Homogenised non-linear soft inclusion for simulation of impact damage in composite structures

This paper presents the development of a homogenised non-linear soft inclusion which captures the geometric and material non-linearity of impact damage zone loaded in tension and compression. The homogenised non-linear soft inclusion can present a conservative worst case damage zone or use experimental data to mimic the behaviour of a particular damage zone in a simple and computationally efficient way that can be used as a structural design tool for composite structures subjected to impact. The development of the non-linear soft inclusion, implemented in an ABAQUS/Explicit VUMAT, is presented at element and coupon level. The non-linear soft inclusion is validated against experimental coupon data and produces a conservative worst case estimate in all cases investigated.     

Buckling of thin-walled composite structures with intermediate stiffeners

The interactive buckling of prismatic, thin-walled composite columns with open sections, reinforced with intermediate stiffeners and with edge reinforcements, has been considered. The columns are assumed to be simply supported. The nonlinear problem has been solved with the Koiter’s asymptotic theory within the first order approximation. The asymptotic theory of the first order nonlinear approximation allows for simultaneous evaluation of the effect of imperfections and interactions of various modes of buckling on the behaviour of thin-walled structures. This evaluation can be only the lower bound estimation of the load carrying capacity. Detailed calculations have been made for several cases of columns.     

Experimental and numerical investigations of the impact behaviour of composite frontal crash structures

The present paper deals with the lightweight design and the crashworthiness analysis of a composite impact attenuator for a Formula SAE racing car, in order to pass homologation requirements. The analysed impact attenuator is manufactured by lamination of prepreg sheets in carbon fibres and epoxy matrix, particularly used for sporting applications, and has a very similar geometry to a square frusta, so as to obtain a progressive and controlled deformation. During the design, attention was focused on the material distribution and gradual smoothing, but also on the lamination process, which can heavily affect the energy absorption capability. To reduce the development and testing costs of a new safety design, computational crash simulations for early evaluation of safety behaviour under vehicle impact test were carried out. The dynamic analysis was therefore conducted both numerically, using an explicit finite element code such as LS-DYNA, and experimentally, by means of an appropriately instrumented drop weight test machine, in order to validate the model in terms of deceleration values during crushing. To assess the quality of the simulation results, a comparative analysis was initially developed on simple CFRP composite tubes subjected to dynamic axial loading. The numerical analysis was conducted using both shell and solid elements, in order to reproduce not only the brittleness of the composite structure but also the effective delamination phenomenon. Both the analyses show a good capacity to reproduce the crushing process; this is confirmed by the fact that model estimated displacements and accelerations are in close agreement with observed values for these variables. This confirms the quality of the methodology and approach used for the design of a racing car impact attenuator.     

Numerical investigation based on the finite element method of the postbifurcation behavior of thin-walled structures

We worked an effective algorithm for investigating the postbifurcation solutions of systems of nonlinear equations of equilibrium of thin-walled structures obtained on the basis of the finite element method. In the work we used an eight-node isoparametric shell finite element (MPFE) of general form with three degrees of freedom in a node. An example is the postbifurcation behavior of two classical structures: a cantilever strip loaded by a concentrated force at the end, and a rectangular plate compressed uniformly by a distributed load on the end face. The obtained results testify to the high accuracy and effectiveness of the method presented here.Translated from Problemy Prochnosti, No. 7, pp. 79–89, July, 1993.     

Modal coupled instabilities of thin-walled composite plate and shell structures

The problem of buckling and initial post-buckling equilibrium paths of thin-walled structures built of plate and/or shell elements subjected to compression and bending has been solved. Plate and shell elements can be made of multi-layer orthotropic materials. A method of the modal solution to the coupled buckling problem within the first-order approximation of Koiter’s asymptotic theory, using the transition matrix method, has been presented. In the solution obtained, the effect of cross-sectional distortions and a shear lag phenomenon is included. The calculations are carried out for a few thin-walled structures.     

Impact response of thin-walled frame structures

This paper describes a finite-element method which was developed to predict the impact response of three-dimensional thin-walled frame structures.The softening effect of the load-deformation characteristics for thin-walled beams under combined axial compression, bending and torsional loads during impact is simulated by making use of a nonlinear Maxwell model.The large deformation of a structure is calculated by using updated nodal coordinates and internal forces, and the flexibility matrix for a curved beam element.Crash tests against a flat barrier were made on three-dimensional frame models. Comparisons between the calculated and experimental force-time relations and the deformed shape of the frame are discussed.     

Impact response of thin-walled plane frame structures

A numerical study of the impact response of plane frame structures with thin-walled members was performed to predict the deformation and absorbed energy of automobiles under crash loading.The collapse characteristics of thin-walled members under axial compression or bending loads are considered in the present analysis. The load-displacement relations are given for curved beam members, and the inelastic deformations of members are described in terms of equivalent internal loads and their histories.Crash tests on simplified plane frame models impacted against a flat barrier were performed to verify the proposed method.Numerical analyses were also made of an oblique barrier impact of an automobile underframe structure and a rear end collision of a vehicle structural system. The analytical predictions were compared with the corresponding test results.     

