WO2009043587A1

WO2009043587A1 - A system for performing a finite element analysis of a physical structure

Info

Publication number: WO2009043587A1
Application number: PCT/EP2008/008385
Authority: WO
Inventors: Thomas Heubrandtner; Thomas Jost; Christian Ruff; Bernhard Fellner
Original assignee: Kompetenzzentrum - Das Virtuelle Fahrzeug Forschungsgesellschaft Mbh; Magna Steyr Fahrzeugtechnik
Priority date: 2007-10-05
Filing date: 2008-10-02
Publication date: 2009-04-09
Also published as: EP2206061A1

Abstract

A device for performing a finite element analysis of a physical structure, wherein the device comprises a modelling unit for modelling the physical structure by a model comprising coupled beams in a spring configuration, each beam characterized by at least six spring parameters, wherein at least a part of the at least six spring parameters is empirically derived, and an evaluation unit for evaluating the physical structure using the model.

Description

A system for performing a finite element analysis of a physical structure

The invention relates to a device for performing a finite element analysis of a physical structure.

Beyond this, the invention relates to a method of performing a finite element analysis of a physical structure. Moreover, the invention relates to a program element.

Furthermore, the invention relates to a computer-readable medium.

Beyond this, the invention relates to a method of use.

The finite element method is a powerful tool for simulating an operation of a technical device and may be helpful in product development and failure analysis.

Wagner, U., Annandale, R., Wϋstner, H., Winkelmuller, G. "A Finite Element Model of the Frontal Deformable Barrier as an Example of Simulating Advanced Requirements", VDI Berichte No. 1283, 1996, pp. 237-249 discloses a comparison of different ways of modelling a physical structure for the purpose of a finite element analysis. Particularly, a solid element model implementing volume elements and a spring model are compared. The solid model is determined as the preferred one among these models.

However, conventional finite element schemes may be time consuming in use, since a large amount of computational burden is introduced.

It is an object of the invention to provide a finite element system allowing for a calculation with a reasonable amount of computational burden.

In order to achieve the object defined above, a device for performing a finite element analysis, a method of performing a finite element analysis, a program element, a computer-readable medium, and a method of using a device for performing a finite element analysis according to the independent claims are provided.

According to an exemplary embodiment of the invention, a (for instance computer-based) device for performing a finite element (FE) analysis of a physical structure (particularly a physical body modelled virtually for a theoretical analysis) is provided, wherein the device comprises a modelling unit for modelling the physical structure based on a model comprising a plurality of (for instance functionally/mechanically) coupled beams in a spring configuration (that is the beams may be treated as spring elements for the purpose of deriving a model for a finite element analysis), each of the spring elements being characterized or specified by at least six (particularly three translational and three rotational degrees of freedom) spring parameters (such as a spring stiffness or a module of elasticity, and/or other parameters indicative of a spring characteristic), wherein at least a part of (or all of) the at least six spring parameters is empirically derived, and an evaluation unit for evaluating the physical structure by a finite element analysis using the model derived by the modelling unit.

According to another exemplary embodiment of the invention, a method of performing a finite element analysis of a physical structure is provided, wherein the method comprises modelling the physical structure by a model comprising coupled beams in a spring configuration, each beam characterized by at least six (for instance three translational and three rotational degrees of freedom) spring parameters, wherein at least a part of the at least six spring parameters is empirically derived, and evaluating the physical structure using the model.

According to yet another exemplary embodiment of the invention, a computer-readable medium (for instance a CD, a DVD, a USB stick, a floppy disk or a harddisk) is provided, in which a computer program of performing a finite element analysis is stored which, when being executed by a processor, is adapted to control or carry out a method having the above mentioned features.

According to still another exemplary embodiment of the invention, a program element (for instance a software routine, in source code or in executable code) of performing a finite element analysis is provided, which program element, when being executed by a processor, is adapted to control or carry out a method having the above mentioned features. According to a further exemplary embodiment of the invention, a device having the above-mentioned features may be used for performing a finite element analysis simulating a crash of a vehicle.

