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It is significant to understand the dynamic behaviour of composite laminates and the induced damage mechanisms in order to use the composite effectively. According to the abovementioned work Khalili et al. In fact the main objective is to provide a general solution for the modelling of dynamic simulation of the impact on composite plate based on PDM and CZM techniques that are available in ABAQUS without using any subroutine.

In order to achieve the mentioned goals, the valid experimental and numerical examples are selected for validating the proposed FEM approach.

First, a valid reference is chosen to verify the CZM technique. Then, several case studies of the impact loading on the composite laminates by considering intralaminar and interlaminar damage are chosen to verify the proposed finite element simulation procedure. In this section, the valid experimental and numerical reference are used to verify the proposed simulation approach.

The results of the present simulation are compared with the experimental and numerical results reported by Cerioni Consequently, the appropriate procedure was suggested for delamination on composite specimen based on CZM approach. The DCB Double Cantilever Beam test is one of the most common tests used to evaluate the mode I interlaminar fracture toughness in a composite laminate. As shown in the Figure 1 the initial delamination is forced to open by applying a displacement that pull the two beams of the specimen away from each other.

The material properties given for composite plies of DCB specimen and cohesive interface are indicated in Table 1 and 2 Cerioni, As indicated in Figure 2 , the cohesive zone model, as shown combines an initially linear elastic behaviour with strength-based failure criterion to predict the damage initiation and a fracture mechanics-based criterion to determine the damage evolution. But from a numerical perspective, it cannot be infinitely large; otherwise, it leads to numerical ill-conditioning Turon et al. Many researchers have suggested various guidelines for selecting the stiffness of the interface.

Zou et al. Turon et al. As Shown in Figure 2 , the point t 0 refers to the beginning of materials response degradation. The process of degradation begins when the traction or separation satisfies certain damage initiation criteria. Each damage initiation criterion also has an output variable associated with it in order to indicate whether the criterion is met.

Perillo et al. The Quadratic nominal stress criterion is assumed to initiate when a quadratic interaction function reaches a value of one. This criterion can be represented as equation 2. In three-dimensional problems, the index n refers to normal traction and the index s and t refer to two shear traction. According to the strength-based failure criterion, the damage evolution would be initiated once the damage initiation condition has been met.

Several constitutive models that have been proposed by the researchers for the damage evolution schemes, linear softening behaviour is usually implemented Camanho et al. The damage evolution law describes the rate at which the material stiffness is degraded once the corresponding initiation criterion is reached. A scalar damage variable, D , represents the overall damage in the material.

It initially has a value of 0 and then monotonically evolves from 0 to 1 upon further loading. The stress components of the traction-separation model are affected by the damage. Camanho et al. Damage evolution can be defined based on the energy that is dissipated as a result of the damage process.

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The area under the traction-separation relation the area that shaded in Figure 2 is equal to the fracture toughness energy, G c. Although the scalar damage variable D is derived from this parameter, the fracture energy G c is the most important parameter which can be determined by means of some standard experimental tests. Khoramishad et al. Cerioni offers explicit solver in order to obtain the finite element solution for avoiding convergence problems and numerical instabilities. In the earlier work Khalili et al. Based on plane strain assumption, the simulation of delamination on DCB composite could be analysis with two-dimensional elements.

Mi et al.

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Finite Element Analysis of Composite Materials using Abaqus (TM)

While Alfano and Crisfield strictly declared that a 3D analysis would be needed since the delamination front was not precisely a straight line. Conventional shell, continuum shell and solid elements are available options in ABAQUS for modelling the composite structures. While cohesive behaviour is used in conjunction with stacked conventional shell elements, the specialized contact formulation may lead to approximate normal contact forces. This may induce approximate transverse shear behaviour in the stacked shells which affect the bending behaviour of the stack. The formulation used for surface-based cohesive, is very similar to that of cohesive elements with traction-separation response.

For cohesive surfaces, the cohesive constraint is enforced at each slave node while in cohesive elements, the cohesive constraints are calculated at the material points. Some researchers like Turon et al. On the other hand, it can yield to large runtime analysis because contact algorithms are computationally heavy especially when the connected mesh are highly refined.

According to Table 1 , the material modelling of composite ply in the present FE simulation has been done by linear elastic with engineering constant option that is available in ABAQUS. The CZM approach is used to simulate the interface failure modelling of cohesive layer between two beams of the specimen. According to Table 2 , the magnitude of the initial stiffness of the cohesive element Figure 2 , E 0 has been imported to the ABAQUS and it does not need to be divided by the cohesive thickness.

