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An extended formulation of the macro-element (ME) based models, representing for both adherends and adhesive along the entire overlap in only one four-node element, is presented. Compared to earlier modelling, continuum ME (CME) and discrete ME (DME) based models, the adherend parts are also modelled as plane continuum media, for which high order displacement fields are freely supposed. Both extended CME (ECME) and extended DME (EDME) based modelling can have their displacement field orders of each continuum layer be set individually, and can be enriched using springs for interfaces or boundary conditions modelling, allowing the stresses to vanish at the free edges. The methodology and formulation of the stiffness matrix for both the adherend without adhesive and the bonded overlap is presented. The assessment is performed for a single-lap joint geometry by comparison results from a plane strain finite element (FE) model with extended ME-based models. Good agreements are shown for both thin and thick adhesive case studies. • Extended formulation of discrete and continuum macro-element using polynomial series, under plane stress or strain conditions. • Influence of kinematics expansion order on the adhesive and adherends stress distribution for a single lap bonded joint. • Enrichment of models with springs for interfaces or boundary conditions modelling. • Natural behaviour of stresses at free edges, along the x-axis. [ABSTRACT FROM AUTHOR]

Composite stepped repairs can achieve high strength recovery without the addition of bolts or fasteners to the structure. They are therefore a major issue in the field of aerospace composite structure damage repair. However, there is no standardized method to design this type of repairs. Many analytical, semi-analytical and finite element models were proposed throughout the years to predict the strength of stepped repairs, using various hypotheses and simplifications. The aim of this paper is to investigate the influence of modelling hypotheses on stress distribution and strength prediction of composite stepped repairs. Five simplified stepped joint models using macro-element (ME) modelling and finite element method (FE) are compared to a full 3D FE model of a stepped repaired panel. The influence of step length and adhesive fracture toughness was investigated to determine the field of validity of each model. Among FE models, it was shown that modelling the equivalent joint under 2D generalized plain strain gives a very close strength prediction to the 3D stepped repair model while saving computation time. Simplified macro-element models under bar or beam hypotheses are fairly close to the results of FE modelling, but the deviation between those and FE is sensitive to step length and adhesive fracture toughness. [ABSTRACT FROM AUTHOR]

This paper presents the development, implementation, and validation of a macro-element suitable for the linear analysis of innovative 3D plug-and-play joints between tubular columns and lightweight steel truss-girders. The macro-element is based on the component method, accounts for the three-dimensional interaction between the tube faces, and its components have a clear physical meaning. Simplified procedures are developed for the closed-form computation of the stiffness matrix of the macro-element based on the geometric and mechanical properties of the nodal zone. This facilitates practical application in everyday design scenarios. Furthermore, the macro-element's architecture is implemented in the framework of OpenSees as a standalone beam-to-column joint finite element. Validation of the conceptual design is accomplished through parametric studies, comparing its performance with models generated in higher-order finite element commercial software, Abaqus. This research offers a valuable resource for the linear analysis and design of innovative 3D plug-and-play joint connections in structural engineering, enhancing efficiency and reliability in construction practices. • Created a macro-element for linear analysis of innovative plug-and-play steel joints. • Accounted for 3D tube face interactions in component-based macro-element design. • Implemented the macro-element as a stand-alone beam-to-column joint FE in a software. • Validated the beam-to-column joint FE against higher-order FE models. [ABSTRACT FROM AUTHOR]

A methodology for the formulation of the stiffness matrix of an enriched finite element, called continuum macro-element (CME), representing for the full length of a bonded overlap and both the adhesive and the adhesive in only one four-node elements, is presented. Compared to earlier macro-elements modelling the bonded overlap as beams on elastic foundation, the CME supposed the adherends and the adhesive as plane continuum media, for which higher-order displacement fields is supposed for the adhesive. The formulation of the stiffness matrix for the adherend outside of the overlap is presented as well to address the stress analysis of single-lap bonded joint for assessment purpose. The assessment is performed by comparisons with the results from (i) a plane strain finite element and (ii) two recent papers by Nguyen and Le Grognec (2021) and Methfessel and Becker (2022). Good agreements are shown. [ABSTRACT FROM AUTHOR]