Data processing for simulation purposes which may be performed according to embodiments of the invention can be realized by a computer program, that is by software, or by using one or more special electronic optimization circuits, that is in hardware, or in hybrid form, that is by means of software components and hardware components.

In the context of this application, the term "finite element analysis" may particularly denote a computer-based procedure (such a computer may comprise a processor having processing capabilities, a memory for storing information or data, and/or an input/output interface for exchanging data with a connected instance) using a finite element (FE) method. Finite element analysis (FEA) or finite element method (FEM) may denote a numerical technique for solution of boundary-value problems, particularly for use in structural analysis. In its application, the physical structure may be represented by a geometrically similar model formed by multiple, linked, simplified representations of discrete regions, i.e., finite elements.

The term "physical structure" may particularly denote any object (particularly any technical apparatus, member, or a portion thereof) in the real world which may be under development or analysis and shall therefore be investigated by a (modified) finite element analysis. Thus, during the finite element analysis, a virtual pendent of the physical structure may be investigated.

The term "beam" or "beam element" may particularly denote a basic building block of a specific finite element having an essentially one- dimensional extension. Such a beam element may be defined by at least one virtual extension/dimension (for instance a length, a cross sectional area), by an alignment direction (such as a vector direction), and by its (linear or non-linear) spring properties (such as spring stiffness, module of elasticity, translational and/or rotational motion behaviour, etc.). A number of such interconnected beam elements may define a substitution of the physical structure for finite element purposes. In contrast to such a beam element, solid elements (3D) and shell element (2D) have an extension along multiple dimensions.

According to an exemplary embodiment of the invention, a finite element analysis of a physical structure such as a honeycomb structure (which may be used as a crash barrier) may be performed by substituting the three-dimensional structure of the honeycomb by an arrangement of a number of functionally coupled (virtual) beam elements such as springs. When such beams are approximated physically as a spring being defined by one or more spring parameters, a meaningful simulation using the finite element method may be performed. According to an exemplary embodiment, such spring parameters may be derived empirically, for instance experimentally. It may be highly advantageous to implement meaningful spring parameters to subsequently obtain meaningful results of a finite element analysis.

In the following, further exemplary embodiments of the device will be explained. However, these embodiments also apply to the method, to the program element, to the computer-readable medium, and to the method of use.

The device may be adapted for performing a finite element analysis of a collision between the physical structure and a further physical structure, wherein the physical structure may be a barrier made of (for instance aluminium) honeycomb and the further physical structure may be a vehicle such as a motorcycle, a car, a truck, etc., or a part thereof, such as a bumper. By simulating the honeycomb structure with a virtual configuration of functionally/mechanically coupled beams, proper accordance between real world experimental results of collisions/crashes between barriers and vehicles can be obtained in a purely simulative manner. The use of empirically derived spring parameters for such a substitution in combination with the essentially six-dimensional configuration of springs allows obtaining a proper and realistic fingerprint of the reality. Hence, there is the possibility to reduce necessary crash tests of physical structures to a great extent.

The modelling unit may be adapted for modelling the physical structure by a model in which the beams are arranged to form a 3D- honeycomb structure. A honeycomb structure comprises or consists of aligned cells, each prescribing a polygon (for example a hexagon). Typical characteristics of a honeycomb structure are anisotropic structural behaviour, and high stiffness, high strength but low weight compared to a solid material.

More particularly, the modelling unit may be adapted for modelling the physical structure by a model comprising planes in which the beams are arranged to form the polygon of the honeycomb structure, and comprising a dimension normal (that is to say perpendicular) to the planes in which dimension the beams are arranged parallel to one another connecting the planes. This may properly simulate the structural properties of a honeycomb structure and allows for a calculation with reasonable computational burden.

The modelling unit may be adapted for modelling the physical structure with the at least six empirically derived spring parameters comprising experimentally derived data. Experimentally derived data may be derived from basic experiments (such as compression and shear tests) with the honeycomb structure (as an example for a barrier). By an analysis of the deformed honeycomb structure, the spring parameters may be determined with high accuracy. Thus, the term ,,empiricar may particularly denote data based on experiment, experience or observational information.