For defining the quadratic nominal stress QUADS Damage criterion, the S and T which are taken from Table 2 are considered as the maximum nominal interfacial strength t 0 in the two directions normal and shear. The 4 nodes, two-dimensional continuum plane strain elements CPE4R and the 4 nodes, two-dimensional cohesive elements COH2D4 are used in the FE simulation of the composite specimens and the cohesive interface.

A very refined mesh using an element length of 0. This element length is recommended by Cerioni and as shown in Figure 3 , only one cohesive element in the cohesive interface was put. Here, a double cantilever beam has been simulated under displacement control. As shown in Figure 4 , the movement of the opening edge in the vertical direction of the composite specimens is applied by the displacement control and is restrained in horizontal direction.

Also, the last node of the bottom of the lower composite specimen has been restrained in vertical direction. In this case study, the present simulation results gained by standard solver of ABAQUS are compared with the available experimental and numerical results by the Cerioni As shown in Figure 5 , there is a good correspondence between the elastic branches of the three curves. Also, the prediction of the onset of the delamination looks adequate. But some mismatch was observed between the present simulation and the results of reference Cerioni, in onset of the delamination. Furthermore, there is a difference in the propagation branch of the simulation model stiffness which has been decreased more quickly in respect of the experimental results.

In addition, better correspondence was observed with experimental results in the present simulation versus simulation of Cerioni In Figure 6 , the present simulation results gained by the explicit solver of ABAQUS are compared with the available experimental and numerical results by the Cerioni Also better results correspondence was observed in explicit solver than standard solver. As mentioned earlier in section 2. In this study the composite specimen uses the SC8R element for investigation the effect of 3D modelling in delamination. According to the earlier work Khalili et al.

The SC8R or S4R elements are an eight-node continuum shell and four-node conventional shell elements with reduced integration, respectively. In case of modelling, cohesive behaviour is possible to be used in conjunction with stacked conventional shell elements. Depending on the load case, the specialized contact formulation may lead to approximate normal contact forces, which in turn may induce the approximate transverse shear behaviour in the stacked shells and consequently affect the bending behaviour of the stack.

Also unlike to 2D modelling, the 3D modelling leads to large runtime analysis. Therefore the cohesive surfaces should be uses in 3D modelling in order to improve the analysis runtime. In the cohesive surface method, the initial stiffness magnitude of the cohesive surface that should be imported to the ABAQUS is different from the magnitude for the cohesive element. In addition it should be divided by the cohesive thickness and does not need to multiply to 50, according to the equation 1.

As indicated in Figure 7 , the force variation as a function of displacement for delamination on DCB composite specimen by using SC8R elements 3D modelling is similar to Figure 6 , in which explicit solver is also used. But the fluctuation in the force history of the 3D modelling versus 2D modeling is considerable. The non-symmetric pattern of the displacement contour which is shown in Figure 8 , leads to the fluctuation of force history. Therefore unlike to the 2D modeling, the fluctuation of force history is considerable in the 3D modelling because the delamination is not precisely a straight line.

By applying the appropriate procedure for delamination based on CZM method mentioned in section 2; here, the impact FE simulation process of composite plates is briefly described regarding CZM and PDM approach. To verify the proposed simulation approach, the results of the present simulation are compared with the valid experimental and numerical results reported by Gonzalez And finally, the appropriate procedure for impact on composite laminated plates is suggested by regarding intralaminar and interlaminar damage. In Figure 9 Gonzalez, , the test specimen and fixture base with details of support area and clamping points of the specimen are indicated.

The plate is subjected to transverse impact by a steel sphere impactor of 16 mm diameter with the mass of 5 kg. In this study, the material failure modelling is based on the progressive damage model that is used mainly to obtain the overall response of the composite laminates. A typical PDM consists of three steps: linear elastic stress analysis, failure analysis, and property-degrading material state variable. There are many material models that can be used to predict the behaviour of composite laminates.

It is intended that the model predicts the behaviour of composite laminates for damage which can be initiated without a large amount of plastic deformation. The equations for these damage initiation criteria are listed in the following equations 5 - 8. Tensile or compressive damage can be initiated in the fiber or the matrix when the respective F equals one. In the above equations, X T , , X c , Y T , Y C , S L and S T denotes the longitudinal tensile strength, the longitudinal compressive strength, the transverse tensile strength, the transverse compressive strength, the longitudinal shear and transverse shear strength respectfully.

