A crash simulation is a
virtual recreation of a destructive
crash test
A crash test is a form of destructive testing usually performed in order to ensure safe design standards in crashworthiness and crash compatibility for various modes of transportation (see automobile safety) or related systems and compon ...
of a
car
A car, or an automobile, is a motor vehicle with wheels. Most definitions of cars state that they run primarily on roads, seat one to eight people, have four wheels, and mainly transport people rather than cargo. There are around one billio ...
or a highway
guard rail system using a
computer simulation
Computer simulation is the running of a mathematical model on a computer, the model being designed to represent the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determin ...
in order to examine the level of safety of the car and its occupants. Crash
simulation
A simulation is an imitative representation of a process or system that could exist in the real world. In this broad sense, simulation can often be used interchangeably with model. Sometimes a clear distinction between the two terms is made, in ...
s are used by
automaker
The automotive industry comprises a wide range of companies and organizations involved in the design, development, manufacturing, marketing, selling, repairing, and modification of motor vehicles. It is one of the world's largest industries ...
s during
computer-aided engineering
Computer-aided engineering (CAE) is the general usage of technology to aid in tasks related to engineering analysis. Any use of technology to solve or assist engineering issues falls under this umbrella.
Overview
Following alongside the con ...
(CAE) analysis for
crashworthiness
Crashworthiness is the ability of a structure to protect its occupants during an impact. This is commonly tested when investigating the safety of aircraft and vehicles. Different criteria are used to figure out how safe a structure is in a crash, ...
in the
computer-aided design
Computer-aided design (CAD) is the use of computers (or ) to aid in the creation, modification, analysis, or optimization of a design. This software is used to increase the productivity of the designer, improve the quality of design, improve c ...
(CAD) process of modelling new cars. During a crash simulation, the
kinetic energy
In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion.
In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...
, or energy of motion, that a
vehicle
A vehicle () is a machine designed for self-propulsion, usually to transport people, cargo, or both. The term "vehicle" typically refers to land vehicles such as human-powered land vehicle, human-powered vehicles (e.g. bicycles, tricycles, velo ...
has before the impact is transformed into
deformation energy
Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...
, mostly by
plastic deformation
In engineering, deformation (the change in size or shape of an object) may be ''elastic'' or ''plastic''.
If the deformation is negligible, the object is said to be ''rigid''.
Main concepts
Occurrence of deformation in engineering application ...
(
plasticity
Plasticity may refer to:
Science
* Plasticity (physics), in engineering and physics, the propensity of a solid material to undergo permanent deformation under load
* Behavioral plasticity, change in an organism's behavior in response to exposur ...
) of the car body material (
Body in White
Body in white (BIW) is the stage in Automotive industry, automobile manufacturing in which a car body's frame has been joined together, that is before painting and before the motor, chassis sub-assemblies, or trim (glass, door locks/handles, sea ...
), at the end of the impact.
Data obtained from a crash simulation indicate the capability of the car body or guard rail structure to protect the vehicle occupants during a
collision
In physics, a collision is any event in which two or more bodies exert forces on each other in a relatively short time. Although the most common use of the word ''collision'' refers to incidents in which two or more objects collide with great for ...
(and also
pedestrian
A pedestrian is a person traveling on foot, by wheelchair or with other mobility aids. Streets and roads often have a designated footpath for pedestrian traffic, called the '' sidewalk'' in North American English, the ''pavement'' in British En ...
s hit by a car) against
injury
Injury is physiological damage to the living tissue of any organism, whether in humans, in other animals, or in plants.
Injuries can be caused in many ways, including mechanically with penetration by sharp objects such as teeth or with ...
. Important results are the deformations (for example,
steering wheel
A steering wheel (also called a driving wheel, a hand wheel, or simply wheel) is a type of steering control in vehicles.