The modelling unit may be adapted for modelling the physical structure with the six empirically derived spring parameters comprising parameters having three degrees of freedom representing a translational motion of the beams, and three degrees of freedom representing a rotational motion of the beams. Therefore, in total, six degrees of freedom may be considered for each beam to characterize the motion along three dimensions as well as the vibrational properties of the respective beam. Thus, the beams may be coupled at their coupling end portions, and each beam may additionally be considered as a flexible structure, wherein the mobility can be described by six additional parameters. Such a model may allow for both to consider the rigidity of a solid structure and the flexibility of the components thereof. Such a linear spring model (for elongations being smaller than a threshold value) may be combined with a non-linear spring model (for elongations being larger than the threshold value).

The modelling unit may be adapted for modelling the physical structure assuming an ideal elastic behaviour of the beams. In other words, for elongations being sufficiently small, particularly smaller than a threshold value, the validity of Hooke's law may be assumed. Additionally or alternatively, the modelling unit may also be adapted for modelling the physical structure assuming a plastic deformation behaviour of the beams. For example, when a predetermined threshold value of elongations is exceeded, it can be assumed that a deformation will not be reversible after switching off the force, but that a plastic deformation will occur. Such a plastic deformation may in general be described by a hardening behaviour (i.e. deformed structure becomes more rigid/harder with increasing elongation) or by a softening behaviour (i.e. structure becomes softer/less hard with increasing elongation). A model implementing a softening behaviour is preferred according to exemplary embodiments of the invention, since this may particularly allow for the evaluation of weak points or weak portions of a structure.

More particularly, the evaluation unit may be adapted for evaluating the physical structure by comparing a mechanical load acting on individual beams with a predetermined threshold value and by removing a respective beam from the physical structure when the mechanical load exceeds the predetermined threshold value. In other words, when the mechanical load or (compression) force exceeds a certain value for specific portions of the modelled physical structure, the plastic deformation of such a structure of the destruction of this portion may be assumed which can be modelled particularly well with the assumption that overloaded beams are simply eliminated from the structure and can no longer serve as stabilizing elements in the network. The device may comprise a comparison unit adapted for comparing experimental data regarding the physical structure with an output of the evaluation unit. By such a comparison, the performance of the device may be improved, since the parameters may be further altered in a feedback manner to properly match with the experimental results.

The device may comprise a database (for instance implemented by a memory unit such as an EEPROM) in which the at least one empirically derived spring parameter is stored individually for each of the beams. According to an exemplary embodiment, honeycomb structure modulation is not performed using volume elements/solid elements or shell elements, but in contrast to this a structure consisting of beam elements may be provided without the inclusion of solid elements or shell elements, exclusively modelling the system by beam elements. This may allow to properly map deformation behaviour in a realistic manner. By taking this measure, honeycomb structures and further crash barriers may be simulated particularly well, and also local deformation properties (that is to say weak points of the structure) may be analyzed. The beam elements may be considered as spring elements having for instance six degrees of freedom (three translational and three rotational modes), wherein each degree of freedom may be approximated by a spring parameter. The individual degrees of freedom may be decoupled from one another in order to allow for a numerically simple calculation scheme without involving too much computational burden. By implementing such a beam model, it is possible to obtain a stable calculation in a fast time, that is to say to enable such a calculation with low CPU time or low computational burden.

Furthermore, the inventor has recognized that by properly adjusting the spring elements using experimental data, the challenge of a meaningful adjustment of the spring functions can be met, so that also a local failure can be estimated or predicted sufficiently well.

Particularly, exemplary embodiments of the invention may allow to properly map softening effects, that is to say the deformation behaviour can be mapped correctly assuming a reduced rigidity with increasing forces. In the domain of plastic deformation, a hardening zone (increase of tension with force), an ideal elastic zone (proportionality between tension and force), and a softening regime (decrease of the tension with increased elongation) can be distinguished. According to an exemplary embodiment, plastic deformation may be particularly simulated using such a softening scheme which allows to obtain a model in which one beam after the other collapses upon increase of the force which provides to properly simulate models of failure.

