Elasto-plastic analysis of bonded joints with macro-elements

Abstract

International audienceThe Finite Element (FE) method could be able to address the stress analysis of bonded joints. Nevertheless, analyses based on FE models are mainly computationally cost expensive and it would be profitable to develop simplified approaches, enabling extensive parametric studies. Firstly, a one-dimensional 1D-bar and 1D-beam simplified models for the bonded joint stress analysis, assuming a linear elastic adhesive material, are presented. These models derive from an approach, inspired by the FE method using a formulation based on a four-node macro-element, which is able to simulate an entire bonded overlap. Moreover, a linear shear stress variation in the adherend thickness is included in the formulation. Secondly, a numerical procedure is then presented to introduce into both models an elasto-plastic adhesive material behavior, while keeping the previous linear elastic formulation. Finally, assuming an elastic perfectly plastic adhesive material behavior, the results produced by simplified models are compared with the results predicted by FE using 1Dbar, plane stress, and three-dimensional (3D) models. Good agreements are shown

An extended semi-analytical formulation for fast and reliable mode I/II stress analysis of adhesively bonded joints

“…ENF, DCB and MMB) and can easily be increased by a factor 3 or 4 since non-linear effects are generally limited to the close vicinity of the overlap edges (see Fig.14-16). Moreover the given procedure has been shown as 50 to 100 times quicker than equivalent 2D/3D FE predictions (Paroissien et al 2013b). …”

A comparison between macro-element and finite element solutions for the stress analysis of functionally graded single-lap joints

“…A JE is a 4-nodes brick element allowing for the modelling of two bonded adherends [15][16][17]. Over a similar period of time, the first and third authors of the present papers and co-workers have been working on the development of the macro-element (ME) technique for the simplified stress analysis of bonded, bolted and hybrid (bonded/bolted) joints made of dissimilar and possibly laminated beams [18][19][20][21][22][23][24]. The JE and ME are based on the same modelling approach.…”

“…The ME technique can be regarded as a mathematical procedure allowing for the resolution of the system of ODEs, under a less restricted application field of simplifying hypotheses, in terms of geometry, material behaviours, kinematics, boundary conditions and loads. Dedicated 4-nodes bonded-bars (BBa) and bonded-beams (BBe) have been formulated [18][19][20][21][22][23][24]. Once the stiffness matrix of the complete structure is assembled from the elementary stiffness matrices and the boundary conditions are applied, the minimization of the potential energy provides the solution, in terms of adhesive stress distributions along the overlap, internal forces and displacements in the adherends at any abscissa along the joint.…”

“…The boundary conditions and loading are applied through the Augmented Lagrangian method [25][26]. Besides, an algorithm based on the Newton-Raphson iterative procedure has been developed to support nonlinear material behaviors of the adhesive and adherends [21][22][23][24]. In the case of nonlinear computation, the overlap length needs to be meshed with n_ME MEs along the overlap length (only) to allow for the update of the material properties within the iterative procedure ( Figure 2).…”

“…In the case of the 1D-beam kinematics, the components of K BBe cannot be determined analytically and several methodologies have been suggested depending on the simplifying hypotheses [8,18,[20][21]. In the present paper, a methodology based on the exponential matrix was used [8,24]…”