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Generic Linking of Finite Element based Models

Final Report Summary - GLFEM (Generic Linking of Finite Element based Models)

Executive summary:

problem Area
to reduce aircraft development costs, reduce lead times and to establish a more competitive supply chain, aeronautical companies need to seamlessly couple their analysis capabilities. Often, these capabilities are embedded in digital codes. The goal of the EU seventh Framework Project "generic linking of Finite Element Models" (glFEM) is to derive innovative methods to couple finite element based structural analysis models of different origin and modelling fidelity.

description of Work
seven approaches to couple finite element based models of different origin were taken from the open literature. These approaches can be divided into tight two-way and weak one-way coupling approaches. All approaches are able to superimpose a detailed finite element model on top of a coarse finite element model. Or replace part of the coarse finite element model with a detailed finite element model. Furthermore, a technique to divide the structure into manageable parts has been developed to efficiently split the dynamic analysis of larger structures.

to implement the coupling approaches changes were made because these methods could otherwise not be implemented into a general purpose Finite Element code. Demonstration of the implemented methods was carried out on typical aerospace problems covering non-linear static and linear dynamic analysis problems.

results and Conclusions
seven methods have been developed to couple Finite Element models of different model fidelity. The developed approaches were demonstrated within a general purpose Finite Element code B2000++ or Abaqus. The methodologies were demonstrated on three use cases typically encountered in the aircraft industry.

applicability
the GLFEM project has enabled the project partners to develop technology to support the European aeronautical industry with technology to seamlessly couple their finite element based analysis models in an automated way. Model interfacing enables companies to cooperate in a definable combination of accuracy, ease of use and intellectual property protection. This contributes to reducing development costs and improving competitiveness.

project Context and Objectives:

the strategic project objective is to reduce aircraft development costs, reduce lead times and to establish a more competitive supply chain. This is achieved by enabling companies within the aeronautical supply chain to seamlessly couple their analysis capabilities by thoroughly solving analysis model interfacing. This advanced interfacing will enable companies in the supply chain to cooperate in new profitable ways providing a definable combination of accuracy, ease of use and intellectual property protection.

the operational project objective is to derive innovative methods to couple finite element based structural analysis models of different origin and modelling fidelity. The application of the coupling methods has to be generic, i.e. it comprises different local phenomena (multi-scale progressive damage, structural singularities, material features), different analysis capabilities (non-/linear static strength, stability, dynamic responses), different scales (large aircraft components down to mesoscopic models of composite fibres), different materials (composites, metals) and different demands of accuracy and efficiency. Secondly, the coupling procedure is to be automatic, i.e. local models are automatically created and analysed where necessary, and the local-global coupling is automatically integrated in the (iterative) global FE analysis. A number of different innovative and scientifically excellent approaches will be developed, demonstrated and, subsequently, compared to each other to identify excellences and limits of the application.

subsequent to the development, the generic applicable coupling approaches will be demonstrated by using prototype implementations applied upon several use cases, which are considered representative for industry, involving several analysis types. The goal is to find the best approach among the ones implemented and assure commercial implementability by porting this best of class to a commercial grade code. Key words addressing the operational project goals are competition, technology re-use, numerical strength and ease of use.

the coupling between global and local analysis models is required within each aircraft development. Global models are generally relatively crudely meshed and they are used in order to calculate the global responses (deformations, aeroelastic behaviour, internal loads etc). Those results need to be extracted and applied to locally refined models, since it is neither possible to have very fine models on the global level (computationally too expensive or not possible at all) nor to calculate detailed responses with a crude mesh. Today, the coupling between global and local analysis models is performed manually requiring a lot of effort and time. Furthermore, it has to be done numerous times for all kind of details and it has to be done repeatedly, with each development cycle (design iteration, loads iteration etc.). Therefore, there will be a tremendous saving of time, resources and cost in the aircraft development process, if the coupling of global and local models can be automated by the methods developed within GLFEM.

project Scope
more "Virtual reality" is one major aim for reducing costs lead times at aircraft development. Within this sense, expensive and time consuming testing should be more and more replaced by virtual testing. GLFEM should pave the way for a new level of virtual reality, by focusing on fundamental and generic coupling approaches for multiscale methods, which
- cover important multiscale mechanical behaviour
- are suitable for later integration into specific industrial development processes
- are reliable and robust with respect to numerical and mathematical constraints

by coupling analysis models, we imply the existence of a global model and a local model, varying in fidelity (e.g. mesh density, element type, homogenised representations etc). As a first division in approaches we distinguish tight and loose coupled models, for which the system of equations are solved respectively in a combined or separated fashion. A second division distinguishes between coupling using iterative solution schemes, as in non-linear analyses or even design optimisation, versus one-shot solution schemes, as in linear analysis solved using a direct solver. Generic self-generating interface definitions leads to a third division in approaches; either altering the mesh near the interface zone by interpolation on a node basis or coupling of element shape function based representations. Solving the resulting combined model is a distinct next step. A fourth division distinguishes between the representatives which are exchanged between different models, either kinematics (displacements, forces) or/and material properties (e.g. homogenised stiffness).