For estimating the spring parameters, it is possible to first carry out basic experiments using for instance an aluminium honeycomb structure. Based on such experiments, characteristics, parameters or statistics may be derived. These data may be fed to the finite element model and may be used as a basis for the calculation model. It is further possible to estimate remaining parameters by a trial and error procedure, and/or by fitting procedures.

According to an exemplary embodiment of the invention, the spring model may consider both a spring stiffness within a specific elongation range as well as plastic deformations when such a range is exceeded. This may allow to map different structural states and to distinguish a stable configuration from a deformed configuration. When, in a main force direction, the force exceeds a threshold value, a corresponding beam may be eliminated from the structure, representing a scenario in which a portion of the structure is no longer capable of contributing significantly to the stability of the entire network.

Although exemplary embodiments of the invention may be particularly used in the context of crash simulation, in which aluminium honeycombs are implemented, other exemplary embodiments of the invention may allow for other applications. Another exemplary application are plastic honeycomb structures for aircraft (for instance carbon fiber reinforced plastic (CFRP or CRP) structures) which can be simulated according to exemplary embodiments of the invention. In comparison with conventional approaches, the deformation behaviour of honeycomb models according to exemplary embodiments may be significantly improved. Furthermore, a local and global deformation behaviour of honeycomb structures may be mapped in a realistic way. It is also possible to map the local failure of aluminium honeycomb structures. This may allow for an improved predictability of entire vehicle simulations using crash barriers.

According to an exemplary embodiment of the invention, it is possible toanalyze crashed barriers. First, basic experiments using aluminium honeycombs may be carried out. After that, basic experiments of barrier portions may be carried out. This may be followed by basic experiments using entire barriers. Benchmark investigations of known barrier models may then be performed. The barrier models obtained may then be validated in a stepwise manner.

A calculation unit such as a CPU (central processing unit) or microprocessor may carry out a finite element analysis based on an essentially standard FE calculation program like LS-DYNA, PAM CRASH, RADIOS or ABAQUS adapted in accordance with a modelling scheme according to embodiments of the invention. This may have the advantage, that after having implemented such a model, such standard routines may be applied without a further need to perform application- specific adaptations.

Particularly, embodiments of the invention may be advantageously applied in the context of the simulation of a crash of the physical structure, for instance a crash of a vehicle, like an automobile. Another field of application of exemplary embodiments of the invention is a simulation or test of integrity of operation of the physical structure. Also NVH (Noise, Vibration and Harshness) of the physical structure may be subject of the investigation. More generally, embodiments of the invention may be applied to any FE-calculation in structural mechanics.

The aspects defined above and further aspects of the invention are apparent from the examples of embodiment to be described hereinafter and are explained with reference to these examples of embodiment.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described in more detail hereinafter with reference to examples of embodiment but to which the invention is not limited.

Fig. 1 illustrates a device for performing a finite element analysis of physical structures according to an exemplary embodiment of the invention. Fig. 2 illustrates a beam model of a honeycomb structure according to an exemplary embodiment of the invention.

Fig. 3 illustrates a local structure failure in the context of a beam model of a honeycomb structure according to an exemplary embodiment of the invention.

Fig. 4 illustrates different deformation states in the context of a beam model of a honeycomb structure, namely a deformed and an undeformed state.

Fig. 5 and Fig. 6 show images illustrating a local failure of a honeycomb structure due to a collision according to an exemplary embodiment of the invention.

Fig. 7 shows a diagram illustrating results of a collision between a sphere and a barrier portion from an experiment and from a simulation.

Fig. 8 illustrates a collision between a sphere and a barrier portion related to the results shown in Fig. 7.

Fig. 9 and Fig. 10 show diagrams comparing characteristics of the results of the collision between the sphere and the barrier portion from different simulations.

