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**Contents:**

Buckling -- 5. Free Edge Stresses -- 6. Computational Micromechanics -- 7. Viscoelasticity -- 8. Continuum Damage Mechanics -- 9. Discrete Damage Mechanics -- Delaminations -- A. Tensor Algebra -- B. Levertijd We doen er alles aan om dit artikel op tijd te bezorgen. Het is echter in een enkel geval mogelijk dat door omstandigheden de bezorging vertraagd is.

Bezorgopties We bieden verschillende opties aan voor het bezorgen of ophalen van je bestelling. Welke opties voor jouw bestelling beschikbaar zijn, zie je bij het afronden van de bestelling. Schrijf een review. E-mail deze pagina. Auteur: Ever J. Unlike other texts, this one takes the theory to a hands-on level by actually solving problems.

It explains the concepts involved in the detailed analysis of composites, the mechanics needed to translate those concepts into a mathematical representation of the physical reality, and the solution of the resulting boundary value problems using the commercial finite element analysis software Abaqus.

The first seven chapters provide material ideal for a one-semester course. Along with offering an introduction to finite element analysis for readers without prior knowledge of the finite element method FEM , these chapters cover the elasticity and strength of laminates, buckling analysis, free edge stresses, computational micromechanics, and viscoelastic models and composites.

Emphasizing hereditary phenomena, the book goes on to discuss continuum and discrete damage mechanics as well as delaminations. More than 50 fully developed examples are interspersed with the theory, more than 75 exercises are included at the end of each chapter, and more than 50 separate pieces of Abaqus pseudocode illustrate the solution of example problems. The text also shows readers how to extend the capabilities of Abaqus via ""user subroutines"" and Python scripting.

Toon meer Toon minder. Similar to the section 2 of this study, the ABAQUS version is used for simulation of the impact on laminated composite plates.

The simulation is performed on the same computer mentioned in the previous section. The material modelling of composite ply has been done by linear elastic with lamina option that is available in ABAQUS. Therefore based on Table 3 of the present FE simulation, the requared materials properties are defined assuming G 13 is equal to G 12 and G 23 is equal to 2 3 G As mentioned earlier in section 3. According to the Table 3 , the mentioned parameters are defined as damage initiation, assuming S T is equal to 2 3 S L.

According to Table 4 , the interlaminar failure properties of interfaces are defined. Also the procedure that is used in this section is similar to section 2.

Therefore the delamination in stacking ply with the same fiber orientation clustering is considered and the interlaminar failure in inner layer of any cluster is ignored. As indicated in Figure 13 , seven cohesive surfaces duo to low-cost analysis are modelled according to the CZM procedure by using the properties of Table 4.

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Based on the preferences of explicit solver mentioned earlier in section 3. The hard contact law is chosen for being applied as the clearance between two surfaces becomes zero. The impactor and the target are set as the master and slave surfaces, respectively with penalty contact algorithm of balanced master-slave contact surfaces.

The impactor was modelled as deformable body with element of C3D8R and the laminated composite are meshed using SC8R elements. According to section 3, three case studies with different level of impact energies were chosen to verify the present FE simulation procedure.

Modeling of composite structures with 3D elements in ABAQUS

Therefore, impactor with initial velocities of 3. The results of impact with impactor velocity of 2. The comparison of the results for the contact force history was indicated in Figure As it is observed, there is appropriate correspondence between the results. Also unlike to the simulation results that presented by Gonzalez the fluctuations of contact force are decreased in the present FE simulation.

In Figure 15 , the FE simulation and experimental variation of energy dissipation of impactor is demonstrated as a function of time for laminated composite plate. The results indicated that the energy absorption by laminated composite plate of the present simulation has less discrepancies than simulation results presented by Gonzalez. In addition, in Figure 16 , the comparison of contact force is indicated as a function of impactor displacement for a composite plate under impact kinetic energy of The present results for the contact force history with impactor velocity of 3.