the scope of prototype implementations has several aspects. Various partners bring in their own expertise and ambition. This implies that the application of the newly developed coupled analysis capability on industrial relevant use cases is performed in a partner-centric fashion. This reduces project complexity, since progress dependencies are limited and the chain of command is clear, for these use case (UC) applications. Close cooperation and maximum synergy during the development of the coupled analysis capability between the developing partners, is assured in different ways:
- One FEM-package is used as common development platform, at which all partners will acquire access. This package has already been selected: B2000. This is an established FEM-package designed to be used as a test bed for new developments and is as such already in use for years at the majority of the involved project partners.
- In addition to B2000, approved analysis model interfacing will also be established in one commercial grade FE-package to demonstrate and assure the generic portability to industrial implementation. Also this package has already been selected: LAGRANGE. LAGRANGE API (Application programming Interface) description and (limited) source code access is open to all project partners, which mimics the environment for other commercial codes.
- Similar work, which is needed for several use cases within the WP-UC matrix structure, is performed only once and subsequently re-used from one use case to another. See Work break down

project goals

the project goals are to develop advanced methods and computational tools for structural analysis, enabling the aforementioned coupling. Hence, models can be created independently by different partners at different locations, concurrently, with a minimum of communication needed. This results in an efficient multi site product development methodology in support of the extended enterprise. Project deliverables describe this multi site methodology by application in the use cases.

though the impact on industry will be felt a few years after conclusion of this upstream research, the industrial advantage will be high, since numerical accuracy and efficiency is increased by local model refinement, without the hassle of manually generating and aligning refinements with the rest of the models. Furthermore, the self–generating interface definition secures free businesses in exchanging their capabilities, without the need to give (sensitive) inside information during model creation and enabling parties within a supply chain to expose only what they agreed to expose (e.g. model input decks).

efficient, reliable and automatic coupling strategies will overcome the time- and cost-consuming procedures of largely manually coupling global and local models within a multi-scale structural FE analysis. The application of such innovative coupling methods will, consequently, allow for substantial time and cost savings during the design and the certification phase of aeroplane structures and, thus, considerably reduce the overall development costs and lead times. Since the coupling methodology also enables model creation at different places by different parties within a supply chain, the competiveness of the aeronautical supply chain will not only benefit through decreased development cost and lead times. It also enables each company within a supply chain to do the job they can do best. It protects their core businesses, and still utilises all skills of all partners and thus strengthen the supply chain competitiveness itself.

project Results:

achievements
A number of different innovative coupling approaches have been developed, demonstrated and, subsequently, validated on a number of relevant industrial Use Cases (UC). These coupling approaches extend the state-of the- art Finite Element (FE) methods that are commonly used in industry today.

these methods have the following features in common:
- They are based on the Finite Element method.
- They are applied to deformation, stress, and stability analysis of slender structures.
- They are able to model specific regions in detail, but without performing re-meshing or mesh refinement.

in other words, the FE model is comprised of several meshes that are not compatible with each other.

the last point is the decisive factor: How the couple incompatible meshes together and to retain computational efficiency and accuracy at the same time? The coupling methods developed in GLFEM give possible answers to this question.

they derive from and improve upon the following methods:
- Kinematic coupling methods.
- Multiscale methods.
- Hierarchical superposition methods.

the main e ort devoted during the GLFEM project focused on the improvement of these methods with respect to the state-of-the-art such as can be found in commercial FE codes. While it was not possible within this project to bring all methods that were proposed and that have been developed to the level that allows their straightforward application in industry, the results obtained on the Use Cases (and on the tests) demonstrate their capabilities and the considerable potential for industrial application.

the following sections are a selection of results of the Use Cases achieved within the GLFEM project.

UC: Non linear delamination in composite panels
this Use Case(UC) was extracted from literature Greenhalg, Singh, and Nilsson (2001) Riccio, Perugini, and Scaramuzzino (2000). The main objective is to investigate and predict the behavior of a sti ened delaminated composite panel through the use of a definite element based procedure.

in order to simulate the delamination growth, fracture elements implemented in B2000++ code SMR Engineering and Development SA (2011), within the frame of previous research activities Riccio et al.

(2000) Riccio, Scaramuzzino, and Perugini (2001), have been employed. The B2000++ fracture elements are based on the Modi ed Virtual Crack Closure Technique (MVCCT, R. Krueger (2002)), by which it is possible to numerically compute the energy release rate on the delamination front for each fracture mode. An empirical delamination growth criterion based on the computed energy release rate and on the critical material toughness is then applied. Fracture elements are placed at the interface between two surfaces initially un-delaminated.

if this criterion is full in a generic location of the delamination front, nodes in that location are released allowing the separation of the two surfaces.

since the energy release rate is a function of both the forces at the crack tip and the Crack Opening Displacement (COD), a very ne three-dimensional mesh is required for the good prediction of these quantities.
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on the other hand, a ne 3D discretization of complex structures is not suitable due to the increasing of the calculation time. Hence, with the aim of extending the eld of applicability of the damage prediction tool to geometrically complex structures, a global/local approach has been used. In particular, a shell/3D modeling approach, for which a local three-dimensional solid nite element model, which represents the area of interest and where a detailed stress distribution evaluation is required, has been used only very close to the delaminated area, while a 2D-shell model has been employed for the areas of minor interest. In such a manner the accuracy of a three-dimensional model has been combined with the computational efficiency of a shell nite element model. In order to couple the shell domain to the solid one, shell-to-solid coupling elements based on kinematic constraints have been used.

in particular, two kinematic coupling approaches were investigated:
- The point-wise kinematic coupling, implemented via Shell to Solid Coupling (SSC) elements which can be automatically created in B2000++.
- The weighted residual kinematic coupling, implemented via the Common Refined Mesh (CRM) method and activated in B2000++ by the add field transfer coupling directive.

intralaminar damage, in the form of matrix cracking and per failure, has been taken into account by using a ply-discount damage material model Borelli, Selitto, and Ludwig (2010) in order to investigate its influence on the global response of the panel.

summary of work performed
in order to predict the compressive behaviour of the sti ened panel by taking into account the evolution of an embedded defect (delamination), non-linear static nite element analyses have been performed. The plydiscount material model was implemented allowing to perform a progressive damage analysis by taking into account the onset and the evolution of the fiber and matrix damage. Two kinematic coupling approaches were investigated in UC1 to perform a comparative study.