Steering wheels are used in most modern land vehicles, including all mass-production automobiles, buses, light and hea ...
intrusions) of the occupant space (driver,
passenger
A passenger is a person who travels in a vehicle, but does not bear any responsibility for the tasks required for that vehicle to arrive at its destination or otherwise operate the vehicle, and is not a steward. The vehicles may be bicycles, ...
s) and the
deceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are vector quantities (in that they have magnit ...
s (for example, head acceleration) felt by them, which must fall below threshold values fixed in legal
car safety
Automotive safety is the study and practice of automotive design, construction, equipment and regulation to minimize the occurrence and consequences of traffic collisions involving motor vehicles. Road traffic safety more broadly includes roadw ...
regulations
Regulation is the management of complex systems according to a set of rules and trends. In systems theory, these types of rules exist in various fields of biology and society, but the term has slightly different meanings according to context. Fo ...
. To model real crash tests, today's crash simulations include virtual models of
crash test dummies
Crash Test Dummies are a Canadian rock band from Winnipeg, Manitoba.
Anchored by Brad Roberts (vocals, guitar) and his distinctive bass-baritone voice, the other band members have fluctuated over the years. Its most prominent line-up consist ...
and of passive safety devices (
seat belts
A seat belt, also known as a safety belt or spelled seatbelt, is a vehicle safety device designed to secure the driver or a passenger of a vehicle against harmful movement that may result during a collision or a sudden stop. A seat belt reduce ...
,
airbags, shock absorbing
dash boards, etc.). Guide rail tests evaluate vehicle deceleration and rollover potential, as well as penetration of the barrier by vehicles.
History
In the years 1970 attempts were made to simulate car crash events with
non-linear
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathe ...
spring-mass systems after
calibration
In measurement technology and metrology, calibration is the comparison of measurement values delivered by a device under test with those of a calibration standard of known accuracy. Such a standard could be another measurement device of known ...
, which require as input the results of physical destructive laboratory tests, needed to determine the mechanical crushing behavior of each spring component of the modeled system. "
First principle
In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. First principles in philosophy are from first cause attitudes and taught by Aristotelians, and nuan ...
" simulations like more elaborate finite element models, however, need only the definition of the structural geometry and the basic material properties (
rheology
Rheology (; ) is the study of the flow of matter, primarily in a fluid (liquid or gas) state but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applie ...
of car body steel, glass, plastic parts, etc.) as an input to generate the numerical model.
The origins of industrial first principle computerized car crash simulation lies in
military defense
A military, also known collectively as armed forces, is a heavily Weapon, armed, highly organized force primarily intended for warfare. Militaries are typically authorized and maintained by a sovereign state, with their members identifiable ...
,
outer space, and civil
nuclear power plant
A nuclear power plant (NPP), also known as a nuclear power station (NPS), nuclear generating station (NGS) or atomic power station (APS) is a thermal power station in which the heat source is a nuclear reactor. As is typical of thermal power st ...
applications. Upon presentation of a simulation of the accidental crash of a military
fighter plane into a nuclear power plant on May 30, 1978, b
ESI Groupin a meeting organized by the
Verein Deutscher Ingenieure (VDI) in
Stuttgart
Stuttgart (; ; Swabian German, Swabian: ; Alemannic German, Alemannic: ; Italian language, Italian: ; ) is the capital city, capital and List of cities in Baden-Württemberg by population, largest city of the States of Germany, German state of ...
, car makers became alerted to the possibility of using this technology for the simulation of destructive car crash tests (Haug 1981).
In the following years, German car makers produced more complex crash simulation studies, simulating the crash behavior of individual car body components, component assemblies, and quarter and half car bodies in white (
BIW). These experiments culminated in a joint project by the Forschungsgemeinschaft Automobil-Technik (FAT), a conglomeration of all seven German car makers (
Audi
Audi AG () is a German automotive manufacturer of luxury vehicles headquartered in Ingolstadt, Bavaria, Germany. A subsidiary of the Volkswagen Group, Audi produces vehicles in nine production facilities worldwide.