Abstract The interest in functionally graded adhesive (FGA) joints has been increasing in recent years. For example, FGAs offer the opportunity to optimize the strength of multi-material bonded joints by locally tailoring the adhesive properties and without modifying the design of the adherends to be joined. The development of dedicated stress analyses to predict the stress distribution is then of the highest interest to control the strength of such joints. The Finite Element (FE) method is able to address the stress analysis of FGA joints but is computationally costly. Simplified stress analyses have then been developed. The objective of this paper is to assess the prediction of simplified stress analyses, solved through the macro-element (ME) technique, with respect to those of FE models. It is shown that the predictions of ME models are in a sufficient agreement with the FE models to be employed at a pre-sizing stage. The influence of the overlap length is then investigated by the means of the simplified stress analyses. A noticeable result is the existence of an overlap length for which the adhesive peak shear stress is minimal, in the 1D-bar kinematics framework. [ABSTRACT FROM AUTHOR]

Abstract The demand for designing lightweight structures without any loss of strength or stiffness has conducted many engineers and researchers to seek for alternative joining methods. In this context, adhesive bonding may appear as an attractive joining method. However the interest of adhesive bonding remains while the structural integrity of the joint is ensured. According to recent literature the cohesive zone model (CZM) appears as a suitable approach able to predict both static and fatigue strength of adhesively bonded joints. This approach of the fracture process of adhesive layers is based on the modeling of the adhesive mechanical behavior through a set of adhesive cohesive properties in either mode I, mode II or mixed-mode I/II. The strength prediction of adhesively bonded joints is then highly dependent on the CZM parameters. The methods used to experimentally characterize them are thus essential. A new methodology, termed direct method, is presented and tested. It is based on the measurement of displacement field of bonded adherends at the crack tip of classical specimens allowing for the loading of the adhesive layer in pure mode I, pure mode II and mixed-mode I/II. The tested adhesive is a methacrylate–based two-component adhesive paste found under the reference SAF30 MIB manufactured by AEC Polymers (ARKEMA group). The adherends are in aluminium 6060. It is shown that it is possible to characterize the cohesive properties of the adhesive layer using the direct method. The numerical tests involve both adherends and adhesive nonlinearities. Nevertheless, the presented experimental implementation passes by the development of a dedicated data pre-processing to interpret the experimental measurements, highlighting the significance of the choice of the measurement means linked to the design of specimen. [ABSTRACT FROM AUTHOR]

Abstract Published foundation models and procedures for calculation of caisson foundation response typically assume a rigid caisson in deformable soil. However, recent published measurement data from a prototype suction bucket jacket has revealed that the lid flexibility of the caisson foundations significantly influences the dynamic foundation stiffness felt by the jacket legs. This paper investigate this soil-structure-interaction problem and presents a modelling approach for including the effect of caisson flexibility in a macro-element. The macro-element, originally developed by assuming a rigid foundation, was modified by included a stiffness correction and a procedure to account for changes in the elastic coupling between horizontal load and moment due to the caisson flexibility. The modified macro-element successfully re-produced the response to general load paths computed by geotechnical finite element analyses, where the foundation was modelled in detail with structural elements and the surrounding soil was represented by continuum elements. The general principles behind the modification is generic in the sense that it can be implemented in other foundation models. Highlights • Caisson flexibility may significantly influence the is foundation stiffness felt by above structure. • Caisson flexibility may significantly influence the coupling between moment and horizontal load. • The caisson flexibility can be implemented as a series coupled three-dimensional spring. • The series coupled extension are implemented in a macro-element in the paper and the approach can be used with other models. • Appropriate sub-modelling can be used for streamlining the computation of caisson flexibility in design. [ABSTRACT FROM AUTHOR]