achievements
0.0.1 Point-wise vs. Weighted Residual kinematic coupling
in order to overcome some of the shortcomings (like stress jumps due to over-constraining) which are inherent to the point-wise coupling methods (such as B2000++ SSC elements), the Common Mesh Refinement (CRM) method was developed and implemented during the GLFEM project. This method belongs to the class of weighted residual kinematic coupling methods. The faces of solid elements and the edges of the shell elements are automatically coupled via boundary conditions which are automatically imposed. In addition, the surfaces where shell and solid elements are adjacent are automatically identified. The weighted residual kinematic coupling method was applied to UC1 as a reference. Six Finite Element models were investigated. In particular, for the models 1, 2 and 3 the lower mesh density (LMD1) was used while for the models 4, 5 and 6 the higher mesh density (LMD2) was adopted.

in summary, three coupling approaches were investigated:
- FE models 1 and 4: The local and the global domains were coupled via SSC elements (point-wise kinematic coupling);
- FE models 2 and 5: The local and the global domains were coupled via Field transfer boundary condition (weighted residual kinematic coupling);
- FE models 3 and 6: The local and global domains were merged. To do that, the whole skin was modeled with solid elements in order to have matching meshes at the interface between the global and local domain. This approach can be considered as the traditional approach for which no global/local elements are needed. It is worth to notice that in this traditional approach, mesh refinements are needed also in the global domain in order to obtain matching meshes at the interface.

in all the FE models, fracture elements were used to simulate the delamination growth.

FE model Local Mesh Density Kinematic Coupling Method
1 LMD1 Point-wise
2 LMD1 Weighted Residual
3 LMD1 n.a. domain merged
4 LMD2 Point-wise
5 LMD2 Weighted Residual
6 LMD2 n.a. domain merged

the reaction vs. applied strain curves obtained with the LMD1 and LMD2 models. In the figure, the curves obtained by using the point-wise kinematic coupling method, the weighted residual method and the traditional approach are compared to each other and with respect to the experimental results. Results of the different FE models are in agreement with each other and the global stiffness of the panel correlates well with the experimentally obtained stiffness.


the three numerical curves obtained with the LMD2 models are compared against experimental data obtained via LDVT. The experimental test was performed in three steps in order to allow inspection of the defect at selected intervals. By analyzing the three experimental curves, it seems that LVDT's calibration was invalidated after each test, hence, LVDT data should be used only for comparative purpose.

no important differences are observed between the results provided by the three different FE models. In particular, the delamination initiation load was found at 3200. It was found a small angle (about 8) between the delamination propagation direction and the plane y=150mm, which means that the delamination propagates in a direction almost perpendicular to the load direction. At an applied strain of about 4266 the delamination reaches the boundary of zone II. Beyond this point the growth results and the results of the analysis in general are no more reliable. This is a limit of these models where the delaminated region cannot change size during the analysis.

the delamination evolution, in terms of shape, does not change significantly passing from LMD1 models to LMD2 models. However, in the second case a better resolution of the delamination shape is observed.

the type of kinematic coupling method that is used has little effect on the results obtained for the delamination growth analysis. Moreover, results obtained with a global/local approach correlate well with those obtained with a traditional approach. The delaminated area is plotted against the applied strain for the following models:
- LMD1 model coupled via the Field Transfer boundary condition
- LMD2 model coupled via the Field Transfer boundary condition
- LMD2 model with the domain merged
the delamination initiation load predicted by the three models is the same. Nevertheless, in the models with a more refined local mesh (LMD2), a slightly faster delamination grow is observed. The mesh dependency of the
VCCT technique is a well-known problem which may be solved by adjusting the mesh parameter with respect to a DCB test.

the global/local approach allows to reduce the CPU time of about 50% (with respect to the corresponding merged model) without losing in accuracy. Models LMD2 coupled via SSC elements or via the field transfer boundary conditions seems to be a good compromise between reduced computational time and accurate results.

at the first load level (Left), the local buckling has occurred but the delamination is not yet grown. At the second load level (Right), the delamination has instead propagated significantly. The stress distribution was extracted at the mid-plane of the 30th ply which is a 0 ply belonging to the upper sub-laminate. When the upper sub-laminate starts to separate from the lower one, the load sustained by the buckled area starts to decrease. In this case, since the local domain was merged to the global domain, the continuity of the stress is guaranteed at the interface (x=200 mm and x=280 mm).

in order to verify the performances of the two investigated coupling methods in terms of stress jumps at the interfaces between the global and local domain, the stress distributions computed by the following models:
- LMD2 model coupled via SSC Elements
- LMD2 model coupled via the Field Transfer boundary condition were compared to the stress distribution which is considered as the reference stress distribution since it is not altered by the introduction of a global/local coupling approach. Stress jumps are present at the interface between the global and local domains (x=200 mm) when using both the point-wise and the weighted residual kinematic coupling. Nevertheless, the stress jumps obtained with the weighted residual method are lower with respect to the ones obtained with the point-wise method. Moreover, the extension of the area affected by "artificial" stress distribution and the deviation from the reference stress distributions are also reduced. Such smaller deviations allow to introduce smaller errors when progressive failure analysis (which is based on a reliable stress computation) is activated.

stress jumps at the interface also occurred at a load level of 1990 (before local buckling). An overview of the stress jumps obtained with the point-wise method and with the weighted residual method. The weighted residual method allows to reduce up to 87% the stress jumps at the interface with respect to the point-wise method.

to evaluate the influence of intralaminar damage on the behaviour of the investigated stiffened panel, the ply discount damage material model was activated for the LMD2 model coupled via field transfer boundary condition. In this way, possible issues due to the coexistence in the FE model of VCCT elements (for delamination growth analysis), ply-discount material model (for progressive failure analysis) and field transfer boundary condition (to couple the shell region to the solid one) were also verified.

