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'''Titulo''': BEDYN: desarrollo de una metodología para caracterizar el comportamiento de estructuras de material compuesto bajo cargas dinámicas</div>

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

'''Title''': BEDYN: development of a methodology to characterize the behaviour of composite structures under dynamic loading</div>

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

Autores: </div>

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

E.V. González<sup>a</sup>, P. Villarroel<sup>a</sup>, J.M. Guerrero<sup>a</sup>, S.A. Medina<sup>a</sup>, P. Maimí<sup>a</sup>, J.A. Artero-Guerrero<sup>b</sup>, A. Cimadevilla<sup>b</sup>, M. Gascons<sup>c</sup>, J. González<sup>c</sup>, E. De Blanpre<sup>d</sup>, V. Jacques<sup>d</sup></div>

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<span style="text-align: center; font-size: 75%;"><sup>a</sup> AMADE, Mechanical Engineering and Industrial Construction Department, Universitat de Girona, Campus Montilivi s/n, Girona 17071, Spain</span></div>

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<span style="text-align: center; font-size: 75%;"><sup>b</sup> Department of Continuum Mechanics and Structural Analysis, University Carlos III of Madrid, Avda. de la Universidad, 30, Leganés 28911, Madrid, Spain</span></div>

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

<span style="text-align: center; font-size: 75%;"><sup>c</sup> COMPOXI, Parc Científic i Tecnològic de la Universitat de Girona, C/ Pic de Peguera, 9, Girona 17003, Spain</span></div>

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<span style="text-align: center; font-size: 75%;"><sup>d</sup> Dassault Aviation, Saint-Cloud 92210, France</span></div>

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==RESUMEN: ==

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La metodología de diseño de estructuras de material compuesto de matriz polimérica bajo cargas estáticas, e incluso cargas de fatiga, está actualmente bien establecida. Sin embargo, para condiciones de carga dinámica intermedia y alta, los métodos aún están en desarrollo y, a menudo, se limitan a investigaciones académicas, sin ningún tipo de estandarización. Es crucial comprender cómo se comportan los materiales utilizados en el sector aeroespacial bajo cargas dinámicas. Los materiales compuestos pueden exhibir efectos de tasa de deformación y las herramientas de análisis basadas en formulaciones estáticas podrían estar muy lejos de la respuesta estructural y del material real, por lo que se necesitan métodos de modelado, análisis y pruebas dinámicas dedicados y robustos para diseñar y certificar estructuras de material compuesto. El objetivo del proyecto BEDYN es abordar una metodología para caracterizar adecuadamente el comportamiento dinámico hasta la ruptura de estructuras de material compuesto de matriz polimérica termoestable sometidas a carga dinámica. BEDYN es un proyecto Europeo del programa Clean Sky 2 Joint Undertaking (JU).

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==ABSTRACT: ==

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The methodology of design of polymer-based composite structures under static loadings, and even fatigue loads, is quite mature and well stablished. However, for intermediate and high dynamic loading conditions, the methods are still under development and often limited to academic research levels, without any type of standardization. It is crucial to understand how the materials used in the aerospace sector behave under dynamic loadings. Composite materials may exhibit strain rate effects and the analysis tools based on static formulations could be far away from the actual material and structural response, therefore robust and industrial dedicated dynamic tests, analysis and modelling methods are then necessary to design and certify composite airframe structures. This is what the proposed project will deal with. The aim of BEDYN project is to address a methodology to properly characterize the dynamic behaviour up to rupture of thermoset polymer-based composite structures submitted to dynamic loading. BEDYN is a European granted Clean Sky 2 Joint Undertaking (JU).

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PALABRAS CLAVE: Tasa de deformación, Carga dinámica, Matriz termoestable, Caracterización de composites, Split Hopkinson Pressure Bar

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KEYWORDS: Strain rates, Dynamic loading, Thermoset resin, Material characterization, Split Hopkinson Pressure Bar

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==1 Introduction==

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When advanced polymer-based composite materials are to be used in aeronautical structural components, a design development program is generally initiated during which the performance of the structure is assessed prior to its use. Typically, the process of design starts with the analysis of a large set of simple small specimens and, when sufficient knowledge is acquired at this level, it is changed over to a more complex structure but carrying out fewer tests. This methodology is quite mature and well stablished for static and even for fatigue loads. However, for intermediate and high dynamic loading conditions, the methods are still under development and often limited to academic research levels, without any type of standardization.