The origins of the compa ...
,
BMW
Bayerische Motoren Werke AG, trading as BMW Group (commonly abbreviated to BMW (), sometimes anglicised as Bavarian Motor Works), is a German multinational manufacturer of vehicles and motorcycles headquartered in Munich, Bavaria, Germany. Th ...
,
Ford,
Mercedes-Benz
Mercedes-Benz (), commonly referred to simply as Mercedes and occasionally as Benz, is a German automotive brand that was founded in 1926. Mercedes-Benz AG (a subsidiary of the Mercedes-Benz Group, established in 2019) is based in Stuttgart, ...
,
Opel
Opel Automobile GmbH (), usually shortened to Opel, is a German automobile manufacturer which has been a subsidiary of Stellantis since 16 January 2021. It was owned by the American automaker General Motors from 1929 until 2017 and the PSA Gr ...
,
Porsche
Dr. Ing. h.c. F. Porsche AG, usually shortened to Porsche (; see below), is a German automobile manufacturer specializing in luxury, high-performance sports cars, SUVs and sedans, headquartered in Stuttgart, Baden-Württemberg, Germany. Th ...
, and
Volkswagen
Volkswagen (VW; )English: , . is a German automotive industry, automobile manufacturer based in Wolfsburg, Lower Saxony, Germany. Established in 1937 by German Labour Front, The German Labour Front, it was revitalized into the global brand it ...
), which tested the applicability of two emerging commercial crash simulation codes. These simulation codes recreated a frontal impact of a full passenger car structure (Haug 1986) and they ran to completion on a computer overnight. Now that turn-around time between two consecutive job-submissions (computer runs) did not exceed one day, engineers were able to better understand the crash behavior and make efficient and progressive improvements to the analyzed car body structure.
Computer-aided engineering
Computer-aided engineering (CAE) is the general usage of technology to aid in tasks related to engineering analysis. Any use of technology to solve or assist engineering issues falls under this umbrella.
Overview
Following alongside the con ...
(CAE) software became lately a norm in the crash test simulation. The combination of
Machine learning
Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task ( ...
and CAE tools allowed a much better acceleration of the simulation software. Engineers used ML to predict:
* The dummy chest acceleration
* The forward displacement of the dummy
* The maximum chest acceleration and the
Head injury criterion
The head injury criterion (HIC) is a measure of the likelihood of head injury arising from an impact. The HIC can be used to assess safety related to vehicles, personal protective gear, and sport equipment.
Normally the variable is derived from t ...
.
Application
Crash simulations are used to investigate the
safety
Safety is the state of being protected from harm or other danger. Safety can also refer to the control of recognized hazards in order to achieve an acceptable level of risk.
Meanings
The word 'safety' entered the English language in the 1 ...
of the car occupants during impacts on the front end structure of the car in a "
head-on collision
A head-on collision is a traffic collision where the front ends of two vehicles such as cars, trains, ships or planes hit each other when travelling in opposite directions, as opposed to a side collision or rear-end collision.
Rail trans ...
" or "frontal impact", the lateral structure of the car in a “
side collision
A side collision is a vehicle crash where the side of one or more vehicles is impacted. These crashes typically occur at intersections, in parking lots, and when two vehicles pass on a multi-lane roadway.
Occurrences and effects
A 2016 stu ...
” or “side impact”, the rear end structure of a car in a "
rear-end collision
A rear-end collision, often called rear-ending or, in the UK, a shunt, occurs when a forward-moving vehicle crashes into the back of another vehicle (often stationary) in front of it. Similarly, rear-end classification of railway accidents, ra ...
" or “rear impact”, and the roof structure of the car when it overturns during a "
rollover". Crash simulations can also be used to assess injury to
pedestrians
A pedestrian is a person traveling on foot, by wheelchair or with other mobility aids. Streets and roads often have a designated footpath for pedestrian traffic, called the ''sidewalk'' in North American English, the ''pavement'' in British Eng ...
hit by a car.