the activation of ply-discount damage material model in the local region does not affect significantly the delamination growth rate. This was due to the fact that in the observed range of load level (3000-4400), only tensile matrix failures in the upper sublaminate were detected and no fibre failures were identified. Finally, when ply-discount damage material model is activated, no important convergence problems were encountered in the solution of the Newton-Raphson equilibrium iterations.

conclusions
the following conclusions can are drawn from the validation activity on UC1:
1. The global/local approach based on kinematic coupling elements allows to investigate and predict the behaviour of a stiffened delaminated composite panel in an efficient and effective way.
2. The introduction of a solid region modeling the area surrounding the delamination does not alter the global stiffness of the stiffened panel.
3. Results obtained with a global/local approach (point-wise or weighted residual kinematic coupling) correlate very well with those obtained with a traditional approach (domains merged). Furthermore the global/local models allow to save up to 50% of the computational time with respect to the traditional approach without losing in accuracy.
4. When using a kinematic coupling, the continuity of the displacement field is assured but stress jumps at the interface between the coupled domains are observed. The stress jumps obtained with the weighted 7 residual method are lower (up to 87%) with respect to the ones obtained with the point-wise kinematic coupling method. Moreover, the extension of the area affected by "artificial" stress distribution and the deviation from the reference stress distributions are also reduced. Such smaller deviations obtained with the weighted residual method allow to introduce smaller errors when progressive failure analysis (which is based on a reliable stress computation) is activated.
5. The activation of ply-discount damage material model in the local region to take into account intralaminar damage does not affect significantly the delamination growth rate. No serious issues due to the coexistence in the FE model of VCCT elements (for delamination growth analysis), ply-discount material model (for progressive failure analysis) and field transfer boundary condition (to couple the shell region to the solid one) were observed in the resolution of the Newton-Raphson equilibrium iterations.

UC2: Buckling of composite panels with local degradation
the analyzed structure is the panel P30 from the COCOMAT EU project cocomat. The geometry, the laminate material data, the experimental set-up, and the experimental results are described in Degenhardt, Wilckens,
klein, Kling, Rohwer, Hillger, Goetting, and Gleiter (2008). The parametric FE models were created from this data, and the numerical results were validated against these experimental results.
summary of work performed In a first step, a parametric global and global-local FE model generation tool was created, making use of the GLFEM submodeling framework. While this tool implements several FE modeling methodologies, a solid-only FE modeling technique was finally chosen. In the next step, global-only post-buckling analyses with varying mesh density were performed. The load-displacement curves and the buckling deformation pattern were compared to the experimentally obtained ones Degenhardt et al. (2008).

the von-Mises yield stresses in the adhesive layer suggested that a cohesive zone approach would be preferable over the virtual crack closure technique (VCCT). A continuum damage model was developed which was validated on mode-I debonding and delamination. Using this damage model, the global-only post-buckling analysis was performed again. The result data indicated where debonding takes place.

for the global-local analysis, the element number of the element that was located at the center of one of the debonding areas was chosen, using the baspl++ SMR Engineering and Development SA (2011) post-processor.

the global-local mesh was generated with the same mesh generation tool, using an 8 times higher mesh density for the local region. The local region is centered around the aforementioned element. A full post-buckling analysis without progressive damage was performed. Stress levels in the cohesive layer near the global-local boundary were inspected, and the load-displacement curve was compared with that of the global-only analysis.

finally, the global-local analysis was performed with progressive damage in the adhesive layer (both for the global and local part).

achievements
application of Tight-Coupling to UC2
the predicted load-displacement curves for the global FE model without degradation correspond, up to global buckling, well to the experimental result for the undamaged panel Degenhardt et al. (2008). For higher loads, a different path is followed, more akin to the results obtained for panel P29.

the cohesive zone model shows, for the given material parameters, good accuracy and a high computational effectiveness on a number of DCB mode-I debonding and delamination test cases. On the P30 panel, analyses showed a debonding pattern that qualitatively matched the von-Mises failure indices. The computational effort was not considerably higher than that of the simulations without progressive damage, and the simulations completed without much problems.

global-local FE analyses showed little differences in the load-displacement relation in comparison with the global analyses. Global-local analyses allowed for slightly more accurate prediction of stresses and of the debonding process while keeping computational costs at reasonable levels. The use of global-local kinematic coupling (two-way) coupling allowed the use of numerically efficient undistorted quadrilateral shell elements, as opposed to triangular or distorted quadrilateral shell elements that have to be used in locally-refined meshes.

however, this use case presented a number of challenges for the two-way kinematic coupling.

the parametric FE model generator is capable of generating FE models for different FE modeling methodologies, and to generate global-local FE models. It contains a simple implementation of a hot-spot criterion and implements a methodology to de ne the areas of the local models. Such automatic FE modeling tools are suited to analysis runs involving a large number of different parameters, such as sensitivity analysis 8 or optimization. However, the hotspot criterion could not be used for the P30 panel, since debonding occurs almost simultaneously at all stringers, and far too many local patches would be created.

comparison with tight coupling for UC1
there are several differences with respect to UC1. While the UC1 panel is at, the creation of the common refined mesh (CRM), which is used to compute the integral to minimize, is more di cult for curved geometries, although the curvature of the UC2 panel is rather gentle. And the regions of interest are not located on the skin but rather in the adhesive layer beneath the blade-type stringers. Thus, the global-local interfaces are more complex. Finally, the regions where local FE models shall be introduced are not pre-defined.

in contrast to UC1, where the FE models were generated with the ANSYS FE code and the global-local coupling information was added afterwards, in this work, the submodeling framework was used (a) to create the global FE model, (b) to create the local FE model(s), and © to de ne the interfaces needed for the kinematic coupling, all fully automatically. Finally, the B2000++ FE solver was used to run the (coupled) simulation.