Abstract Functionally graded adhesive (FGA) joints involve a continuous variation of the adhesive properties along the overlap allowing for the homogenization of the stress distribution and load transfer, in order to increase the joint strength. The use of FGA joints made of dissimilar adherends under combined mechanical and thermal loads could then be an attractive solution. This paper aims at presenting a 1D-bar and a 1D-beam simplified stress analyses of such multimaterial joints, in order to predict the adhesive stress distribution along the overlap, as a function of the adhesive graduation. The graduation of the adhesive properties leads to differential equations which coefficients can vary the overlap length. For the 1D-bar analyses, two different resolution schemes are employed. The first one makes use of Taylor expansion power series (TEPS) as already published under pure mechanical load. The second one is based on the macro-element (ME) technique. For the 1D-beam analysis, the solution is only based on the ME technique. A comparative study against balanced and unbalanced joint configurations under pure mechanical and/or thermal loads involving constant or graduated adhesive properties are provided to assess the presented stress analyses. The mathematical description of the analyses is provided. [ABSTRACT FROM AUTHOR]

The load transfer in hybrid (bolted/bonded) – denoted HBB – single-lap joints is complicated due to the association of two different transfer modes (discrete and continuous) through elements with different stiffnesses. The Finite Element (FE) method can be used to address the stress analysis of those joints. However, analyses based on FE models are computationally expensive and it would be profitable to use simplified approaches enabling extensive parametric studies. Two among the authors of this paper participated in the development of a dedicated 1D-beam approach [25]. This paper presents an extension of this framework enabling (i) the analysis of HBB joints made of dissimilar laminated or monolithic adherends, and (ii) the introduction of non linear material behaviour for both the adhesive layer and the fasteners. The output data are the distributions of displacements and forces in the adherends and fasteners, as well as those of adhesive shear and peeling stresses, allowing for a fast assessment of the material behaviour and strength prediction of HBB joints. The use of this model is illustrated in the identification of the failure mechanisms of HBB joints under quasistatic loadings, based on experimental and numerical tests on single-lap HBB joint. It is worth mentioning that the model can support pure bonded and pure bolted configurations. It can be used during the presizing phase at the design office (possibly independently on commercial software), to obtain quickly mechanical performances and to help in decision making. Moreover, it was shown that the judicious choice of the adhesive material allows for a significant increase of the static and fatigue strength compared to pure bolted or bonded corresponding configurations [17,24]. The model can then be used to formulate at best adhesive materials to optimize the mechanical performance of HBB joints according to work specifications. [ABSTRACT FROM AUTHOR]

In the present work, extended finite element method (XFEM) in conjunction with multiscale finite element method (MsFEM) is employed to model heterogeneous materials i.e. matrix having particles and/or voids. This approach, named as multiscale extended finite element method (MsXFEM), is used to determine the effective elastic properties of heterogeneous materials. The elastic properties are calculated by analyzing a representative volume element (RVE) under periodic boundary conditions. Three cases of particles and voids in the matrix i.e. matrix with hard particles, matrix with voids, and matrix with voids and hard particles both, are considered for analysis. The particles and voids are randomly distributed in the matrix. A strain energy based homogenization is carried out numerically for reinforcement volume fractions up to 50%. RVEs containing large number of discontinuities are analyzed by the proposed MsXFEM. The evaluated effective properties of the heterogeneous material are compared with the results available in the literature. These simulations show that the use of MsXFEM leads to a significant reduction in the CPU time as compared with the standard XFEM. [ABSTRACT FROM AUTHOR]

Recent earthquakes have demonstrated the high vulnerability of cultural heritage buildings, whose seismic assessment and rehabilitation constitute an important issue in seismic regions around the world. The high nonlinear behaviour of masonry material requires ad hoc refined finite element numerical models, whose complexity and computational cost are generally unsuitable for practical applications. For these reasons many authors proposed simplified numerical strategies to be used in engineering practice. However, most of these alternative methods are oversimplified since based on the assumption of in plane behaviour of masonry walls. In this paper a discrete-modelling approach for the simulation of both the in plane and out of-plane response of masonry structures is proposed. The method is applied to a basilica plan church, which has been partially investigated in the literature. The results show the capability of the proposed discrete element approach to simulate the nonlinear response of monumental structures also in those cases in which the ‘in’ and the ‘out’ of plane response cannot be decoupled, as it happens for many structural layouts typical of churches, ancient palaces and several other monumental structures. [ABSTRACT FROM AUTHOR]