Lightweight design and crash analysis of composite frontal impact energy absorbing structures

Carbon fibre composites have shown to be able to perform extremely well in the case of a crash and are being used to manufacture dedicated energy-absorbing components, both in the motor sport world and in constructions of aerospace engineering. While in metallic structures the energy absorption is achieved by plastic deformation, in composite ones it relies on the material diffuse fracture. The design of composite parts should provide stable, regular and controlled dissipation of kinetic energy in order to keep the deceleration level as least as possible. That is possible only after detailed analytical, experimental and numerical analysis of the structural crashworthiness.This paper is presenting the steps to follow in order to design specific lightweight impact attenuators. Only after having characterised the composite material to use, it is possible to model and realise simple CFRP tubular structures through mathematical formulation and explicit FE code LS-DYNA. Also, experimental dynamic tests are performed by use of a drop weight test machine.Achieving a good agreement of the results in previously mentioned analyses, follows to the design of impact attenuator with a more complex geometry, as a composite nose cone of the Formula SAE racing car. In particular, the quasi-static test is performed and reported together with numerical simulation of dynamic stroke. In order to initialize the collapse in a stable way, the design of the composite impact attenuator has been completed with a trigger which is consisted of a very simple smoothing (progressive reduction) of the wall thickness. Initial requirements were set in accordance with the 2008 Formula SAE rules and they were satisfied with the final configuration both in experimental and numerical crash analysis.     

Numerical investigation of the response of sandwich-type panels using thin-walled tubes subject to blast loads

The response of a novel lightweight panel design under blast loading is numerically investigated. The sandwich-type panel uses thin-walled square tubes as the core material with mild steel outer plates. A parametric study is carried out with ABAQUS/Explicit to examine the effects and interaction between design variables in three different tube layouts. Tube position, thickness and aspect ratio as well as top plate thickness are varied. Buckling stability and absorption performance are shown to be highly sensitive to tube placement due to interaction effects between the top plate and tubes. For each panel an optimal tube positioning is obtained corresponding to nearly perfect axial progressive symmetric tube buckling. Tube thickness is shown to influence the onset of buckling and hence affects the stability of the core, while energy absorption performance is also highly configurable. Tube aspect ratio shows only a small effect on core buckling stability and energy absorption. Top plate thickness influences absorber performance significantly while having a small effect on buckling stability. A simple theoretical analysis is presented and shows reasonable agreement with the numerical simulations.     

Numerical design of thin-walled structural members on account of their strength

The numerical design and optimization problems for the reinforced thin-walled structural members on account of a local strength criterion are considered. Two types of the elements of construction are analysed in detail: wafer plates and honeycomb-like shells. The optimal design concerns the following factors: the values of the effective stiffness moduli; the minimization of the weight; the ability to sustain the required ultimate strains. The computations are based on the application of the general homogenized shell model. The effective computational algorithm for a global minimum search for the function of several variables under the restrictions and the computer software are developed and applied. The asymptotically correct results for the effective stiffness moduli and the local stress distributions, which are available in the framework of the general homogenized shell model, ensure that the gain of optimization will not be overlapped by modelling errors. The effectiveness and advantages of the developed approach is illustrated by several numerical examples. The optimal design computational algorithm is extended to the case of fatigue failure analysis.     

Numerical simulation of brittle fracture of thin-walled structures1

The model of brittle material, allowing for the determination of initiation and growth of cracks in thin-walled structures up to their destruction, is offered. Solutions of some problems are submitted: destruction of a plate at a homogeneous stress state; destruction of a beam at a pure bending; dynamic deformation and destruction of a plate with the concentrated mass having various initial speeds. Destruction of part of the material of the plate is shown to result in dynamic loss of stability of the solution.     

Prediction of structural response for low velocity impact

The complete modeling for impact on flexible structures can always be done through a three-dimensional finite element model. The FEM approach is often very costly both from modeling and calculation duration point of views, so it can be simplified by using simplified impact models. The selection of an impact model depends on the structural response, thus one should be able to predict the expected structural response a priori in order to select an appropriate impact model. Impact duration is an important parameter that can be helpful for predicting the expected structural response. This paper provides guidelines for the prediction of the structural response on the basis of impact duration and the fundamental period of the impacted structure. A criterion for defining a precise upper limit of low velocity impact is also developed.     

Application of manufacturing constraints to structural optimization of thin-walled structures

Topology optimization can be a very useful tool for creating conceptual designs for vehicles. Structures suggested by topology optimization often turn out to be difficult to implement in manufacturing processes. Presently, rail vehicle structures are made by welding sheet metal parts. This leads to many complications and increased weight of the vehicle. This article presents a new design concept for modern rail vehicle structures made of standardized, thin-walled, closed, steel profiles that fulfil the stress and manufacturing requirements. For this purpose, standard software for topology optimization was used with a new way of preprocessing the design space. The design methodology is illustrated by an example of the topology optimization of a freight railcar. It is shown that the methodology turns out to be a useful tool for obtaining optimal structure design that fulfils the assumed manufacturing constraints.     

