Computational Methods for Debonding in Composites

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232 J.A. Oliveira et al. (a) (b) Fig. 11.4 Particle generation scheme for periodical RUC: (a) random representative unit-cell and (b) unit-cell periodicity (a) (b) Fig. 11.5 RUC periodicity: (a) original and (b) deformed geometries Node association procedures are divided in three different stages: on corners, edges and faces. Cell corners are linked since, in terms of periodicity/continuity, they all represent the same point in neighbouring cells. The same is done between parallel edges and parallel faces of the RUC. Afterwards, nodes are separated according to the region where they belong and boundary nodes are separated between master and slave nodes. Finally, for each node on a slave region, the program looks for the ideal node on the master region to control the slave and creates indexes that connect both nodes. Based on these indexes, it is then possible to impose the periodicity boundary constraints which are a special case of multi-freedom constraints. When working with structured finite element meshes, it is always possible to find a master node that matches the place of a given slave. However, this is not true for unstructured meshes. In this case, the mesh is often not periodic, meaning that the node distribution on a master boundary may not be the same as in the matching slave. Thus, it is necessary to check which master node is closer to where the slave is and, by association, the master is expected to be.
11 Prediction of Mechanical Properties of Composite Materials by AEH 233 11.5 Numerical Applications One of the main objectives of this work is to validate both the use of the asymptotic expansion homogenisation method and the use of unstructured finite element meshes. The AEH is applied to the prediction of the mechanical properties of composite materials with continuous fibre reinforcement. The results are obtained for structured and unstructured finite element meshes and compared with analytical and experimental results in order to validate the implemented procedures. The authors start by evaluating the applicability of the use of unstructured tetrahedral finite element meshes within the AEH method. The continuous parallel fibre reinforcement composite material studied is schematically illustrated in Fig. 11.6, along with the adopted RUC. The composite material is made of an aluminium (Al) matrix and boron (B) reinforcement. The mechanical properties of these materials are listed in Table 11.1 [12]. The homogenised elastic properties of the composite material are calculated for a reinforcement volume fraction fr = 47%. Several numerical simulations are done using two types of finite element: (i) linear tetrahedra and (ii) linear hexahedra. For each finite element type, the authors performed a convergence analysis [16] for the homogenised elasticity matrix D h that results from the homogenisation procedure applied to the representative unit-cell (see Fig. 11.6). Six different mesh refinement levels were considered for each finite element type. Numerical simulation results show that the homogenised elasticity matrices D h are orthotropic. The orthotropic character of the composite material lies on the (a) (b) Fig. 11.6 Schematic representation of (a) the continuous parallel fibre reinforcement composite material and (b) the adopted representative unit-cell Table 11.1 Elastic properties of the matrix (m) and reinforcement (r) materials of the aluminium matrix composite reinforced with boron fibres Property Value Matrix elastic modulus, Em [GPa] 68.3 Matrix Poisson coefficient, νm [-] 0.3 Reinforcement elastic modulus, Er [GPa] 379.3 Reinforcement Poisson coefficient, νr [-] 0.1
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Mechanical Response of Composites
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Pedro P. Camanho • C.G. Dávila S
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Preface The methodology for designi
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Acknowledgements The Editors of thi
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x Contents 3 Practical Challenges i
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xii Contents 8.2.4 Modelling Effect
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xiv Contents 13.1.2 EffectiveProper
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xvi List of Contributors Clara Schu
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Chapter 1 Computational Methods for
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1 Computational Methods for Debondi
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28 R. Rolfes et al. functions by me
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30 R. Rolfes et al. Microscale fibe
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32 R. Rolfes et al. symmetric, whic
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34 R. Rolfes et al. Fig. 2.5 Discre
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36 R. Rolfes et al. Unit cell (a) S
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38 R. Rolfes et al. stress state. T
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40 R. Rolfes et al. biaxial compres
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42 R. Rolfes et al. Damage Evolutio
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44 R. Rolfes et al. Fig. 2.14 Radia
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46 R. Rolfes et al. Table 2.2 Elast
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48 R. Rolfes et al. A dev is the de
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50 R. Rolfes et al. uniaxial compre
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52 R. Rolfes et al. Stress in MPa -
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54 R. Rolfes et al. 2.4.2 Results o
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56 R. Rolfes et al. 12. Hughes TJR
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58 B.N. Cox et al. inform models; a
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60 B.N. Cox et al. 3.2 The Structur
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62 B.N. Cox et al. be successfully
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64 B.N. Cox et al. high fluxes of c
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66 B.N. Cox et al. provides poor in
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68 B.N. Cox et al. For example, a c
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70 B.N. Cox et al. failures in comp
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72 B.N. Cox et al. mixed-mode crack
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74 B.N. Cox et al. 24. Elices M, Gu
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Chapter 4 Analytical and Numerical
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4 Analytical and Numerical Investig
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100 C. Schuecker and H.E. Petterman
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Chapter 6 Study of Delamination in
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6 Study of Delamination with in Com
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Chapter 7 Interaction Between Intra
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7 Interaction Between Intraply and
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Chapter 8 A Numerical Material Mode
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8 A Numerical Material Model for Pr
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14 Development of DST for the Model
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294 H. Miled et al. for this type o
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296 H. Miled et al. Fig. 15.2 Diffe
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298 H. Miled et al. Each member of
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300 H. Miled et al. temperature is
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302 H. Miled et al. Fig. 15.7 Compa
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304 H. Miled et al. Table 15.3 Prop
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306 H. Miled et al. Eqs. 15.28 and
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308 H. Miled et al. 15.4.2 Effectiv
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312 H. Miled et al. 9. Carreau P, D
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Computational Methods for Debonding in Composites

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