The Finite Element (FE) method is able to address the stress analysis of adhesively bonded joints. However, analyses based on FE models are computationally expansive and it would be profitable to develop simplified approaches enabling extensive parametric studies. Firstly, a 1D-beam simplified model for the bonded joint stress analysis assuming a linear elastic adhesive material is presented. This model, derived from an approach inspired by the Finite Element (FE) method and based on the semi-analytical formulation of a 4-nodes macro-element, is able to simulate entire bonded overlaps at low computational costs. Secondly, a numerical procedure allowing for non-linear adhesive stress–strain relationships to be accounted for is presented. This procedure allows for various non-linear adhesive behaviors (ie. softening, plastic, etc.) to be accounted for with no restriction on the specimen geometry. The possible mixed-mode I/II response of the adhesive layer is introduced through an extension of the classical Cohesive Zone Modeling (CZM) procedure. The aforementioned procedure is then illustrated using a bi-linear softening adhesive behavior. However the procedure is not limited to this particular behavior only. The results obtained are finally compared to those of more time-consuming 2D FE strength predictions. Good agreement is shown. [ABSTRACT FROM AUTHOR]

The main aim of this work is to develop, verify and apply in simulation study an efficient hybrid approach to study seismic response of a soil-structure system taking into account all the important components as: (1) the line time-harmonic source with its specific geophysical properties; (2) the inhomogeneity and heterogeneity of the wave path from the source to the local geological region; (3) the geotechnical properties of the near-field local geological profile and finally (4) the properties of the engineering structure itself. Plane strain state is considered. The hybrid computational tool is based on the boundary element method (BEM 1 1 Boundary element method. ) for modeling the infinite far-field geological media and finite element method (FEM 2 2 Finite element method. ) for treating the dynamic behavior of the structure and the near-field finite soil geological region. Each of the two techniques is applied in that part of the whole model where it works more efficiently. The hybrid numerical scheme is realized via the sub-structure approach, direct BEM 1 , conventional FEM 2 and insertion of the BEM 1 model of the seismically active far-field geological media as a macro-finite element (MFE 3 3 Macro-finite element. ) in the FEM 2 commercial program ANSYS. The accuracy and verification study of the proposed method is presented by solution of numerical test examples simulating different seismic scenarios. The obtained results show clearly that the hybrid model is able to demonstrate the sensitivity of the synthetic signals to the source properties, to the heterogeneous character of the wave path, to the relief peculiarities of the local layered geological deposit and to the specific properties of the engineering structure. [ABSTRACT FROM AUTHOR]

Modal analyses are essential steps in structural design. Simple and quick numerical procedures and design tools for modal and dynamic analysis of bonded joints would be an attractive option to increase the efficiency of the design process in its early phases. This paper offers a simple and quick numerical tool dedicated to the modal analysis of single lap bonded joints with balanced and unbalanced adherends with various boundary conditions. Based on the macro-element technique developed with Taylor expansion in power series, this paper gives all the steps to develop the mass matrix associated with a macro-element. The mass matrix has been developed so far for 1D-bar and 1D-beam kinematic frameworks. The results obtained with the macro-element technique and a Finite Element analysis give similar results. [ABSTRACT FROM AUTHOR]