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During their service life, aerospace structures can be subjected to a variety of dynamic loading cases. Crash/impact is one of the most concerning cases due to its possible disastrous consequences. Impacts on aerospace structures can be produced by the accidental or deliberate hit of an object into aircraft. Hailstones, bird strikes, runaway debris, tyre fragments or even other fragments from the aircraft structure that could be ejected in case of an accident (i.e. uncontained rotor engine failure) are examples that occur in the aerospace sector. Therefore, it is crucial to understand how the materials used in the aerospace sector behaves under dynamic loadings.

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Composite materials may exhibit strain rate effects, therefore robust and industrial dedicated dynamic coupon and element level tests, analysis and modelling methods are then necessary to design and certify composite airframe structures. The analysis tools based on static formulations could be far away from the actual material and structural response, and hence a dedicated methodology is needed for dynamic loading states. This is what the European project entitled ''Development of a methodology to characterize the BEhaviour of composite structures under DYNamic loading'', with the acronym BEDYN, will deal with.

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==='''1.1''' Objetives ===

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The aim of BEDYN is to address a methodology to properly characterize the dynamic behaviour up to rupture of thermoset polymer-based composite structures submitted to dynamic loading. Different associated objectives are accounted:

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:* Define a modelling approach suited to industrial needs for emergency situations applications (e.g. bird strike on a composite structure).

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:* Define associated dynamic tests (samples, experimental setup, etc.).

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:* Define a calibration and validation process.

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:* Demonstrate and evaluate the proposed methodology based on tests performed within the project.

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==='''1.2''' Project details===

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BEDYN is a granted Clean Sky 2 Joint Undertaking (JU) project for call H2020-CS2-CFP10-2019-01, with Dassault Aviation as Topic Manager (TM). The project started on July 2020 and it will finish in June 2023 (36 months), with a total budget of 500 k€. The Grant Agreement is #886519 and the logo is included in <span id='cite-_Ref100508971'></span>[[#_Ref100508971|Figure 1]].

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

<span style="text-align: center; font-size: 75%;"> [[Image:Draft_Martinez_538258202-image1.png|90px]] </span></div>

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<div id="_Ref100508971" class="center" style="width: auto; margin-left: auto; margin-right: auto;">

<span style="text-align: center; font-size: 75%;">'''Figure 1. '''Logo of the project.</span></div>

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The project will be carried out by a consortium with different and complementary background and capabilities. The consortium is formed by: two universities, AMADE-UdG and UC3M; and a company, COMPOXI. The main role of each partner is associated with their main specialization, in detail:

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:* AMADE-UdG: project leader. Specialized on the development of modelling strategies for the simulation of structures manufactured with advanced composite materials; characterization of materials and structures under quasi-static loading; and development of data reduction methods of complex experimental tests.

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:* UC3M: analysis and testing for the characterization of advanced composite structures under dynamic loading conditions.

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:* COMPOXI: company specialized in manufacturing of composite coupons, elements, details and substructures for the aeronautical industry.

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The topic of the project is collected to Airframe Integrated Technology Demonstrator (ITD), Part A WP A-1.4 oriented to “Virtual Modelling for Certification”, and specifically to WP A-1.4-2 on “Advanced criteria for rapid dynamic / crash modelling for safety”.

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==2 Work Packages==

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<span id='_Ref536639166'></span>Basically, BEDYN project can be split into two differentiable sets of works: numerical and experimental. In accordance with the objectives of the project, the experimental part corresponds to defining the appropriate test methods to fully characterize thermoset-based composite materials under dynamic conditions, and to analyse different topics such as flexure response, notch effect and bearing response. The numerical part is focused on defining constitutive models and a simulation strategy accounting for dynamic effects, aligned with industrial purposes and thus a good balance of accuracy and computational analysis times.

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These works are organized into 7 Work Packages (WP), the first 5 dedicated to technical tasks and the last 2 focused on management and communication activities. The relationship among the different WPs is schematically shown in <span id='cite-_Ref100571509'></span>[[#_Ref100571509|Figure 3]]. The specifications and inputs from TM are key-points at each of the WPs.

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The project starts and finishes in WP1, which contains the numerical activities to be performed (including the review, formulation and implementation of constitutive models and modelling strategy), but also, it includes the analysis of experimental results carried in the other WPs, as well as the validation of the whole methodology proposed for dynamic analysis.

