# Finite Element Modelling Of Composite Materials And Structures Pdf

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- Finite element analysis of composite materials using Abaqus
- Finite element modelling of composite structures under crushing load
- Finite element analyses of sandwich structures: a bibliography (1980–2001)

Gives a bibliographical review of the finite element analyses of sandwich structures from the theoretical as well as practical points of view. Both isotropic and composite materials are considered. Topics include: material and mechanical properties of sandwich structures; vibration, dynamic response and impact problems; heat transfer and thermomechanical responses; contact problems; fracture mechanics, fatigue and damage; stability problems; special finite elements developed for the analysis of sandwich structures; analysis of sandwich beams, plates, panels and shells; specific applications in various fields of engineering; other topics. The analysis of cellular solids is also included.

## Finite element analysis of composite materials using Abaqus

Shahravi a. E-mail: meisam. The delamination in stacking ply with the same fiber orientation is considered as interlaminar damage and the delamination in an inner layer of any cluster is ignored. Hashin criterion is used for intralaminar damage initiation and evolution without using any subroutine.

First, the appropriate procedure for delamination on composite specimen was suggested based on CZM approach in double cantilever beam to verify the intralaminar damage simulation. Then by considering several case studies with different impact energies, the results of present simulation is verified with the relevant and available experimental results and numerical references in the existing literature.

According to the available experimental results the present simulation results are more acceptable and accurate than the results of similar numerical works, especially in higher impactor velocity.

Composite structures are widely used in many industrial applications like aerospace and defence industry due to their inherently high specific mechanical properties. In many situations, these composite structures are subjected by high and low velocity impact. Composite structures are very sensitive to non-visual damage that strongly influence their residual load bearing capability.

Lack of knowledge of the impact effects on composite structures is a factor in limiting the use of composite materials Abrate, To understand the responses of composite structures under high velocity projectile impacts, various experimental and numerical studies have been conducted. Cantwell and Morton examined the initiation and development of damage in composite structures with a series of low and high velocity impact tests. Guoqi et al. Cheng et al. This model was based on a continuum approach which was built on the basis of an orthotropic constitutive behaviour with stress-based failure criteria and a simplified degradation model of the failure of composites.

Silva et al. Cerioni presented a numerical simulation of delamination in composite materials under static and fatigue loading by cohesive zone models. Zhao et al. Khalili et al. Gonzalez investigated the damage induced in composite plates under drop-weight impact loading by analytical description and experimental test plan for assessment of the virtual test performance by finite element simulation.

Ramadhan et al. Simulation of damage induced in composite laminates has been performed with macro, meso and micro-scale of modelling. Investigating the overall response of the composite laminate with treating the composite as fully homogenized is called marco-scale analysis.

In the meso-scale approach the composite treated as effective anisotropic materials while involving the analysis of the composite to the scale of the constituents is called micro-scale approach. Although the finite element method could be used to simulate the composite laminate damage induced in all the mentioned scale modelling, extremely computational efficient method in macro-scale approach.

The complex damage mechanisms of composite laminates, could be divided in intralaminar and interlaminar damage. The intralaminar damage mechanisms correspond to fiber fracture and matrix cracking, while the other correspond to the delamination of the plies. Continuum Damage Mechanics CDM has been employed by many researchers for progressive damage analyses of composite laminates. The continuum damage model is the most accurate technique to predict size effects in composites and is applicable to general geometries and boundary conditions.

In addition, it doesn't require any calibration Camanho et al. Also a progressive damage method -which builds nonlinear mechanics models for composite materials and has capacity of accurately simulating the structural failure process from initial damage to ultimate failure- attracts wide spread attention in composite structure analyses Tan, ; Shokrieh, ; Camanho and Matthews, In order to use PDM additional material testing is required to adjust the empirical evolutions laws.

Moreover, PDM is suitable for structural analysis and its parameters could be determined by experiment test Shokrieh, Delamination or interfacial cracking between composite layers, is one of the most common types of damage in composite laminates due to their relatively weak interlaminar strengths. The formulation of the cohesive finite elements is based on the Cohesive Zone Model CZM approach and was originally introduced by Barenblatt and Dugdale Barenblatt, ; Dugdale, The CZM approach is one of the most commonly used tools to investigate interfacial fracture.

It is based on the Griffith's theory of fracture and assumed a cohesive damage zone developed near the crack tip and described the crack propagation in perfectly brittle materials Turon et al.

The CZM approach was developed in a continuum damage mechanics framework and resulted in improving its applicability by using fracture mechanics concepts. The cohesive zone model combines a strength-based failure criterion to predict the damage initiation, and a fracture mechanics-based criterion to determine the damage propagation Khoramishad et al. The earlier work Khalili et al. The element type, solution method, impactor modelling method, meshing pattern and contact modelling are investigated and verified with several case studies with various conditions.

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.

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. 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.

## Finite element modelling of composite structures under crushing load

A review on analytical failure criteria for composite materials[J]. Article views PDF downloads Cited by Figures 5. Alessandro De Luca, Francesco Caputo. Previous Article Next Article. A review on analytical failure criteria for composite materials.

Textile composites are composed of 3D complex architecture. To assess the durability of such engineering structures, the failure mechanisms must be highlighted. Examinations of the degradation have been carried out thanks to tomography. The present work addresses a numerical damage model dedicated to the simulation of the crack initiation and propagation at the scale of the warp yarns. For the 3D woven composites under study, loadings in tension and combined tension and bending were considered. Based on an erosion procedure of broken elements, the failure mechanisms have been modelled on 3D periodic cells by finite element calculations.

Brinson, L. December 1, December ; 59 4 : — The properties of composite solids containing multiple, viscoelastic phases are studied numerically. The dynamic correspondence principle of viscoelasticity is utilized in a finite element model to solve boundary value problems for obtaining global complex moduli of the composite. This numerical procedure accounts for the coupled interactive deformation of the phases and thus the resultant accuracy is limited only by that of finite element analyses in general.

## Finite element analyses of sandwich structures: a bibliography (1980–2001)

Part 1 Review of composite materials: Overview; Fundamentals of composites. Part 2 Fundamentals of finite element analysis. Part 3 Finite elements applied to composite materials: Composites and finite element analysis; Definition of composite materials in finite element analysis.

Shahravi a. E-mail: meisam. The delamination in stacking ply with the same fiber orientation is considered as interlaminar damage and the delamination in an inner layer of any cluster is ignored. Hashin criterion is used for intralaminar damage initiation and evolution without using any subroutine.

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*The journal will publish the latest and most innovative research results dealing with analytical methods and numerical simulations, experimental investigations, and research and development studies relevant to the knowledge and application of new and advanced materials and composites in engineering structures, including basic individual structural components such as beams, plates, and shells.*

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