The discrepancies between the dynamic response obtained with "Beam on the nonlinear Winkler Foundation" method, as a 1D model, and the actual pile behaviour in the liquefiable ground have been identified and marked in the vast body of literature. In this study, a 1D formulation is presented for the soil-pile system which provided considerable insights on the physics of the soil behaviour around the pile in the liquefiable ground and its dependence on soil properties. Unlike the mechanical models that may or may not be generalizable, the presented method is controlled by the soil properties. By a concept that the pile response is mainly influenced by the response of soil located on a unit volume in the pile vicinity, a macro-element is hypothesized by introducing a volumetric constraint incorporating the soil volume changes. The nonlinearity of macro-element is coupled in between volumetric and distortional behaviours where an incremental plastic work is assumed. Hence a stiffness matrix operator is used, instead of a scalar value, to link the pile resistance components with displacement components. A hypo-elastic bounding surface model was developed in this framework to capture the complex mechanism of soil-pile interaction in the liquefiable ground and presents a very good accord with available field measurement and centrifuge study while the computational time reduces to a couple of minutes for an earthquake excitation. An application for the presented 1D modelling approach is presented by calculating the instantaneous period and damping of the soil-pile interaction system in the liquefiable ground. • A 1D formulation is presented for the soil-pile system in liquefiable ground. • a macro-element is hypothesized by introducing a volumetric constraint incorporating the soil volume changes. • The nonlinearity of macro-element is coupled in between volumetric and distortional behaviours. • A stiffness matrix is used in linking pile resistance to the displacement components. • Instantaneous first-mode period and damping of the soil-pile system were calculated. [ABSTRACT FROM AUTHOR]

This paper focuses on the development and the identification procedure of a new model for reinforced concrete joint elements subject to earthquake loadings. Based on the macro-elements concept framework, thermodynamics equations are derived to express robust constitutive equations which are able to simulate different kinds of wall-slab junction. The particular case-study of thermal break elements used for sustainable buildings is explored. [ABSTRACT FROM AUTHOR]

Highlights: [•] A macroelement formulation for pushover analysis of masonry buildings is presented. [•] An equilibrated force-based beam FE formulation is adopted. [•] A no-tension plasticity like constitutive relationship is used for the masonry. [•] A lumped plastic shear hinge is introduced. [•] The experimental results on masonry wall prototypes are reproduced. [ABSTRACT FROM AUTHOR]

Abstract: Seismic behaviour of steel–concrete composite high-rise buildings, composed of external steel frames (SFs) and internal concrete tube (CT), with rectangular plan is investigated in this paper. A macro-element based model is established for seismic analysis of composite high-rise buildings aiming at predicting their global responses under earthquakes. By employing this macro-element based model, natural frequencies and vibration modes, storey and inter-storey drifts, overturning moments and storey shear forces of composite structures, induced by earthquakes, are able to be obtained with much less computation time and cost compared with using micro-element based analytical models. To validate its efficiency and reliability, the macro-element based model is employed to analyse a 1/20 scaled-down model of a 25-storey steel–concrete composite high-rise building subjected to simulated earthquakes with various intensities through a shaking table. Natural frequencies and storey drifts of the model structure are obtained from numerical analyses and compared with those from shaking table test results. It has been found that the calculated dynamic responses of the composite model structure subjected to minor, basic, major and super strong earthquakes agree reasonably well with those obtained from experiments, suggesting that the proposed macro-element based model is appropriate for inelastic time-history analyse for global responses of steel–concrete composite high-rise structures subjected to earthquakes with satisfactory precision and reliability. This research thus provides a practical model for elastic and inelastic deformation check of high-rise composite buildings under earthquakes. [Copyright &y& Elsevier]

Abstract: This paper presents a macro-element to simulate dynamic Soil-Structure Interaction (SSI). This new numerical tool is suitable for dynamic (seismic) loadings on structures with shallow foundations. It takes into account the plasticity of the soil, the uplift of the foundation, effects and the radiation damping. The foundation is supposed infinitely rigid while its movement is entirely described by a system of global variables (forces and displacements) defined in its center. The nonlinear behavior of the soil and the uplift of the foundation are reproduced using the classical theory of plasticity. Uplift and plasticity are combined using the theory of multi-mechanisms. Failure is described by an interaction diagram of the ultimate bearing capacity of the foundation under combined loads. The performance of the macro-element is validated using the experimental results of the structure Camus IV. Furthermore, a parametric study on the behavior of a seven-story building shows the capability of the macro-element to consider different types of soils. Based on the results obtained it seems now possible to use this approach to investigate numerically the behavior of a wider variety of configurations. [Copyright &y& Elsevier]