It should be mentioned Gonzalez has only reported the contact force history for this level of impact energy. The comparison of the results for the contact force history, energy absorption and contact force as a function of the impactor displacement is shown in Figure 18 , Figure 19 and Figure 20 respectively in case of impactor velocity is 3. Here, appropriated correspondence is observed.

The comparison of contact force history of three case studies Figure 14 , Figure 17 and Figure 18 is indicated that unlike to the present simulation, increasing impactor velocity leads to increasing the discrepancy between simulation and experimental results of Gonzalez Therefore the validity of the present impact simulation procedure is not dependent on the impactor velocity.

In addition as indicated in Figure 18 , the maximum contact force that reported by Gonzalez experimentally point A is equal to 8. The discrepancy in contact force point A is equal to Therefore, the accuracy of the present impact simulation is prefer than the Gonzalez simulation especially in higher impactor velocity. The best procedure is proposed which can serve as benchmark method in damage modeling of composite structures under high velocity impact for future investigations.

In addition, materials model, solution method, element type and method of cohesive definition are considered. It is observed that, less CPU run-time is required for simulation of delamination problems 2D modelling.

Furthermore, cohesive surface rather than cohesive element should be used in 3D modelling for improving the analysis runtime. Contrary to cohesive surface, there is no need to divide the initial stiffness of the cohesive element -which should be imported to the ABAQUS- by the cohesive thickness. It can be declared that, explicit solver of ABAQUS is the appropriate choice for modelling progressive damage and cohesive zone. In this study, the simulation of impact on laminated composite plates based on CZM and PDM are verified by the experimental and numerical results available in the literature.

By considering damage evolution behaviours of matrix and fiber cracking and interface delamination in three case studies with different levels of impact energies, our simulation results have an appropriate correspondence with the results of similar works especially in the aspect of force-time, force-displacement and energy time histories curves. According to the simulation results, the delamination in clustering ply is significant but the interlaminar failure in an inner layer of any cluster could be ignored. Like to Gonzalez , we have used ABAQUS finite element simulation; unlike to him, our simulation results are more accurate -about 12 percent better correspondence in maximum contact force- than his simulation results especially in higher impactor velocity.

On the other hand, our results correspond to his experimental results appropriately. Finally, the proposed method can serve as a benchmark for simple impact simulation of composite structures based on CZM and PDM in the future investigations, such as optimization study and engineering application of composite laminates under impact. Abrate, S. Cantwell, W.

Comparison of the low and high velocity impact response of CFRP. Composites, Guoqi, Z.

Penetration of laminated Kevlar by projectiles—I. Experimental investigation. International Journal of Solids and Structures, 29 4 , Cheng, W.

High velocity impact of thick composites. International journal of impact engineering, Silva, M. Numerical simulation of ballistic impact on composite laminates. International Journal of Impact Engineering, Cerioni, A. Simulation of delamination in composite materials under static and fatigue loading by cohesive zone models, Ph. Zhao, G. Journal of composite materials, Khalili, S.

Finite element modeling of low-velocity impact on laminated composite plates and cylindrical shells. Composite Structures, Gonzalez, E. Simulation of interlaminar and intralaminar damage in polymer-based composites for aeronautical applications under impact loading, Ph.

Ramadhan, A. Chou, S. Journal of Composite Materials, A continuum damage model for composite laminates: Part I—Constitutive model. Mechanics of Materials, Camanho, P. Prediction of size effects in notched laminates using continuum damage mechanics. Composites science and technology, Zou, Z.

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Modelling interlaminar and intralaminar damage in filament-wound pipes under quasi-static indentation. Tan, S. A progressive failure model for composite laminates containing openings. Shokrieh, M. Progressive fatigue damage modeling of composite materials. A progressive damage model for mechanically fastened joints in composite laminates. Turon, A. An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models. Engineering fracture mechanics, Barenblatt, G. The mathematical theory of equilibrium cracks in brittle fracture.

Advances in applied mechanics, 7: Dugdale, D.

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