0.0.2 FE modeling
apart from the measured deviations in overall length and radius, no imperfections were considered. The ends of the panel are clamped.

initially, a combination of shell and solid elements was used. This approach offered fast prediction of initial buckling and initial to moderate post-buckling, but required some care to obtain reliable analysis results as it did not prove to be very consistent: As the mesh density is progressively refined, the load-displacement curve should converge. This was rather di cult to achieve.

therefore, the final FE models were made of solid elements only. The skin, the adhesive layer, and the stringer foot are meshed separately, using HE3X3X2.S.TL 18-node nonlinear hexahedral solid elements. These pure-displacement elements have 3 3 nodes in-plane and 2 nodes in the transverse direction. They exhibit no instabilities, and work well in bending and for the cohesive material model described below.

the adhesive layer is colored in green, the skin in dark blue, and the stringer foot and stringer web in red.

0.0.3 FE model generation with the submodeling framework
the B2000++ input files are generated with a custom-written, parametric Python script called \gen.py" that makes use of the submodeling framework. The script is run from the command-line. The script implements other FE modeling techniques (such as the shell-solid FE models) as well. It can also create global-local FE models by analyzing an existing global FE model.

1Alternatively, 27 node hexahedral elements can be used for the laminate.
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0.0.4 Global post-buckling analysis without progressive damage
three FE models of different mesh densities were generated. The post-buckling analyses were run with a load controlled solution scheme and using artificial damping for stabilization. The maximum applied edge shortening at the end of the analysis was 4mm, and the maximum edge shortening applied between increments was 0.04mm.

cycle 2001 was chosen because it is very similar to the first cycle, but goes beyond the stringer buckling.

load-displacement curves for global-only analysis without progressive damage.
from these results, the following conclusions are drawn:
- In the linear regime, the analyses match the experimental results.
- The first buckling point (skin buckling) is accurately predicted at 0.44mm edge shortening (667 ") and 47kN.
- In initial post-buckling (after skin buckling but before stringer buckling), there is very good agreement between the numerical and the experimental results.
- The point where the stringers start to buckle is accurately predicted at 1mm edge shortening (1515 ") and 87kN. At 1.08mm edge shortening, the global buckling pattern is established.
- While there is good agreement between the solutions for Mesh Refinement (MR)=2 and MR=4, they follow a different path than the solution for MR=1. In particular, they exhibit kinks; this does not correspond to the experiment.

the experimental behavior can be recovered by using a coarse mesh or by modifying the numerical analysis parameters (e.g. maximum size of the load increment). In other words, the perfect panel exhibits a bifurcation point, and it depends on modelling or numerical imperfections (for the FE analysis) or manufacturing and loading imperfections (for the experiment), which of the two paths will be followed.

the initial global-only analysis was performed without any degradation. The von-Mises failure indices, calculated with a yield stress of 8MPa in the adhesive layer, indicate failure at the border.

an acceptable element length of 8mm (corresponding to MR=2) was found by conducting a Double Cantilever Beam test, reported in Deliverable D5.2.1. The post-buckling analysis for MR=2 was repeated with the cohesive damage model (refer to D5.2.1 for an explanation) for the adhesive layer. Global failure started already at 2.44mm edge shortening, at this point, the analysis was stopped. Up to this point, convergence of the Newton iterations and execution speed was not significantly worse than for the same analysis without progressive damage.2

it clearly differs from the analysis without progressive damage. The progressive damage analysis follows the experimentally obtained load-displacement curve (and the corresponding buckling modes).

the analyzed panel exhibits lateral debonding after initiation of stringer buckling, as was predicted by the von-Mises failure criterion. For the 2 This is mainly due to the low value of 8MPa for R1, this gives a very smooth exponential degradation curve which is beneficial to numerical efficiency. The numerical efficiency would be lessened for higher values of R1.

11 post-buckling path followed (in this case, that of the experiment), debonding is particularly pronounced on the central stringer.

while debonding process predicted by the simulation is in line with the applied von-Mises failure criterion,it is much more aggressive than in the experiment where cyclic loading up to 2mm was performed several thousands of times, with the first 2000 times having no influence on the load-displacement curve. Thus, the FE model and in particular the material model and the material parameters { despite producing correct results on DCB and multi-mode bending (MMB) FE models { do not reproduce the experimental behaviour of the P30 panel.

A possible explanation for the early debonding in the FE analyses may be found in the relatively low value of R1 = 8MPa for the tensile strength. For example, Psarras et. Al Psarras, Pinho, and Falzon (2012) used a value of 61MPa for the same combination of adhesive and laminate, however, no supporting experimental test data are given.

the DCB and MMB test cases are dominated by the energy release rates, whereas R1 has only little influence, hence, the validity of the results presented in Balzani, Wagner, Wilckens, Degenhardt, Busing, and Reimerdes (2011) are not affected. Clearly, the situation is different for the P30 panel. Thus, such tests alone are not sufficient to determine all material parameters needed to conduct progressive damage analysis on FE models with complex buckling patterns.

there is another difference between simulations and the experiment: In Degenhardt et al. (2008), the pictures showing the debonding (obtained with optically activated Lockin-Thermography) suggest that the debonding process may be initiated beneath the stringer junction rather than at the stringer boundary. This could be explained by the actual stringer geometry at the junction: There is a curvature of the laminate when going from the stringer foot to the stringer web, and the gap is filled with a wedge-shaped fillet. Therefore, the stringer web may act in similar fashion as a cantilever beam, initiating the debonding at the center. In the FE models presented here, this curvature does not exist as the junction is simplified. Thus, the FE models cannot reproduce this behavior.