Fig. 11 and Fig. 12 illustrate an experiment of a collision involving an entire barrier.

Fig. 13 and Fig. 14 show diagrams comparing characteristics of results of the experiment of Fig. 11 and Fig. 12 and of results from different simulations.

Fig. 15 shows a result of a simulation of an entire barrier collision according to an exemplary embodiment of the invention.

Fig. 16 shows a result of an experiment of an entire barrier collision.

Fig. 17 and Fig. 18 illustrate an experiment of a collision involving an entire barrier. Fig. 19 and Fig. 20 show diagrams comparing characteristics of results of the experiment of Fig. 17 and Fig. 18 and of results from different simulations.

Fig. 21 and Fig. 22 illustrate an experiment of a collision involving an entire barrier.

Fig. 23 and Fig. 24 show diagrams comparing characteristics of results of the experiment of Fig. 21 and Fig. 22 and of results from different simulations.

Fig. 25 illustrates a beam model of a honeycomb structure according to an exemplary embodiment of the invention.

Fig. 26 shows a diagram illustrating results of a collision between a sphere and a barrier portion from an experiment and from a simulation.

DESCRIPTION OF EMBODIMENTS The illustration in the drawing is schematically. In different drawings, similar or identical elements are provided with the same reference signs.

In the following, referring to Fig. 1, a device 100 for performing a finite element analysis of a honeycomb structure (for instance usable as a crash barrier) according to an exemplary embodiment of the invention will be explained.

The device 100 comprises a first interface 101 which may also be denoted as an input interface. Via the input interface 101, a user or connected apparatus may input data as a basis for a finite element analysis to be performed by the device 100. For example, the first interface 101 may be connected to an input/output unit which may comprise an input element such as a keypad, a button, a joystick, etc. Furthermore, the device 100 comprises a second interface 102 which may also be denoted as an output interface. Via the output interface 102, results of a finite element analysis may be displayed to a user. For example, the second interface 102 may be coupled to an output unit such as a display, for instance an LCD display, a cathode ray tube, or the like.

For performing a finite element analysis, a user may define the finite element analysis by providing corresponding data to the input unit 101. This data may specify the finite element analysis, the physical structure to be analyzed and/or experimental parameters such as masses of colliding structures, velocity of a collision, etc.

This and other data may be supplied to a modelling unit 103 which is adapted for modelling the finite element analysis to be performed. More particularly, the modelling unit 103 is adapted for modelling the honeycomb structure by a model comprising coupled beams in a spring configuration which springs may be characterized by a number of empirically/experimentally measured spring parameters. This modelling will be described in more detail referring to Fig. 2. Thus, the modelling unit 103 will generate a theoretical model which is a realistic approximation of the physical properties of a real physical honeycomb structure (i.e. a solid body in the real world), which is thereby substituted by a virtual honeycomb structure for calculation purposes. The results of such a model, in which the honeycomb structure is described/approximated by a number of coupled beams which all have spring-like properties may then be supplied to an evaluation unit 104 adapted for evaluating the behaviour of the real world honeycomb structure using the theoretical model provided by the modelling unit 103. Particularly, the device 100 shown in Fig. 1 may be capable of performing a finite element (FE) analysis of an interaction between a modelled first structure and a modelled second structure. More . particularly, an analysis of a collision between a modelled crash barrier and a vehicle (which may be modelled as well) may be performed which collides with the crash barrier. A result of the FE evaluation may either be output directly via the second interface 102 or may be supplied to a comparison unit 105 which compares the calculated result with experimental data obtained by a real experiment of a collision between a real vehicle and a real barrier to verify the reliability and practical relevance of the results of the finite element analysis. It is also possible to feed back results from the comparison unit 105 to the modelling unit 103, to further improve or iteratively refine the model used as a basis for the finite element analysis.

Beyond this, as shown in Fig. 1, a memory unit 106 is shown which may be fed with data and which may store the data provided by the user via the first interface 101 and which may also be fed with data used by the modelling unit 103 for modelling one or more physical structures involved in a scenario to be analyzed. The database unit 106 may store the empirical and/or experimental data used as a basis for the model.