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All other technical WPs, are focused on experimental activities. On one side, these experimental activities deal with the complete characterization of a thermoset composite material under dynamic loading, including elastic properties ( <math display="inline">{E}_{11}</math>, <math display="inline">{E}_{22}</math>, <math display="inline">{\nu }_{12}</math>, <math display="inline">{G}_{12}</math>), strength properties (fibre: <math display="inline">{X}_{T}</math>, <math display="inline">{X}_{C}</math>; matrix: <math display="inline">{Y}_{T}</math>, <math display="inline">{Y}_{C}</math>; shear: <math display="inline">{S}_{L}</math>) and fracture toughness (interlaminar: <math display="inline">{G}_{IC}</math>, <math display="inline">{G}_{IIC}</math>, <math display="inline">{G}_{\%C}</math>; translaminar for a given laminate). The characterization also includes an adhesive bonded joint, thus in addition to the dynamic characterization of the associated fracture toughness, the strengths must be also described. On the other hand, other topics will be analysed experimentally: flexure response, notch effect and bearing. For all tests, specimens, test setups and well-suited data reduction methods must be defined based on literature reviews or novel test methods. Since in the literature there is no agreement on the effect of dynamic loads on some material properties (for both material characterizations: ply and delamination), and in some cases, it has never been studied, this topic is a challenge. Finally, simple flat-shaped structures will be manufactured for testing under out-of-plane gelatine-impact, as experimental data for the validation of the whole methodology. Accordingly, three different specimen types can be identified: “coupon”, for characterizing basic properties of the composite material (ply), interlaminar (delamination) and adhesive interfaces; “element”, they include what can be understood as small size demonstrator; “structure”, they are devoted for characterizing the behaviour at a subcomponent level under out-of-plane dynamic loads.

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These experimental tasks will be carried out in four different WPs: WP2, definition of specimens; WP3, design of test setups and data reduction methods; WP4, manufacturing of specimens and new test rigs; and finally, WP5 the execution of the experimental test campaign.

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

 [[Image:Draft_Martinez_538258202-image2-c.png|282px]] </div>

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<div id="_Ref100571509" class="center" style="width: auto; margin-left: auto; margin-right: auto;">

<span style="text-align: center; font-size: 75%;">'''Figure 3.''' BEDYN’s Work Packages.</span></div>

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In <span id='cite-_Ref100615364'></span>[[#_Ref100615364|Table 1]], the expected outcomes for each of the WPs are summarized.

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<div id="_Ref100615364" class="center" style="width: auto; margin-left: auto; margin-right: auto;">

<span style="text-align: center; font-size: 75%;">'''Table 1. '''Outcomes for each WP.</span></div>

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{| style="width: 100%;border-collapse: collapse;" 

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|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">WP1. Dynamic modelling of material and structure </span>

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<span style="text-align: center; font-size: 75%;">* Definition of a modelling methodology compatible with industrial needs for the prediction of the behaviour of composite structures subjected to dynamic loads.</span>

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<span style="text-align: center; font-size: 75%;">* Review of support analysis tools and methods for the definition of specimens in WP2, and test setups and data reduction methods in WP3, for dynamic loading characterization.</span>

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<span style="text-align: center; font-size: 75%;">* Analysis of experimental results from WP5.</span>

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<span style="text-align: center; font-size: 75%;">* Validation of the predictive modelling methodology.</span>

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|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">WP2. Test specimens</span>

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<span style="text-align: center; font-size: 75%;">* Define test coupons, elements and structures: samples, sizes and geometries, materials, stacking sequences, and associated material properties or structure responses.</span>

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|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">WP3. Test setup design</span>

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<span style="text-align: center; font-size: 75%;">* Define the test setup for each loading ratio and specimen category (coupons, elements and structures): tester, test rig and instrumentation. </span>

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<span style="text-align: center; font-size: 75%;">* Define the data reduction schemes for post processing the raw data extracted from each test.</span>

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<span style="text-align: center; font-size: 75%;">* Generate machining drawings for adapted mounts or test rigs.</span>

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|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">WP4. Manufacturing: coupons, elements, structures and test rigs</span>

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<span style="text-align: center; font-size: 75%;">* Manufacturing and cutting of panels to obtain the specimens.</span>

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<span style="text-align: center; font-size: 75%;">* Preparation of specimens for testing.</span>

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<span style="text-align: center; font-size: 75%;">* Mechanical manufacturing of required adapted mounts and test rigs.</span>

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|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">WP5. Quasi-static and dynamic tests</span>

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<span style="text-align: center; font-size: 75%;">* Perform quasi-static tests and apply associated data reduction methods.</span>

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<span style="text-align: center; font-size: 75%;">* Perform dynamic tests and apply associated data reduction methods.</span>

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<span style="text-align: center; font-size: 75%;">* Report of experimental results for each specimen category (coupon, element and structure).</span>

|}

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==3 Methodology==

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For the development of the project, there are several Key Steps (KS) on which the BEDYN methodology will rely. These KS are described below according to the three main subjects that can be identified in the project: modelling, dynamic testing and manufacturing.

