360104

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