Prior to damage initiation, the material in ABAQUS Progressive damage modelling is linearly elastic with the stiffness matrix of a plane stress orthotropic material. Thereafter, the effect of damage is taken into account by reducing the value of stiffness coefficients. If any of the damage variables become one, stress can no longer be supported in the respective direction because the stiffness goes to zero.

Finite Element Analysis of Composite Materials using AbaqusTM

As it's indicated in Figure 10 , these should be beyond the point of initial damage as linear damage evolution. Prior to damage initiation the positive slope of the stress-displacement curve corresponds to linear elastic material behavior. Whereas the negative slope is achieved by evolution of the respective damage variables after damage initiation. So the damage evolution is expressed as a stress-displacement relation. This point is the damage initiation criterion which met for each failure mode.

For each failure mode, the energy dissipated should be specified due to failure G c , which corresponds to the area of the triangle OAC in Figure Thereafter the damage initiated, unloading from a partially damaged state such as point B in Figure 10 , occurs along a linear path toward the origin with degraded stiffness and strength due to damage induced.

As mentioned in the earlier work Khalili et al. Also as it is mentioned in section 2. In this contact method, the contact constraint is applied when the clearance between two surfaces becomes zero. There is no limit in the contact formulation on the magnitude of contact pressure which can be transmitted between the surfaces. The surfaces are separated when the contact pressure between them becomes zero or negative, then the constraint is removed.

The contact force is a function of the penetration distance. And it is applied to the slave nodes to oppose the penetration while equal and opposite forces act on the master surface at the penetration point. Balanced master-slave weighting means that the corrections produced by both sets of contact calculations are weighted equally. The penalty contact algorithm for balanced master-slave contact surfaces computes contact forces that are linear combinations of the calculated pure master-slave forces.

As mentioned in section 2. But in the 3D modelling, cohesive surfaces are preferable due to their low-cost analysis. Conventional shell, continuum shell and solid elements are available options in the modelling of the composite laminates in ABAQUS. The choice of an element type used for the plates or shells as target structures depends on their side to thickness ratio as well as the impactor velocity.

Increasing the thickness of target and impactor velocity lead to increase in the shear deformation. In order to obtain the optimum number of elements, an analysis of the number of elements sensitivity is performed. In Figure 12 mesh pattern of the circular area surrounding the contact region and the convergence study of the number of elements are shown. This study indicated that the element number of 15 in edges of circular impact area is the optimum number of elements. 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. 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. 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.

Also, the last node of the bottom of the lower composite specimen has been restrained in vertical direction.

Ever J. Barbero

In this case study, the present simulation results gained by standard solver of ABAQUS are compared with the available experimental and numerical results by the Cerioni As shown in Figure 5 , there is a good correspondence between the elastic branches of the three curves. Also, the prediction of the onset of the delamination looks adequate.

But some mismatch was observed between the present simulation and the results of reference Cerioni, in onset of the delamination. Furthermore, there is a difference in the propagation branch of the simulation model stiffness which has been decreased more quickly in respect of the experimental results.

In addition, better correspondence was observed with experimental results in the present simulation versus simulation of Cerioni In Figure 6 , the present simulation results gained by the explicit solver of ABAQUS are compared with the available experimental and numerical results by the Cerioni Also better results correspondence was observed in explicit solver than standard solver. As mentioned earlier in section 2. In this study the composite specimen uses the SC8R element for investigation the effect of 3D modelling in delamination.

According to the earlier work Khalili et al. The SC8R or S4R elements are an eight-node continuum shell and four-node conventional shell elements with reduced integration, respectively. In case of modelling, cohesive behaviour is possible to be used in conjunction with stacked conventional shell elements. Depending on the load case, the specialized contact formulation may lead to approximate normal contact forces, which in turn may induce the approximate transverse shear behaviour in the stacked shells and consequently affect the bending behaviour of the stack.

Also unlike to 2D modelling, the 3D modelling leads to large runtime analysis. Therefore the cohesive surfaces should be uses in 3D modelling in order to improve the analysis runtime. In the cohesive surface method, the initial stiffness magnitude of the cohesive surface that should be imported to the ABAQUS is different from the magnitude for the cohesive element.

In addition it should be divided by the cohesive thickness and does not need to multiply to 50, according to the equation 1. As indicated in Figure 7 , the force variation as a function of displacement for delamination on DCB composite specimen by using SC8R elements 3D modelling is similar to Figure 6 , in which explicit solver is also used. But the fluctuation in the force history of the 3D modelling versus 2D modeling is considerable.