Abstract: In structural engineering, soil–structure interaction (SSI) is an important phenomenon that has to be taken into account. This paper presents a 3D non-linear interface element able to compute SSI based on the “macro-element” concept. The particularity of the macro-element lies in the fact that the movement of the foundation is entirely described by a system of generalised variables (forces and displacements) defined at the foundation centre. The non-linear behaviour of the soil and the uplift mechanism of the foundation are reproduced using the plasticity theory. The failure surface is defined using an adequate overturning mechanism. Coupling of the different mechanisms is straight forward following the theory of multi-mechanisms. The macro-element is able to simulate the 3D behaviour of a rigid shallow foundation of circular, rectangular or strip shape, submitted to cyclic loadings. It is implemented into FEDEASLab, a finite element MATLAB toolbox. Comparisons with experimental results under cyclic loadings show the performance of the approach. [Copyright &y& Elsevier]

Abstract: A bivariate cubic super spline is constructed on Powell–Sabin type-1 split with the additional smoothness at vertices in the original triangulation being , which permits the Hermite interpolation up to the second order partial derivatives exactly on all the vertices in the original triangulation. The locally supported dual basis and computational details using derivatives around each vertex are given. [Copyright &y& Elsevier]

In the framework of the adhesive bonding, the assessment of interfacial properties has an essential role in determining the adhesive joints' global responses. Various surface preparations are available for each type of metallic substrate. There are plenty of tests widely used for mechanical characterisation to determine the adhesive properties and few tests to assess interfacial properties. For such a case, a specific three-point bending test can be applied to examine the interactions between adhesive and substrate. On the other hand, a direct comparison of the critical force is not always possible because of geometrical incompatibility. A practical solution for the last issue is applying a coupled stress-energy criterion (CC) since the interface properties are independent of the substrate thickness. Hence, CC and the macro-element technique were applied to determine the interfacial properties using an aluminium alloy 2024-T3 as substrate and the adhesive DGEBA/DETA™ under many preparation conditions. As a result, the three-point bending test's overall behaviour was established in terms of interface strength (adherence), including incremental energy release rate and critical stress. Thus, this paper can be read as the first work towards the ability to predict the interface failure in the frame of three-point bending test using different geometries. In conclusion, the occurrence of an adhesive or cohesive failure and the unstable or a stable failure propagation of the bonded joints were sorted and classified as a function of interface properties. [ABSTRACT FROM AUTHOR]

Many current materials and structural systems are layered. The structural performances of these multilayered systems are dependent on interfaces, the presence of which is inherent to them. A methodology for the simplified stress analysis of such structures under 1D-bar kinematics is presented. The macro-element technique is used to solve the set of ordinary differential equations involved. A dedicated macro-element is formulated through the approximation of displacements fields by Taylor expansion power series. The predictions of the simplified stress analysis are in close agreements with those obtained by FE analyses. Finally, the influence of adhesive thickness and of the overlap length on the adhesive stress peaks is presented. [ABSTRACT FROM AUTHOR]

In the framework of lightweight structures, the bonded joints appear as a suitable solution for increasing the mass-to-strength ratio. However, the full understanding of the interface debonding is a key obstacle to be overcome in critical systems. For characterizing adhesive-to-adherend interface crack initiation, the three-point bending test has been shown as a useful test that provides an identifiable small round zone. The samples were manufactured using an aluminum alloy 2024-T3 etched with nitric acid. The adhesive consisted in an epoxy pre-polymer DGEBA, DETA amine and an organosilane GLYMO directly introduced in the mixture. A coupled stress and energy criterion was used for the assessment of the properties of the interfacial debonding, since a stress concentration appears near to the corner of the specimen. For a quick computation, the application of the coupled criterion (CC) used the macro-element technique. On the other hand, most finite–element-based software has already implemented the cohesive zone modeling (CZM). In this sense, the fracture parameters computed via CC were used for the assessment of cohesive zone modeling of adhesive-to-adherend interface crack initiation. The results of fracture initiation using the CZM showed a good agreement in a macroscale response with the experimental campaign, thus providing a useful tool for a rapid estimation of cracking initiation. [ABSTRACT FROM AUTHOR]