Benefits
A crash simulation produces results without actual
destructive testing
In destructive testing (or destructive physical analysis, DPA) tests are carried out to the specimen's failure, in order to understand a specimen's performance or material behavior under different loads. These tests are generally much easier to ca ...
of a new car model. This way, tests can be performed quickly and inexpensively in a computer, which permits optimization of the design before a real prototype of the car has been manufactured. Using a simulation, problems can be solved before spending time and money on an actual crash test. The great flexibility of
printed
Printing is a process for mass reproducing text and Printmaking, images using a master form or template. The earliest non-paper products involving printing include cylinder seals and objects such as the Cyrus Cylinder and the Cylinders of Nabon ...
output and
graphical display enables designers to solve some problems that would have been nearly impossible without the help of a computer.
Analysis
Large number of crash simulations use a method of analysis called the
Finite Element Method
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat tran ...
. The complex problems are solved by dividing a surface into a large but still finite number of elements and determining the motion of these elements over very small periods of time. Another approach to crash simulations is performed by application of
Macro Element Method. The difference between two mentioned above methodologies is that the structure in case of Macro Element Method consists of smaller number of elements. The calculation algorithm of structure deformation is based on experimental data rather than calculated from partial differential equations.
Pam-Crash started crash simulation and together with
LS-DYNA
LS-DYNA is an advanced general-purpose multiphysics simulation software package developed by the former Livermore Software Technology Corporation (LSTC), which was acquired by Ansys in 2019. While the package continues to contain more and more p ...
is a software package which is widely used for application of Finite Element Method. This method allows detailed modeling of a structure, but the disadvantage lies in high processing unit requirements and calculation time.
The Visual Crash Studio uses Macro Element Methodology. In comparison with FEM it has some modeling and boundary condition limitations but its application does not require advanced computers and the calculation time is incomparably smaller. Two presented methods complement each other. Macro Element Method is useful at early stage of the structure design process while Finite Element Method performs well at its final stages.
Structural analysis
In a typical crash simulation, the car body structure is analyzed using spatial
discretization
In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numeri ...
, that is, breaking up the continuous movement of the body in real time into smaller changes in position over small, discrete time steps. The discretization involves subdividing the surface of the constituent, thin,
sheet metal
Sheet metal is metal formed into thin, flat pieces, usually by an industrial process.
Thicknesses can vary significantly; extremely thin sheets are considered foil (metal), foil or Metal leaf, leaf, and pieces thicker than 6 mm (0.25  ...
parts into a large number (approaching one million in 2006) of
quadrilateral
In Euclidean geometry, geometry a quadrilateral is a four-sided polygon, having four Edge (geometry), edges (sides) and four Vertex (geometry), corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''l ...
or triangular regions, each of which spans the area between "nodes" to which its corners are fixed. Each element has mass, which is distributed as concentrated masses and as
mass moments of inertia to its connecting nodes. Each node has 6 kinematic
degrees of freedom
In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinite ...
, that is, one node can move in three linear directions under
translation
Translation is the communication of the semantics, meaning of a #Source and target languages, source-language text by means of an Dynamic and formal equivalence, equivalent #Source and target languages, target-language text. The English la ...
and can
rotate
Rotation or rotational/rotary motion is the circular movement of an object around a central line, known as an ''axis of rotation''. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis interse ...
about three independent axes. The spatial
coordinates
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the Position (geometry), position of the Point (geometry), points or other geometric elements on a manifold such as ...
(''x''),
displacement
Displacement may refer to:
Physical sciences
Mathematics and physics
*Displacement (geometry), is the difference between the final and initial position of a point trajectory (for instance, the center of mass of a moving object). The actual path ...
(''u''),
velocity
Velocity is a measurement of speed in a certain direction of motion. It is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of physical objects. Velocity is a vector (geometry), vector Physical q ...