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==='''3.1''' Modelling ===

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====3.1.1 KS1. Selection and development of the modelling strategy====

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The modelling strategy for the prediction of structures under dynamic loading will be based on using Continuum Damage Mechanics (CDM) implemented in Abaqus explicit finite element code. In particular, conventional shell elements together with cohesive elements or surface-based cohesive interfaces will be used (see the sketch in <span id='cite-_Ref100619731'></span>[[#_Ref100619731|Figure 4]]). The use of shell elements is considered because of their kinematic simplicity and their useful capability to model a certain number of plies using a single shell element. Accordingly, the experimental characterization of the material will not be at laminate level, but rather at the ply level. This approach is compatible with industrial applications, allowing the simulation of any stacking sequence and composite structure. Its accuracy has been proven previously by the consortium simulating Low-Velocity Impact (LVI) and Compression After Impact (CAI) events, for laboratory coupons [1, 2] and aeronautical structures [3]. An important issue to be studied is the element distortion problem, which often appears when using a CDM approach in fast loading problems and it may suddenly stop the simulation.

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====3.1.2 KS2. Adapted intralaminar and interlaminar constitutive models====

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Although the selection of the constitutive models is implicitly done in the modelling strategy (KS1), they should be considered as a separate Key Step, given their complexity and the difficulties involved. Initially, and always after having made a complete bibliographic review of this topic, the constitutive models of the consortium that have been tested successfully for other loading cases (mostly static loading, but also in LVI tests and recently, they have been adapted for fatigue simulations), will be adapted for the simulation with dynamic loading. The reference models will be [4, 5] for intralaminar damage and [6] for interlaminar prediction. For example, for the interlaminar damage modelling the dynamic approaches described by May et al. [7, 8] will be considered. To achieve this adaptation, it will be necessary to know before which material properties are strain rate dependent. This may not have an answer, because there may not be an experimental test that gives a reliable answer. Even so, a generalist formulation can be performed so that the model is able to be defined strain rate dependent for some desired material properties.

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

 [[Image:Draft_Martinez_538258202-image3-c.png|192px]] </div>

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<div id="_Ref100619731" class="center" style="width: auto; margin-left: auto; margin-right: auto;">

<span style="text-align: center; font-size: 75%;">'''Figure 4. '''Modelling strategy based on conventional shell elements and a cohesive interaction (cohesive elements or cohesive surfaces), using surface elements tied to shell elements [1-3].</span></div>

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==='''3.2''' Dynamic testing ===

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====3.2.1 KS3. Dynamic material characterization====

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In the Building Block Approach method, different structure levels must be tested to increase test complexity while maintaining confidence levels on the experimental and numerical results. In BEDYN project, it is proposed to perform a basic material characterization in both, intralaminar and interlaminar levels (the last includes the co-bonded interface and the delamination interface). The tests considered are summarized in <span id='cite-_Ref100680781'></span>[[#_Ref100680781|Table 2]] and <span id='cite-_Ref100680783'></span>[[#_Ref100680783|Table 3]]. The use of the Split Hopkinson Pressure Bar (SHPB) bar will be required for both compressive and tensile configurations. Different coupon geometries will be used to obtain the different properties required for the model in the dynamic regime. However, there are still particular properties at which there is no available tests, such as for the dynamic interlaminar fracture toughness characterization. AMADE-UdG and UC3M were working in the development of this experimental characterization and it will be used for the present project (limited to pure mode I crack propagation; see sketches in <span id='cite-_Ref100619022'></span>[[#_Ref100619022|Figure 5]]). The selection of the specimen and test setups will be mainly done by Finite Element simulations. An important result to be satisfied is the load equilibrium during the dynamic tests to properly obtain the corresponding characterization without any inertial effect.

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

 [[Image:Draft_Martinez_538258202-image4.png|264px]] </div>

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<div id="_Ref100619022" class="center" style="width: auto; margin-left: auto; margin-right: auto;">

<span style="text-align: center; font-size: 75%;">'''Figure 5. '''Test rig to characterize fracture toughness in pure mode I using a high-speed servo-hydraulic machine (patented with international application number PCT/ES2021/070415 and publication number WO/2022/003219).</span></div>

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For SHPB test, the use of high speed camera will allow to apply Digital Image Correlation (DIC) method to obtain displacement and strain rate fields. To obtain the stress state and static equilibrium, the SHPB theory will be used.

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A unidirectional tape of epoxy/carbon fibre prepreg material and an epoxy adhesive film will be used (see <span id='cite-_Ref100659849'></span>[[#_Ref100659849|Table 4]]). Two different strain rates, plus static tests will be performed. It is worth mentioning that the static tests will be based, whenever possible, on standardized test methods. The specimen sample considered for each test configuration will be of 3+1 specimens (three for testing plus one for reserve). All specimens will be stored at laboratory conditions, 23ºC and 50%RH.