This study aims at modelling the suction bucket foundation in clay from full finite element analyses to simplified macro-element. To ensure the reliability of finite element simulation results as much as possible, two well-known constitutive models, the Modified Cam-Clay model (MCC) and the Hardening Soil model (HS), are adopted respectively for the foundation soil which is normally consolidated clay with parameters directly determined from laboratory tests instead of inverse analysis or fitting using simple models in previous studies. The finite element analyses using both models are validated by comparing centrifugal tests and further extended to study the failure patterns in V–H–M (V ertical force– H orizontal force– M oment) space through radial displacement tests. Based on all results, two new alternative analytical formulations based on both models are then proposed to describe the three-dimensional (3D) failure envelope in V–H–M space. Finally, two new alternative macro-element design models of suction bucket foundation in clay under the same framework of hypoplasticity for both monotonic and cyclic loading conditions are proposed. By comparing with experimental results, the effectiveness and efficiency of both macro-element models are verified applicable and the one based on HS has slightly better performance than the one of MCC. • The suction bucket foundation in clay is first analysed via finite element method using advanced models. • Two new alternative analytical formulations are proposed to describe the 3D failure envelope in V–H–M space. • Two new hypoplastic macro-elements of suction bucket foundation in clay are proposed. [ABSTRACT FROM AUTHOR]

The cohesive zone modelling (CZM) is extensively used for the simulation of delamination propagation of composite laminated materials. The Finite Element (FE) method is able to support the CZM. Nevertheless, a refined mesh in the cohesive zone is required to describe accurately the energy dissipation. A 1D-beam simplified analysis based on the macro-element (ME) technique has been developed for the stress analysis of bonded joints, supporting damage evolution adhesive material law. The objective of this paper is to provide a validation of the ability of this macro-element technique for the simulation of delamination propagation in pure mode I of composite laminates. This validation is led through a comparative study between experimental test results, 3D FE model predictions and 1D-beam ME predictions. The experimental test campaign allows in particular for the assessment of the interlaminar strength and critical energy release rate in pure mode I. The thermoset unidirectional (UD) prepreg composite material IMA/M21E is used for this paper. [ABSTRACT FROM AUTHOR]

Bolting technologies have been commonly used to assemble structural members in order to carry loads. However, the main drawback of these joints is the local reduction of the strength-to-stress ratio. Compared to the bolted joints, adhesive bonding technology allows for the increase of static and fatigue strength while reducing the weight. The Finite Element (FE) method is able to address the stress analysis of bonded joints. Nevertheless, analyses based on FE models are computationally expensive. Therefore, it is profitable to develop new simplified approaches enabling extensive parametric studies. A semi-analytical technique was developed to model the joints based on the formulation of 4-node special elements, termed macro-elements, which is able to simulate an entire bonded overlap at low computational costs. In this paper, a multilayered bonded-bars and a multilayered bonded-beams macro-elements are derived from bonded-bar and bonded-beam macro-elements. 1D-bar and 1D-beam simplified stress analyses of such multilayered joints are presented in order to predict the adhesive stress distributions along the overlap. For validation purpose, the results obtained by the simplified 1D-bar and 1D-beam model are compared with the results predicted by 1D-FE models. Good agreements are shown. Finally, the parametric studies are performed in order to understand the mechanical behavior of multilayered adhesively bonded structures. This presented simplified stress analysis can be used to deduce the sizing guidelines as a consequence of these parametric studies. [ABSTRACT FROM AUTHOR]