Stress analysis in adhesive joints with a multiparticle model of multilayered materials (M4)

Abstract We propose a new model to calculate the stresses in adhesive joints. It is well known that the classical models only deal with adhesive joints with constant layer thickness. The model we propose is up to calculate the stresses in adhesive joints with any geometry and with anisotropic adherends. If we consider an adhesive joint as a multilayered medium, our model describes it as a surface with as many particles in each point of the surface as the number of layers in the medium (three layers for a simple lap joint and six layers for a double lap joint). For this reason, it is named multiparticle modelisation of multilayered materials (M4 in the following of the text). The M4 models are developed at ENPC Chabot B. These de l’ecole nationale des fonts et chaussees, 1997; Ehrlacher A, Caron JF, Chabot A, Doucot E, Naciri T. Modelisation multiphasique des plaques composites en flexion, 1er Congres de Mecanique, 13–16 Avril 1993, E.N.I.M Rabat; Naciri T, Ehrlacher A, Chabot A. Compos. Sci. Technol. 1998; 58:337 for the calculation of interlaminar stresses in composite materials. The model we propose is an application of a M4 model to adhesive joints. It deals with every geometry which we can find in the literature. It only suffices to know the layer thickness in each point on the overlap to calculate the stresses in the joint. In this paper, we firstly present the classical steps to build the M4. This construction is based on the Hellinger–Reissner (Reissner E. JMath Phys, 1950; 29: 90–5) formulation. Secondly, through some joint shapes, we show that we can have a good prediction of stresses in the adhesive layer and that the M4 is a pertinent tool to study adhesive joints.