The evaluation unit 104 and the modelling unit 103 may be coupled to the database 106 for bidirectional data communication.

As can be taken from Fig. 1, the function of the units 103 to 105 may be realized by a CPU (central processing unit) or by a microprocessor 107. The database 106 may be realized by a memory device such as an EEPROM. The model selected or defined by the modelling unit 103 may model the honeycomb structure by a number of interconnected beams each having spring properties, which may be described for instance by parameters such as a spring stiffness, six rotational and/or translational motion modes. Both an elastic (linear) behaviour and a plastic (non- linear) deformation may be considered by such a model. In the domain of forces in which a plastic deformation may occur, a softening behaviour may be assumed (i.e. decreasing tension with further increasing forces). When a threshold value of a mechanical load/force which may be defined by a user via the interface 101 or by experimental data stored in the database 106 is exceeded, a destruction of a corresponding portion of the honeycomb structure may be assumed so that the corresponding beam may be removed from the virtual beam structure defined by the modelling unit 103. This may be a meaningful and numerically simple way of considering weakening of the material in response to a heavy load acting on the material. Fig. 2 shows a beam model 200 of a honeycomb structure according to an exemplary embodiment of the invention. A base plate 201 is shown as well as a model for the solid main body of the honeycomb structure which comprises the polygons (hexagonal) of the honeycomb structure 201 in a xy plane. Along a z-direction perpendicular to the xy-plane, vertical beams 202 to connect the planes comprising the polygons are shown. Fig. 2 therefore shows a basic modelling approach which illustrates a number of three-dimensionally coupled beams 201, 202. This may allow to properly map the deformation behaviour or the deformation modes of the honeycomb structure. Furthermore, local failure may be investigated accurately with such a beam model. Furthermore, the calculation time may be significantly reduced and the numerical stability may be improved as compared to conventional approaches.

Fig. 3 to Fig. 6 show different specific views of such a beam model. Fig. 3 illustrates local structure failure in an xz-plane.

Fig. 4 shows that different deformation states may be studied, and that deformed and non-deformed portions may be distinguished.

Fig. 5 shows a scenario in the xz-plane in which a moving further physical structure 500 such as a vehicle crashes the honeycomb structure 200.

The scenario of Fig. 5 is shown in a three-dimensional view in Fig. 6.

Fig. 7 to Fig. 9 show results of an experiment and corresponding simulations for adjusting material properties. Fig. 8 illustrates an experiment in which a (semi-)spherical physical structure 800 collides with a crash barrier portion 200 (which is modelled in accordance with Fig. 2 including the model of a sheet metal which is used in crash barriers). Based on such an experiment, parameters such as spring parameters may be obtained which may be used as empirically derived parameters for FE analysis. Fig. 7 shows a diagram 700 illustrating the results of a crash performed experimentally with the setup of Fig. 8 and calculated by a computer carrying out a finite element analysis. Along an abscissa 701, a dimension/position is plotted in millimeters. Along a first ordinate 702 the force is plotted in kN. A first curve 704 shows the force distribution in a first experiment.

A second curve 705 shows the force distribution in a second experiment. A third curve 706 shows the force in a simulation according to an exemplary embodiment of the invention.

For the experiment performed in accordance with Fig. 7, component experiments have been carried out. A portion of an IIHS

(Insurance Institute for Highway Safety) barrier having a honeycomb and a cover plate were used. A deformation with different plunger geometries has been studied. The simulation and the validation of the system showed a good accordance between the FE model and the experiment. The result is very accurate and stable.

Fig. 9 shows a diagram 900 having an abscissa 901 along which different simulation models are plotted. A model according to an exemplary embodiment of the invention is illustrated with reference numeral 902, the first conventional method is denoted with reference numeral 903 and the second conventional method is denoted with reference numeral 904. Along an ordinate 905 of the diagram 900, the number of elements in a component experiment is shown.