The non-symmetric pattern of the displacement contour which is shown in Figure 8 , leads to the fluctuation of force history. Therefore unlike to the 2D modeling, the fluctuation of force history is considerable in the 3D modelling because the delamination is not precisely a straight line. By applying the appropriate procedure for delamination based on CZM method mentioned in section 2; here, the impact FE simulation process of composite plates is briefly described regarding CZM and PDM approach.

To verify the proposed simulation approach, the results of the present simulation are compared with the valid experimental and numerical results reported by Gonzalez And finally, the appropriate procedure for impact on composite laminated plates is suggested by regarding intralaminar and interlaminar damage. In Figure 9 Gonzalez, , the test specimen and fixture base with details of support area and clamping points of the specimen are indicated. The plate is subjected to transverse impact by a steel sphere impactor of 16 mm diameter with the mass of 5 kg.

In this study, the material failure modelling is based on the progressive damage model that is used mainly to obtain the overall response of the composite laminates. A typical PDM consists of three steps: linear elastic stress analysis, failure analysis, and property-degrading material state variable. There are many material models that can be used to predict the behaviour of composite laminates. It is intended that the model predicts the behaviour of composite laminates for damage which can be initiated without a large amount of plastic deformation. The equations for these damage initiation criteria are listed in the following equations 5 - 8.

Tensile or compressive damage can be initiated in the fiber or the matrix when the respective F equals one. In the above equations, X T , , X c , Y T , Y C , S L and S T denotes the longitudinal tensile strength, the longitudinal compressive strength, the transverse tensile strength, the transverse compressive strength, the longitudinal shear and transverse shear strength respectfully. Prior to damage initiation, the material in ABAQUS Progressive damage modelling is linearly elastic with the stiffness matrix of a plane stress orthotropic material.

Thereafter, the effect of damage is taken into account by reducing the value of stiffness coefficients. If any of the damage variables become one, stress can no longer be supported in the respective direction because the stiffness goes to zero. As it's indicated in Figure 10 , these should be beyond the point of initial damage as linear damage evolution. Prior to damage initiation the positive slope of the stress-displacement curve corresponds to linear elastic material behavior.

Whereas the negative slope is achieved by evolution of the respective damage variables after damage initiation. So the damage evolution is expressed as a stress-displacement relation. This point is the damage initiation criterion which met for each failure mode. For each failure mode, the energy dissipated should be specified due to failure G c , which corresponds to the area of the triangle OAC in Figure Thereafter the damage initiated, unloading from a partially damaged state such as point B in Figure 10 , occurs along a linear path toward the origin with degraded stiffness and strength due to damage induced.

As mentioned in the earlier work Khalili et al. Also as it is mentioned in section 2. In this contact method, the contact constraint is applied when the clearance between two surfaces becomes zero. There is no limit in the contact formulation on the magnitude of contact pressure which can be transmitted between the surfaces. The surfaces are separated when the contact pressure between them becomes zero or negative, then the constraint is removed.

The contact force is a function of the penetration distance. And it is applied to the slave nodes to oppose the penetration while equal and opposite forces act on the master surface at the penetration point. Balanced master-slave weighting means that the corrections produced by both sets of contact calculations are weighted equally. The penalty contact algorithm for balanced master-slave contact surfaces computes contact forces that are linear combinations of the calculated pure master-slave forces.

As mentioned in section 2. But in the 3D modelling, cohesive surfaces are preferable due to their low-cost analysis. Conventional shell, continuum shell and solid elements are available options in the modelling of the composite laminates in ABAQUS. The choice of an element type used for the plates or shells as target structures depends on their side to thickness ratio as well as the impactor velocity.

Increasing the thickness of target and impactor velocity lead to increase in the shear deformation. In order to obtain the optimum number of elements, an analysis of the number of elements sensitivity is performed. In Figure 12 mesh pattern of the circular area surrounding the contact region and the convergence study of the number of elements are shown. This study indicated that the element number of 15 in edges of circular impact area is the optimum number of elements.

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.

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. 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.


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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. Modelling interlaminar and intralaminar damage in filament-wound pipes under quasi-static indentation.

Tan, S. A progressive failure model for composite laminates containing openings.

Finite Element Analysis of Composite Materials using Abaqus (TM) : Ever J. Barbero :

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,