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

<span style="text-align: center; font-size: 75%;">'''Table 2. ''' ''Coupon'' specimens I/II.</span></div>

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{| style="width: 48%;margin: 1em auto 0.1em auto;border-collapse: collapse;" 

|-

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Type</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Tester</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Reference</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Results</span>

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|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Longitudinal compression</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">SHPB-C</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Ploeckl et al. (2017) [9]<br/>BEDYN research</span>

|  style="border: 1pt solid black;vertical-align: top;"|<math display="inline">{E}_{11C}</math><span style="text-align: center; font-size: 75%;">, </span> <math display="inline">{\nu }_{12}</math><span style="text-align: center; font-size: 75%;">, </span> <math display="inline">{X}_{C}</math>

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|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Transverse and off-axis tensile</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">SHPB-T</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Kuhn et al. (2015) [10]</span>

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<span style="text-align: center; font-size: 75%;">Quino et al. (2020) [11]<br/>BEDYN research</span>

|  style="border: 1pt solid black;vertical-align: top;"|<math display="inline">{E}_{22T}</math><span style="text-align: center; font-size: 75%;">, </span> <math display="inline">{\nu }_{12}</math><span style="text-align: center; font-size: 75%;">, </span> <math display="inline">{Y}_{T}</math>

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<span style="text-align: center; font-size: 75%;">Failure envelope: </span>

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<math display="inline">{\sigma }_{22T}</math><span style="text-align: center; font-size: 75%;"> - </span> <math display="inline">{\sigma }_{12}</math>

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|-

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Transverse and off-axis compression </span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">SHPB-C</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Koerber et al. (2010) [12]</span>

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<span style="text-align: center; font-size: 75%;">Ploeckl et al. (2017) [9]</span>

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<span style="text-align: center; font-size: 75%;">BEDYN research</span>

|  style="border: 1pt solid black;vertical-align: top;"|<math display="inline">{E}_{22C}</math><span style="text-align: center; font-size: 75%;">, </span> <math display="inline">{Y}_{C}</math>

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<span style="text-align: center; font-size: 75%;">Failure envelope: </span>

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<math display="inline">{\sigma }_{22C}</math><span style="text-align: center; font-size: 75%;"> - </span> <math display="inline">{\sigma }_{12}</math>

|}

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

<span style="text-align: center; font-size: 75%;">'''Table 3. ''' ''Coupon'' specimens II/II: interlaminar and adhesive bonded joint specimens.</span></div>

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{| style="width: 48%;margin: 1em auto 0.1em auto;border-collapse: collapse;" 

|-

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Type</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Tester</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Reference</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Results</span>

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|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Double Cantilever Beam - Pure mode I (DCB)</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Instron  servo hydraulic dynamic </span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">AMADE-UdG procedure</span>

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<span style="text-align: center; font-size: 75%;">(see </span><span id='cite-_Ref100619022'></span>[[#_Ref100619022|<span style="text-align: center; font-size: 75%;">Figure 5</span>]]<span style="text-align: center; font-size: 75%;">)</span>

|  style="border: 1pt solid black;vertical-align: top;"|<math display="inline">{G}_{IC}</math><span style="text-align: center; font-size: 75%;">: onset and propagation, interlaminar and adhesive bonded joint</span>

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|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">End Notched Flexure - Pure mode II (ENF)</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">SHPB-C</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Lißner et al. (2020) [13]</span>

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<span style="text-align: center; font-size: 75%;">Shamchi et al. (2022) [14]</span>

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<span style="text-align: center; font-size: 75%;">BEDYN research</span>

|  style="border: 1pt solid black;vertical-align: top;"|<math display="inline">{G}_{IIC}</math><span style="text-align: center; font-size: 75%;">: onset and propagation, interlaminar and adhesive bonded joint</span>

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|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Single Leg Bending Test - Mixed-mode 41% (SLB)</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">SHPB-C</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Lißner et al. (2020) [13]</span>

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<span style="text-align: center; font-size: 75%;">BEDYN research</span>

|  style="border: 1pt solid black;vertical-align: top;"|<math display="inline">{G}_{\%C}</math><span style="text-align: center; font-size: 75%;">: onset and propagation, interlaminar and adhesive bonded joint</span>

|-

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">Butt Joint (BJ)</span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">SHPB-T</span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">Neumayer et al. (2016) [15]</span>