Fig. IO shows a diagram 1000 having an abscissa 1001 along which the three experiments of Fig. 9 are plotted again. Along an ordinate 1001, the CPU time for calculating the component experiment is plotted. As can be taken from Fig. 9 and Fig. 10, the calculation time can be significantly reduced according to exemplary embodiments of the invention, and the mapping is very accurate. The first conventional model 903 is instable and the calculation time is high. In the second conventional model 904, the element number is very small, and a long calculation time is obtained.

In the following, referring to Fig. 11 to Fig. 16, an entire barrier experiment will be explained.

An IIHS barrier 1100 is crashed against a simplified vehicle structure 1101, as shown schematically in Fig. 11.

Fig. 12 shows a comparison of the surface of the crashed barrier, wherein a good agreement between the FE model and the experiment can be seen. The dark portions in Fig. 12 correspond to the experiment, whereas the lighter portions in Fig. 12 relate to the simulation. In the performed experiment, a sill with a B column has been mapped. The velocity has been 25 km/h, and the mass 1.500 kg.

As can be taken from diagrams 1300, 1400 shown in Fig. 13 and Fig. 14, a proper agreement between simulation and experiment has been obtained, and the model can therefore be validated. A proper global and also local agreement between the model prototype can be obtained. However, small local differences on the deformation are still included due to the high degree of simplicity of the model.

Along an ordinate 1301 of the diagrams 1300 and 1400, an elongation is plotted in mm. Along an ordinate 1302, a is plotted in mm/(ms²). Along an ordinate 1401, an energy is plotted in kJ.

Referring to Fig. 13, a first curve 1303 relates to the experiment. A second curve 1304 relates to the model according to an exemplary embodiment of the invention. A third curve 1305 relates to the first conventional model and a fourth curve 1306 relates to the second conventional model. In Fig. 14, a first curve 1402 shows the kinetic energy of the experiment, whereas a second curve 1403 shows the internal energy of the experiment. A third curve 1404 relates to the kinetic energy of the simulation of the experiment according to an exemplary embodiment of the invention. A fourth curve 1405 relates to the internal energy of the simulation of the experiment according to an exemplary embodiment of the invention.

Still referring to the previously described whole barrier experiment, a comparison of the deformation of the honeycomb structure in the simulation and in the experiment are shown in Fig. 15 and Fig. 16.

Fig. 15 shows a result of a simulation 1500, whereas Fig. 16 shows a result of an experiment 1600. As can be taken from a comparison of Fig. 15 and Fig. 16, a proper mapping of the deformation zones in the main block of the barrier can be obtained. The main block remains undeformed to a large extent. A proper mapping of the local failure of the bumper can be seen as well. The mapping of the bumper compression (rotation) into the main block (local failure) is an interesting result as well.

In the following, referring to Fig. 17 to Fig. 20, another entire barrier experiment will be explained.

An IIHS barrier has been collided against an I-carrier. The I-carrier beam 1700 is shown in Fig. 17 as well as the vehicle 1701.

Fig. 18 shows the bumper 1702 of the vehicle 1701 after the collision. The diagrams 1900 and 2000 shown in Fig. 19 and Fig. 20 correspond to the diagrams of Fig. 13 and Fig. 14. They show a validation and a proper accordance between simulation and experiment. A proper global accordance of the FE model is obtained. Further, the mapping of the local deformation is proper. In the following, referring to Fig. 21 to Fig. 24, another entire barrier experiment will be explained. In this experiment, an IIHS barrier 2100 has been crashed against a sillboard 2101.

Fig. 21 illustrates the experiment. Fig. 22 shows the vehicle 2101 after the crash, wherein a bumper

2102 is deformed.

As can be taken from a diagram 2300 shown in Fig. 23 and a diagram 2400 shown in Fig. 24, a proper accordance between simulation and experiment can be achieved, and the model is validated. Fig. 25 illustrates a beam model 2500 of a honeycomb structure according to an exemplary embodiment of the invention.

Additional beam elements 2502 are shown which are modelled to have spring properties. Such a model has the property to properly match the buckling load of a non-damaged honeycomb structure. The insertion of additional elements into the model may allow for such a mapping. In this context, use is made of the effect of beam resolution.