0.0.6 Global-local FE model generation
the \gen.py" script described in Deliverable D5.2.1 is capable of generating global-local FE models by defining cut-outs on the stringer. On the command-line, the \{failed-element" option can be used to specify a set of global elements to replace. The algorithm works as follows:
1. Find the stringer that is nearest to the element and find the position on that stringer.
2. Using pre-defined width and length, a box is defined around that position.
3. When multiple global elements are specified, merge any overlapping boxes.
4. Create the global mesh, omitting all elements inside the boxes.
5. Create the local meshes by meshing only the elements inside the boxes.
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6. Determine the global-local interfaces (lists of element faces and edges) and set up the kinematic coupling instructions.
7. Write both meshes and all additional information to a B2000++ input file.

alternatively, the \gen.py" scripts allows to determine the elements to replace automatically, by analyzing the failure indices of a previous analysis. However, because onset of damage is not localized but occurs almost everywhere in the adhesive layer, far too many local FE models would be created when using this option.

therefore, a single region around the global element with the element number 7395 was chosen, this choice being entirely subjective.

the option \{mr-local=4" concerns the refinement of the local model w.r.t. the global. In conjunction with \{mr=2", the mesh refinement (MR) on the local level is actually 8.

global-local post-buckling analysis
initially, the same analysis parameters were used as for the global-only analysis described earlier. The convergence of the Newton iterations was markedly less good than for the global-only analysis. A closer examination revealed that, for a load increment where dissipation occurs (buckling), the convergence during the Newton iterations is initially good but slows down. In conjunction with the high number of Newton iterations (500) and the number of consecutive divergences (250) { these parameters had been chosen because of the progressive damage model { the computational efficiency is greatly reduced.

this problem has been solved by setting the maximum number of Newton iterations to lower values (e.g. 50) and the number of divergences as well (e.g. 4), and by allowing for the so-called \non-quadratic convergence":
in this case, a higher tolerance for the norm of the residual forces is automatically used when the convergence is slow.

the global-local analysis confirms the observations made on the global-only model that the stress concentrations occur along the skin-stringer boundary and confirms that the P30 panel with the given material parameters is prone to lateral debonding.

the same situation as for the global-only analysis is encountered when the global-local simulation is repeated with progressive damage: Debonding occurs from very early on, when the stringers start to buckle. The debonding process inside the local FE model does not differ from the behavior observed at the adjacent global region.

summarizing, it can be concluded that the global-local analysis of the P30 panel predicted the load displacement relation and the stresses in the cohesive layer with good accuracy. Numerical problems due to the kinematic coupling could be reduced with the aforementioned coupling methodology, but some care with the numerical analysis parameters is required to preserve computational efficiency.

conclusion
the common-refined mesh (CRM) weighted-residual kinematic coupling method has been demonstrated on UC2, using the COCOMAT P30 panel. The kinematic coupling was done such that no artificial stress jumps occurred at the global-local interface, therefore, the prediction of strains and stresses inside the adhesive layer was very accurate.

the results that were obtained with the progressive damage model showed onset of debonding in similar fashion as the much simpler von-Mises failure criterion. The extreme debonding behavior does not correspond to the experimental results; it is attributed to the selected material parameters, in particular R1.

the global-local FE analysis technique is of limited use with the P30 panel and the given material parameters, as the debonding process is simultaneously initiated at many regions, and it can be simulated with a global-only model. FE analyses with DCB models showed that for higher values of R1, a much smaller mesh density is required. In this case, debonding can only be simulated on the local level, and global-local FE analysis would become more appropriate. Global-local analysis is also more useful when only a very small number of critical regions are present.
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UC4: Panel design in fuselage design
use Case 4 is focused on demonstrating a coupling approach on an aircraft fuselage level. The geometries used are based on common aircraft data from which affective values are chosen by the authors for composite lay-up, material properties and loading. A complete description can be found in Deliverable D5.1.1.

summary of work performed

the challenges for Use Case 4 are:
- detection of hotspots,
- creation of local submodels,
- coupling between global and local model

use Case 4 focusses on the fuselage section of a realistic aircraft structure. This includes rather complex and large barrel segment models with a large number of stringers and frames. During the project and the development of the coupling approach it became apparent that there are performance limitations in terms of memory usage when using such large models. Therefore, the use case had to be modified and downsized. The simulations performed are non-linear and without damage progression. In all cases the hot-spots are automatically detected via a composite failure criterion (LaRC04) and the local models are automatically created and included in the simulation.

since no experimental results are available for the effective fuselage and panel models, validation will be performed by creating a very densely meshed global model in B2000++ using the sub-modelling framework developed in GLFEM. The results in terms of stress for static analysis will be compared with the coupling method results. This model can also be used as a calculation benchmark for comparison in terms of efficiency and accuracy with the developed coupling method.

the cases used for validation of the NLR approach are defined as a building block approach starting with a panel section and finally a complete fuselage section including window cut-outs. The first three validation cases are discussed in detail in Deliverable D5.2.1. Here, the last case is presented which can be found in Deliverable D5.2.1 as well.

achievements
hierarchical superposition method
A modified fuselage is analyzed that includes cut-outs, representing windows. This case is of interest to the designer because high stresses are calculated around window sections and detailed stress analysis is typically necessary.