​

<span style="text-align: center; font-size: 75%;">BEDYN research</span>

|  style="border: 1pt solid black;"|<math display="inline">{\tau }_{I}</math><span style="text-align: center; font-size: 75%;">: pure mode I strength adhesive bonded joint</span>

|-

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">Single Lap Shear - SLS</span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">SHPB-C</span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">BEDYN research</span>

|  style="border: 1pt solid black;"|<math display="inline">{\tau }_{II}</math><span style="text-align: center; font-size: 75%;">: pure mode II strength adhesive bonded joint</span>

|}

​

​

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

<span style="text-align: center; font-size: 75%;">'''Table 4. '''Material specifications and loading rates.</span></div>

​

{| style="width: 74%;margin: 1em auto 0.1em auto;border-collapse: collapse;" 

|-

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Item </span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Definition</span>

|-

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Composite Material</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Hexply® M21EV/34%/UD200/IMA/150ATL</span>

|-

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Adhesive</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">FM® 300M</span>

|}

​

​

====3.2.2 KS4. Dynamic structure characterization====

​

In order to analyse the effect of different properties as the notch effect (size effect), flexural behaviour and the bearing effect, ''element'' (i.e. small size demonstrator) and ''structure'' (i.e. subcomponent level) specimens will be considered in the test matrix. The element and structure tests considered are collected in <span id='cite-_Ref100681452'></span>[[#_Ref100681452|Table 5]] and <span id='cite-_Ref100681453'></span>[[#_Ref100681453|Table 6]]. The use of the SHPB bar will be required for both compressive and tensile configurations.

​

The scope of these tests are: two stacking sequences, two notch sizes and two fastener diameters for bearing tests (see <span id='cite-_Ref100681296'></span>[[#_Ref100681296|Table 7]]). It has to be noted that if specimen sizes are not adequate, it may be difficult to detect any clear effect. The specimen sample considered for each test configuration will be of 3+1 specimens (three for testing plus one for reserve). Also, two different high strain rates plus the quasi-static tests will be performed. To avoid any possible size effect, the specimens used for quasi-static testing will be with the same features as the ones used dynamically.

​

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

<span style="text-align: center; font-size: 75%;">'''Table 5. ''' ''Element'' type specimens.</span></div>

​

{| style="width: 48%;margin: 1em auto 0.1em auto;border-collapse: collapse;" 

|-

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Type</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Tester</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Reference</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Results</span>

|-

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">Three point bending</span>

​

<span style="text-align: center; font-size: 75%;">(3PB) </span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">SHPB-C</span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">Zhang et al. (2012) [16]</span>

​

<span style="text-align: center; font-size: 75%;">BEDYN research</span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">Flexural strength</span>

|-

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">Filled Hole Tension (FHT)</span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">SHPB-T</span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">BEDYN research</span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">Notch effect:</span>

​

<span style="text-align: center; font-size: 75%;">Remote strength</span>

|-

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">Filled Hole Compression (FHC)</span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">SHPB-C</span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">BEDYN research</span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">Notch effect:</span>

​

<span style="text-align: center; font-size: 75%;">Remote strength</span>

|-

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">Compact Tension (CT)</span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">SHPB-T</span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">Hoffman et al. (2018) [17]</span>

​

<span style="text-align: center; font-size: 75%;">BEDYN research</span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">Notch effect:</span>

​

<math display="inline">{G}_{C}\,</math> <span style="text-align: center; font-size: 75%;">translaminar fracture toughness</span>

|-

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">Composite-aluminium bolted joint (Bearing)</span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">SHPB-T</span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">BEDYN research</span>

|  style="border: 1pt solid black;"|<span style="text-align: center; font-size: 75%;">Bearing: </span>

​

<span style="text-align: center; font-size: 75%;">Remote strength</span>

|}

​

​

<div id="_Ref100681453" class="center" style="width: auto; margin-left: auto; margin-right: auto;">

<span style="text-align: center; font-size: 75%;">'''Table 6. ''' ''Structure ''specimens.</span></div>

​

{| style="width: 48%;margin: 1em auto 0.1em auto;border-collapse: collapse;" 

|-

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Type</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Tester</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Reference</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Results</span>

|-

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Out-of-plane gelatine impact on flat-shaped laminates (500 mm x 500 mm)</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Gas gun</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">BEDYN research</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">DIC - high speed cameras</span>

​

<span style="text-align: center; font-size: 75%;">Non-destructive Inspections</span>

|}

​

​

Regarding the testing at the subcomponent level, it will be used the pneumatic launcher from UC3M lab in which a bird substitute projectile will impact against a flat panel. The results of these tests will be used for the validation and verification of the BEDYN methodology by the TM. A total of 4 specimens will be manufactured, 2 for each stacking sequence to be tested at 2 different gelatine impact velocities, with 1 repetition for each configuration. All impact tests will be recorded with at least 3 high speed video-cameras, allowing also to obtain the strain rate and the strain field of the structure. Testing at a component level and beyond will not be considered in this proposal.