Fig. 26 shows a diagram 2600 illustrating results of a collision between two structures from an experiment and from a simulation.

Along an abscissa 2601, a dimension is plotted in millimeters. Along an ordinate 2602 the force is plotted in kN.

A first curve 2604 shows the force distribution in an experiment. A second curve 2605 shows the force distribution in a simulation according to an exemplary embodiment of the invention.

It should be noted that the term "comprising" does not exclude other elements or features and the "a" or "an" does not exclude a plurality. Also elements described in association with different embodiments may be combined.

It should also be noted that reference signs in the claims shall not be construed as limiting the scope of the claims.

Claims

C l a i m s

1. A device for performing a finite element analysis of a physical structure, wherein the device comprises a modelling unit adapted for modelling the physical structure by a model comprising coupled beams in a spring configuration, each beam characterized by at least six spring parameters, wherein at least a part of the at least six spring parameters is empirically derived; an evaluation unit adapted for evaluating the physical structure using the model.

2. The device according to claim 1, adapted for performing a finite element analysis to simulate a collision between the physical structure and a further physical structure.

3. The device according to claim 2, adapted for performing a finite element analysis to simulate a collision between a barrier as the physical structure and a vehicle as the further physical structure.

4. The device according to any one of claims 1 to 3, wherein the modelling unit is adapted for modelling the physical structure by a model in which the beams are arranged to form or simulate a honeycomb structure.

5. The device according to claim 4, wherein the modelling unit is adapted for modelling the physical structure by a model comprising a plane in which the beams are arranged to form the honeycomb structure, and comprising a dimension normal to the plane in which dimension the beams are arranged parallel to one another.

6. The device according to any one of claims 1 to 5, comprising a database in which the at least one empirically derived spring parameter is stored for each of the beams.

7. The device according to any one of claims 1 to 6, wherein the modelling unit is adapted for modelling the physical structure with the at least six spring parameters comprising experimentally derived data.

8. The device according to any one of claims 1 to 7, wherein the modelling unit is adapted for modelling the physical structure with the at least six spring parameters comprising parameters having three degrees of freedom representing a translational motion of the beams, and three degrees of freedom representing a rotational motion of the beams.

9. The device according to any one of claims 1 to 8, wherein the modelling unit is adapted for modelling the physical structure assuming an ideal elastic behaviour of the beams.

10. The device according to any one of claims 1 to 9, wherein the modelling unit is adapted for modelling the physical structure assuming a plastic deformation behaviour of the beams.

11. The device according to claim 10, wherein the modelling unit is adapted for modelling the physical structure by modelling the plastic deformation behaviour of the beams by a softening behaviour.

12. The device according to any one of claims 1 to 11, wherein the evaluation unit is adapted for evaluating the physical structure by comparing a force acting on individual beams with a predetermined threshold value and by removing a respective beam from the physical structure when the force exceeds the predetermined threshold value.

13. The device according to any one of claims 1 to 12, comprising a comparison unit adapted for comparing experimental data regarding the physical structure with an output of the evaluation unit.

14. The device according to any one of claims 1 to 13, wherein the modelling unit is adapted for modelling the physical structure by a model consisting of the coupled beams in the spring configuration, each beam characterized by the at least six empirically derived spring parameters.

15. A method of performing a finite element analysis of a physical structure, wherein the method comprises modelling the physical structure by a model comprising coupled beams in a spring configuration, each beam characterized by at least six spring parameters, wherein at least a part of the at least six spring parameters is empirically derived; evaluating the physical structure using the model.

16. A computer-readable medium, in which a computer program of performing a finite element analysis is stored, which computer program, when being executed by a processor, is adapted to carry out or control a method according to claim 15.

17. A program element of performing a finite element analysis, which program element, when being executed by a processor, is adapted to carry out or control a method according to claim 15.

18. A method of using a device of any one of claims 1 to 14 for performing a finite element analysis of a crash of a vehicle.