Instantaneous response of elastic thin-walled structures to rapid heating

A generalized modelling and analysis approach of thermally induced coupled vibrations of elastic thin-walled configurations with arbitrary open cross-sections are presented in conjunction with a unified implicit transient methodology. Limited research which takes into account the influence of rapid thermal heating effects on structures involving various forms of coupling appears in the literature. As a consequence, the dynamic response of such thin-walled structures of arbitrary open cross-section to rapid heating are described here. Effects involving triple, double, and no coupling between bending and torsional vibrations caused by sudden heating on these structures are examined. Numerical test cases are presented which describe the influence of sudden heating on elastic thin-walled structures of arbitrary open cross-sections.     

A comparison of the deformation of magnesium alloys with aluminium and steel in tension, bending and buckling

A comparison was made between high pressure die cast and wrought magnesium alloys and formed mild steel and aluminium in tensile, bending and buckling deformation. It was found that the energy absorption properties of magnesium alloys were particularly good in bending and buckling, absorbing up to 50% more energy than the aluminium and over 10 times more energy than the mild steel. The primary reason for the good performance of Mg alloys was that the low density means that sections of increased thickness can be made without increasing weight. This is particularly beneficial in bending as the strength of a section in bending is proportional to the square of the thickness. However, it was also observed that the high rate of work hardening of Mg alloys is particularly important and this allows for considerably more energy to be absorbed. A simple analytical strut buckling model has been modified to incorporate work hardening and a good correlation has been observed between this model and the experimental results.     

Numerical study of the structural behaviour of impacted composite laminates subjected to compression load

Composite materials allow all the benefits which a high specific strength involves, in a design process their application involves many critical problems. Currently, these problems, such as environmental conditions, notch sensitivity, damaging under low velocity impacts, are taken into account by means of the application of conservative design safety factors regarding the ultimate tensile strength. In order to try to reduce these safety factors, this work aimed to study and to understand the impact damage growing mechanisms due to compression loads. To this purpose, compression tests have been experimentally performed on composite panels, which have been previously subjected to low velocity impact phenomena, considering impact energies of 6 J, 10 J and 13 J respectively. Moreover, numerical model able to simulate Low Velocity Impacts (LVI) and Compression After Impacts (CAI) onto CFRP panels is proposed. A single explicit finite element analysis has been carried out by using the Abaqus^® finite element code; the need to build a numerical model, which allows simulation in only one analysis both LVI and CAI steps, depends on the difficulty to import the impact damage distribution into a separate compression analysis. In fact, in only one analysis the compression step can occur directly onto the impacted plate, which allows to consider the effective impact damage distribution as the starting configuration for quasi static analysis under operating loads.     

Experimental investigation of impact on composite laminates with protective layers

This paper presents an experimental study of low energy impacts on composite plates covered with a protective layer. In service, composite materials are subjected to low energy impacts. Such impacts can generate damage in the material that results in significant reduction in material strength. In order to reduce the damage severity, one solution is to add a mechanical protection on composite structures. The protection layer is made up of a low density energy absorbent material (hollow spheres) of a certain thickness and a thin layer of composite laminate (Kevlar). Energy absorption ability of these protective layers can be deduced from the load/displacement impact curves. First, two configurations of protection are tested on an aluminium plate in order to identify their performance against impact, then the same are tested on composite plates. Test results from force–displacement curves and C-scan control are compared and discussed and finally a comparison of impact on composite plates with and without protection is made for different configurations.     

Impact response of elasto-plastic granular and continuum media: A comparative study

A comparative study of the impact response of three-dimensional ordered granular sphere packings and continuum half-spaces made of elastic-perfectly plastic materials is conducted. Energy dissipation and plastic zone volume are characterized, and scaling laws with respect to material properties, size and loading variables are derived for both continuum and discrete (granular) systems. Due to stress concentration at contacts, energy dissipation in granular systems occurs at much smaller impact loads than in continuum systems. At higher impact loads, the fraction of energy dissipated and the extent of plastic zone are much larger in the discrete system than in the continuum case. Though the size of plastic zone is much larger in discrete systems, the volume of material involved in dissipating a fraction of impact energy is comparable for continuum and granular systems.     

Finite element modelling of crash response of composite aerospace sub-floor structures

Composite energy-absorbing structures for use in aircraft are being studied within a European Commission research programme (CRASURV – Design for Crash Survivability). One of the aims of the project is to evaluate the current capabilities of crashworthiness simulation codes for composites modelling. This paper focuses on the computational analysis using explicit finite element analysis, of a number of quasi-static and dynamic tests carried out within the programme. It describes the design of the structures, the analysis techniques used, and the results of the analyses in comparison to the experimental test results. It has been found that current multi-ply shell models are capable of modelling the main energy-absorbing processes at work in such structures. However some deficiencies exist, particularly in modelling fabric composites. Developments within the finite element code are taking place as a result of this work which will enable better representation of composite fabrics. Received 12 December 1999