​

<div id="_Ref100681296" class="center" style="width: auto; margin-left: auto; margin-right: auto;">

<span style="text-align: center; font-size: 75%;">'''Table 7.''' Summary of specifications for Element type specimens.</span></div>

​

{| style="width: 67%;margin: 1em auto 0.1em auto;border-collapse: collapse;" 

|-

|  style="border: 1pt solid black;vertical-align: top;"|<span id='_GoBack'></span><span style="text-align: center; font-size: 75%;">Item </span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Definition</span>

|-

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Fasteners: FHT, FHC and Bearing </span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Titanium</span>

|-

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Aluminium plate: Bearing</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">2024-T3</span>

|-

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Lay-ups for ''Element'' and ''Structure ''type specimens</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Layup #1: [-45/0<sub>2</sub></span><span style="text-align: center; font-size: 75%;">/45/90/45/0<sub>2</sub></span><span style="text-align: center; font-size: 75%;">/-45/0]<sub>S</sub></span>

​

<span style="text-align: center; font-size: 75%;">Layup #2: [45/0/-45/90/-45/0/45/90/-45/0/45/90]<sub>S</sub></span>

|-

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">FHT and Bearing</span>

​

<span style="text-align: center; font-size: 75%;">(FHC, just Size #1 is tested)</span>

|  style="border: 1pt solid black;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Size #1: hole 4 mm; width 24 mm (T = 2 mN)</span>

​

<span style="text-align: center; font-size: 75%;">Size #2: hole 8 mm; width 48 mm (T = 16 mN)</span>

|}

​

​

The total number of tests to be performed including material characterization, elements and structures is of 476, 184 quasi-static plus 292 dynamic.

​

==='''3.3''' Manufacturing ===

​

====3.3.1 KS5. Quality of the specimens and milling operations====

​

Since the material properties and structure responses are essential data for the development of the BEDYN methodology, to manufacture and to milling specimens with high quality is a Key Step in the project. However, due to the high specialization of COMPOXI in the manufacture of composite structures, as it is demonstrated in previous projects developed by the company, the manufacturing quality will be guaranteed for any specimen type.

​

====3.3.2 KS6. Quality of the adapted mounts and test rigs ====

​

AMADE-UdG and UC3M have proven experience in the experimental characterization of materials in both, quasi-static and dynamic regimes. Moreover, both research groups have the experience of developing new test setups (including the manufacturing of different adapted mounts and test rigs) to perform innovative experimental testing conditions. The successful previous experience of the partners will assure the expected quality for this activity.

​

Therefore BEDYN will represent major advances or even pioneering works in the characterization of coupons based on the laminate level. Also same degree of advances are expected for the characterization in the elements level in which only scarce information can be found about the behaviour of such complex structures under high strain rate loading. The few works published in the scientific literature does not reach the strain rate that are present in an impact event. BEDYN will focused in this high strain rate range using the SHPB apparatus for reaching that level of loading rates.

​

==4 Conclusions==

​

The BEDYN project will address a methodology to properly characterize the dynamic behaviour up to rupture of thermoset polymer-based composite structures submitted to dynamic loading. The methodology includes the definition of test methods for the complete characterization of composite materials under dynamic loading as well as the definition of a finite element modelling strategy for the prediction of composite structures loaded dynamically. The project is challenging since dynamic test methods are scarce in the literature, without no standardization and often without consensus in the associated works for a given property. Therefore, the project implies the selection of specimens, test setups (tester and instrumentation) and well-suited data reduction methods. The methodology is completed with the selection of a modelling strategy for industrial purposes which will be fed by the dynamic material data cards defined.

​

The BEDYN project will contribute towards the consolidation of the use of numerical simulation in the design phase of polymer-based composite structures under dynamic loading. The BEDYN project will address innovative technologies, allowing better product development thanks to an increased knowledge of the behaviour of composite materials under dynamic loading. Maturing and validation of technologies is a key aspect of integrating research in the development process of industrial activities and next generation aircrafts.

​

==Acknowledgements ==

​

This project has received funding from the Clean Sky 2 Joint Undertaking (JU) under grant agreement No. 886519. The JU receives support from the European Union’s Horizon 2020 research and innovation programme and the Clean Sky 2 JU members other than the Union.

​

==References==

​

[1] A. Soto, E. V. González, P. Maimí, F. M. De La Escalera, J. S. De Aja, and E. Alvarez, ‘Low velocity impact and compression after impact simulation of thin ply laminates’, ''Composites Part A: Applied Science and Manufacturing'', vol. 109, pp. 413–427, 2018.