FEA modelling
the fuselage section geometry and material parameters are documented in Deliverable D5.2.1.
analysis is performed @ 700 N/mm equivalent tension. The mesh density for coarse and detailed models are:
- course mesh (150 mm, ne min = 1, 4900 elements),
17
1. ECCOMAS case (compression) 2. Panel omega stringer (curved) and
C-frames
composite panel geometry with three I-stringers based on literature testcase Greenhalg et al. (2001).
the general size of the panel is a length of 300 [mm] and a width of 360 [mm].
composite curved panel with four omega stringers and three frames. The panel features a stringer pitch of 200 [mm] and a frame pitch of 600 [mm].
3. Fuselage section 4. Fuselage section with window cut-outs
composite barrel geometry based on panel #2 topology. It includes 10 stringers and three frames and a radius of 500 [mm]

composite barrel geometry including window cutouts.
the same dimensions from case #3 are used.
- detailed mesh (10 mm, ne min = 1, 120000 elements),
- coupling approach with coarse global mesh (150 mm, ne min = 1, refinement: 2 2, 3 3, 4 4, 5 5.

results
the computed results of the fuselage section with window cut-outs using a coarse and fine mesh. The analysis of the fuselage section with window cut-outs shows the stress concentrations near the cut-outs. At these stress concentration locations the local models will be created. The computed LaRC04 failure criterion has maximum value of 1.56 for the coarse mesh and 1.86 for the fine mesh.

the coarse model used to calculate the stresses underestimates the stress concentration near the windows.

here the local models can be used to re ne these high stress areas and computed higher stress concentration factors.

results in show that adding local models via the coupling approach, increases the accuracy of computed stress concentrations that are expected near the window borders. Computed results of the local models are in good agreement with the reference values. The computed failure index of the reference fine mesh has a maximum value of 1.86 and a maximum value of 1.84 is calculated for the coupling approach.

A stiffness comparison is performed with load/displacement for the reference ( fine mesh), coarse mesh and coupling approach with a 5 5 refinement. The difference in stiffness is small less than 1%.

coarse mesh Fine mesh
mesh
displacement of coarse mesh
LaRC04 output

the solver system uses one server node with 24 GB of internal memory. This is performed in steps from 700N/mm to 750 N/mm, 800 N/mm and 850 N/mm.

barrel with cutouts and different load cases
5 5 refinement @ 700 N/mm 5 5 refinement @ 750 N/mm
5 5 refinement @ 800 N/mm 5 5 refinement @ 850 N/mm

as can be observed the local model size increases as the tension load increases. Up to the point of 850 N/mm where the global and local models are too large for the solver system and an out of memory error stops the calculations.

conclusion
in this paragraph the validation cases for the NLR coupling approach with respect to use case 4 are described.

the approach enables automatic creation and insertion of local re ned models in a global model geometry. The aim is to allow calculation of stress and strain values more easily then inspecting the global model and creating and coupling the local models manually.

overall the cases discussed in this paragraph can be divided into boundary condition (BC) related stress concentrations and internal stress concentrations. Because of the automatic insertion of the local model which depends on the failure index threshold, little control can be imposed on the location of the local model; this only depends on the global element stress state.

22
aim of the approach as shown before is
(1) automatic detection of hotspots,
(2) creation of local submodels
and
(3) coupling between global and local model.

the coupling approach is capable of automatic insertion of local models and including it in the simulation. Quantitative comparison of the results shows good performance when dealing with internal stress concentrations.

convergence is observed in the fourth case with barrel including cut-outs where the detailed FEM result (reference) is reached with refined local meshes.

note: The relation between loading level and failure index threshold for the creation of local models has to be chosen carefully. A high load level or low failure index threshold will create very large local models which require significant computational power to solve.

bibliography
C. Balzani, W. Wagner, D. Wilckens, R. Degenhardt, S. Busing, and H.-G. Reimerdes. Adhesive Joints in Composite Laminates A Combined Numerical/Experimental Estimate of Critical Energy Release Rates.
technical report, Karlsruher Institut fur Technologie, Institut fur Baustatik, 2011.
R. Borelli, A. Selitto, and T. Ludwig. D2.1.3 { report on tight coupling strategies and their application to delamination growth and matrix/ fibre damage. Technical Report D2.1.3 GLFEM Consortium, 2010.
cocomat. COCOMAT EU project. URL http://www.cocomat.de/.
R. Degenhardt, D. Wilckens, H. Klein, A. Kling, K. Rohwer, W. Hillger, H.C. Goetting, and A. Gleiter.
experiments to detect damage progression in axially compressed CFRP panels under cyclic loading. Key Engineering Materials, 383:1{24, 2008.
E. Greenhalg, S. Singh, and K. F. Nilsson. Mechanisms and Modelling of Delamination Growth and Failure of Carbon-Fibre Reinforced Skin-Stringer Panels, volume Composite Structures: Theory and Practice of ASTM special technical publication, pages 49 { 71. American Society for Testing and Materials, 2001. ISBN 9780803128620.
S. Psarras, S. T. Pinho, and B. G. Falzon. Finite Element Analysis - New Trends and Developments, chapter Damage-Tolerant Design of Stiffener Run-Outs: A Finite Element Approach. InTech, DOI: 10.5772/50377 2012. ISBN 978-953-51-0769-9.
R. Krueger. The virtual crack closure technique: history, approach and applications, NASA/CR-2002-211628.
technical report, NASA, 2002.
A. Riccio, P. Perugini, and F. Scaramuzzino. Modelling compression behaviour of delaminated composite panels.
computers and Structures, 78(13):73 { 81, 2000. ISSN 0045-7949. doi: 10.1016/S0045-7949(00)00106-1. URL
http://www.sciencedirect.com/science/article/pii/S0045794900001061.
A. Riccio, F. Scaramuzzino, and P. Perugini. Embedded delamination growth in composite panels under compressive load. Composites Part B: Engineering, 32(3):209 { 218, 2001. ISSN 1359-8368. doi: 10.1016/S1359-8368(00)00057-3. URL http://www.sciencedirect.com/science/article/pii/S1359836800000573.
SMR Engineering and Development SA. The B2000++ Finite Element System, 2011.

potential Impact:

in the Work Programme the expected impacts for AREA 7.1.4.1: "Aircraft Development Cost" under ACTIVITY 7.1.4: "Improving Cost Efficiency" are divided into contributions of the following "objectives for technology readiness" by 2020:
- To reduce aircraft development costs by 50%,
- To create a competitive supply chain able to halve time to market,
- To reduce travel charges.
the aim stated within AREA 7.1.4.1 is to ensure cost efficiency in air transport focussing on the reduction of aircraft acquisition costs. Innovative solutions and technologies must result in lower lead time and costs of the aircraft and its systems from design to production, with a more competitive supply chain.