​

[2] E. V. González, P. Maimí, E. Martín-Santos, A. Soto, P. Cruz, F. M. De La Escalera, J. S. De Aja, ‘Simulating drop-weight impact and compression after impact tests on composite laminates using conventional shell finite elements’, ''International Journal of Solids and Structures'', vol. 144, pp. 230–247, 2018.

​

[3] A. Soto, E. V. González, P. Maimí, J. A. Mayugo, P. R. Pasquali, and P. P. Camanho, ‘A methodology to simulate low velocity impact and compression after impact in large composite stiffened panels’, ''Composite Structures'', vol. 204, pp. 223–238, 2018.

​

[4] P. Maimí, P. P. Camanho, J. Mayugo, and C. Dávila, ‘A continuum damage model for composite laminates: Part I–Constitutive model’, ''Mechanics of materials'', vol. 39, no. 10, Art. no. 10, 2007.

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[5] P. Maimí, P. P. Camanho, J. Mayugo, and C. Dávila, ‘A continuum damage model for composite laminates: Part II–Computational implementation and validation’, ''Mechanics of materials'', vol. 39, no. 10, Art. no. 10, 2007.

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[6] A. Turon, E. V. González, C. Sarrado, G. Guillamet, and P. Maimí, ‘Accurate simulation of delamination under mixed-mode loading using a cohesive model with a mode-dependent penalty stiffness’, ''Composite Structures'', vol. 184, pp. 506–511, 2018.

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[7] M. May, T. R. Lässig, and S. J. Hiermaier, ‘An Investigation on the Influence of Loading Rate on the Fracture Toughness of UHMW-PE Composites’, 2016.

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[8] M. May, ‘Numerical evaluation of cohesive zone models for modeling impact induced delamination in composite materials’, ''Composite Structures'', vol. 133, pp. 16–21, 2015.

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[9] M. Ploeckl, P. Kuhn, J. Grosser, M. Wolfahrt, and H. Koerber, ‘A dynamic test methodology for analyzing the strain-rate effect on the longitudinal compressive behavior of fiber-reinforced composites’, ''Composite Structures'', vol. 180, pp. 429–438, 2017.

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[10] P. Kuhn, M. Ploeckl, and H. Koerber, ‘Experimental investigation of the failure envelope of unidirectional carbon-epoxy composite under high strain rate transverse and off-axis tensile loading’, in ''EPJ Web of Conferences'', 2015, vol. 94, p. 01040.

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[11] G. Quino, V. L. Tagarielli, and N. Petrinic, ‘Effects of water absorption on the mechanical properties of GFRPs’, ''Composites Science and Technology'', vol. 199, p. 108316, Oct. 2020, doi: 10.1016/j.compscitech.2020.108316.

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[12] H. Koerber, J. Xavier, and P. P. Camanho, ‘High strain rate characterisation of unidirectional carbon-epoxy IM7-8552 in transverse compression and in-plane shear using digital image correlation’, ''Mechanics of Materials'', vol. 42, no. 11, Art. no. 11, 2010.

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[13] M. Lißner, E. Alabort, B. Erice, H. Cui, B. R. Blackman, and N. Petrinic, ‘On the dynamic response of adhesively bonded structures’, ''International Journal of Impact Engineering'', vol. 138, p. 103479, 2020.

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[14] S. P. Shamchi, M. F. S. F. de Moura, Z. Zhao, X. Yi, and P. M. G. P. Moreira, ‘Dynamic mode II interlaminar fracture toughness of electrically modified carbon/epoxy composites’, ''International Journal of Impact Engineering'', vol. 159, p. 104030, 2022, doi: [https://doi.org/10.1016/j.ijimpeng.2021.104030. https://doi.org/10.1016/j.ijimpeng.2021.104030.]

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[15] J. Neumayer, P. Kuhn, H. Koerber, and R. Hinterhölzl, ‘Experimental determination of the tensile and shear behaviour of adhesives under impact loading’, ''The Journal of Adhesion'', vol. 92, no. 7–9, Art. no. 7–9, 2016.

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[16] Y. Zhang, B. Sun, and B. Gu, ‘Experimental characterization of transverse impact behaviors of four-step 3-D rectangular braided composites’, ''Journal of composite materials'', vol. 46, no. 24, Art. no. 24, 2012.

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[17] J. Hoffmann, H. Cui, and N. Petrinic, ‘Determination of the strain-energy release rate of a composite laminate under high-rate tensile deformation in fibre direction’, ''Composites Science and Technology'', vol. 164, pp. 110–119, 2018.

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