A further detailing of AREAs into topics is given in the Work Programme. The current project relates to topic AAT2008.4.1.1:"Design Systems and Tools" For this topic it is stated in the Work Programme that the current project should make contributions in the before mentioned "objectives for technology readiness" by (among others):
1. Development of advanced methods and computational tools in the fields of structural analysis.
2. Concepts and methodologies for efficient multi-site product development in support of the extended enterprise.

the answer on the question "How does GLFEM contribute towards the expected impacts" is:
- By enabling companies within the aeronautical supply chain to seamlessly couple their analysis capabilities by thoroughly solving analysis model interfacing and by providing a definable combination of accuracy, ease of use and intellectual property protection. The project deliverables are advanced methods and computational tools for structural analysis. More specifically the deliverables enable coupling of finite element based structural analysis models of different origin and modelling fidelity, with no interaction during initial model creation.
- The coupling is generic (linear, non-linear, static, dynamic, shell-to-shell, solid-to-shell) and automatic. It is applied on 4 different exemplary use cases. Several approaches have been pursued in competition, making use of a common finite element research package.
- Models can be created independently by different partners at different locations, concurrently, with a minimum of communication needed. This results in an efficient multi site product development methodology in support of the extended enterprise. Additional project deliverables describe this multi site methodology.

the entire project was dedicated to "derive, implement, apply and describe" innovative methods and tools to couple finite element based structural analysis models of different origin and modelling fidelity, with no interaction during initial model creation. So the main technical work ("derive, implement, apply") within the proposal. A second step was to "describe", to disseminate freely via publications in peer reviewed journals and a public available book. The developed knowledge, the recipe how to apply this knowledge within more industrial circumstances, are made public. Actual industrialisation lies outside the scope of this project.

dissemination of project results
being an upstream research project, the GLFEM project has delivered a number of (structural finite element based) model coupling capabilities to the European Industry and European scientific community.

reaching users has lead to the decision to have all (Foreground) deliverables public. Summarising these deliverables there are 3 project milestones, defined at month 28, 30 and 40, directly related to dissemination. At M28 a "State of the Art theoretical overview and evaluation of coupling methods" is delivered. This has resulted in the technical part of a complementary industrial proposal in 2011. Further downstream development towards implementation in commercial codes are envisaged. At M30 a Report on practical implementation of coupling methods has been delivered. This milestone is intended as public roadmap for more downstream implementations outside GLFEM. At M40 the "Final overview of GLFEM project; theory, implementation, and application" has been delivered as a manuscript for a public book.

however, the potential beneficiaries are of different kinds; hence interested in different results, need to be reached by different means and at different times. A Dissemination Action Plan (DAP) has therefore been defined to achieve this goal in the most efficient way.

dissemination Objectives
the GLFEM DAP is focused on the following objectives:
- Disseminate the main scientific achievements of GLFEM: the pro and cons of the different approaches
- Disseminate the use case applications of GLFEM
- Convince that independent concurrent model creation strengthens European (Aircraft) Competitiveness
- Highlight key additional bottlenecks and opportunities where additional effort should be focused through other R&T initiatives

dissemination Audiences
the GLFEM DAP is focused on the following audiences:
- European Aircraft Industry actors: major manufacturers, network of sub-contractors, aero-structure SME's,
- Software and Hardware Solution providers, to promote additional adaptation of their solutions to the emerging needs and means
- Engineering schools, Universities,
- R&T Centres
- Other European industry sectors that could take benefit of coupling methodology, such as Engine, Automotive, Train, Building and Ship industry

the 3 miles stones at M28, M30 and M40 represent: "The ingredients", "The recipe" and "Diner served". Hence they cover all what is needed. It is believed that each of the audiences can find what they are looking for in the (public) documentation about one (or more) of these milestones.

what to disseminate
the GLFEM DAP is focused on the following content to be disseminated:
- "State of the Art theoretical overview of coupling methods"
- "Report on practical implementation of coupling methods"
- "Final overview of GLFEM project; theory, implementation, and application"

format of dissemination that is performed
- Production of scientific articles and presentations
- Production of a public book

which means / channel / media dissemination is performed
the dissemination content, calendar and actors were managed and monitored through WP6, using a set of rules which include a Validation process for all communications, to ensure that these communications respect IPR (of background knowledge only) of the individual members. The targeted media are:
- Communication in international conferences.
- Public Book
- Use of EU network to reach other EC projects and cross-share lessons learned

exploitation of project results
the GLFEM results have reached a maturity level that does not permit a direct immediate or short-term commercial exploitation. For further development, demonstration and industrialisation a complementary more industry focused project is needed in the different areas covered by the project in order to operationally deploy and commercially exploit the capabilities and solutions validated in GLFEM.

in order to facilitate this future exploitation step the purpose of the dissemination mile stones was geared towards exploitation in a next project. At M28 a "State of the Art theoretical overview of coupling methods" has been delivered. This was used in the technical part of a complementary industrial call in 2011. However, this proposal did not receive enough points to be considered for funding. At M30 a "Report on practical implementation of coupling methods" has been delivered. This milestone is intended as public roadmap for more downstream implementations outside GLFEM. At M40 the "Final overview of GLFEM project; theory, implementation, and application" has been delivered as a manuscript for a public book. This book displays theory and implementation specifics to be used in a downstream project, as well as "show cases" (the application of use cases) to justify a complementary more downstream project.

list of Websites:

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