(''v''), and
acceleration
In mechanics, acceleration is the Rate (mathematics), rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are Euclidean vector, vector ...
(''a'') of each node is mostly expressed in a three-dimensional rectangular
Cartesian coordinate system
In geometry, a Cartesian coordinate system (, ) in a plane (geometry), plane is a coordinate system that specifies each point (geometry), point uniquely by a pair of real numbers called ''coordinates'', which are the positive and negative number ...
with axes ''X'',''Y'', and ''Z''.
If the nodes move during a crash simulation, the connected elements move, stretch, and bend with their nodes, which causes them to impart forces and
moments to their nodal connections. The forces and moments at the nodes correspond to the inertia forces and moments, caused by their translational (linear) and
angular acceleration
In physics, angular acceleration (symbol α, alpha) is the time rate of change of angular velocity. Following the two types of angular velocity, ''spin angular velocity'' and ''orbital angular velocity'', the respective types of angular accele ...
s and to the forces and moments transmitted by the
resistance of the structural material of the connected elements as they deform. Sometimes, additional external
structural loads
A structural load or structural action is a mechanical load (more generally a force) applied to structural elements. A load causes stress, deformation, displacement or acceleration in a structure. Structural analysis, a discipline in engineer ...
are applied, like gravity loads from the self weight of the parts, or added loads from external masses.
The forces and moments of all nodes are collected into a
column vector
In linear algebra, a column vector with elements is an m \times 1 matrix consisting of a single column of entries, for example,
\boldsymbol = \begin x_1 \\ x_2 \\ \vdots \\ x_m \end.
Similarly, a row vector is a 1 \times n matrix for some , c ...
(or column matrix), and the time dependent
equations of motion
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathem ...
(in dynamic equilibrium) can be written as follows.
:
where vector
(mass times acceleration vector) collects the inertia forces at the nodes,
collects the external nodal loads, and
collects the internal resisting forces from the deformation of the material. ''M'' is a
diagonal matrix
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagon ...
of the nodal masses. Each vector (''u'', ''v'', ''a'', ''F'', etc.) has
dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coo ...
6 times the total number of nodes in the crash model (about 6 million “
degrees of freedom
In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinite ...
” for every 1 million "nodes" in 3-D thin shell finite element models).
Time analysis
A crash simulation uses time discretization as well to separate the continuous changes in time into very small, usable segments. The dynamic
equations of motion
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathem ...
hold at all times during a crash simulation and must be integrated in time, ''t'', starting from an
initial condition
In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted ''t'' = 0). Fo ...
at time zero, which is just prior to the crash. According to the explicit
finite difference
A finite difference is a mathematical expression of the form . Finite differences (or the associated difference quotients) are often used as approximations of derivatives, such as in numerical differentiation.
The difference operator, commonly d ...
time integration method used by most crash codes, the accelerations, velocities, and displacements of the body are related by the following equations.
:
:
:
In these equations the subscripts ''n''±1/2, ''n'', ''n''+1 denote past, present, and future times, ''t'', at half and full-time intervals with time steps
and
, respectively.
Solution
The above
system of linear equations
In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variable (math), variables.
For example,
: \begin
3x+2y-z=1\\
2x-2y+4z=-2\\
-x+\fracy-z=0
\end
is a system of th ...
is solved for the accelerations,
, the velocities,
, and the displacements,
, at each discrete point in time, ''t'', during the crash
duration. This solution is trivial, since the mass matrix is diagonal. The computer time is proportional to the number of finite elements and the number of solution time steps. The stable solution time step,
, is limited for
numerical stability
In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context: one important context is numerical linear algebra, and ...
, as expressed by the
Courant–Friedrichs–Lewy condition
In mathematics, the convergence condition by Courant–Friedrichs–Lewy (CFL) is a necessary condition for convergence while solving certain partial differential equations (usually hyperbolic PDEs) numerically. It arises in the numerical analysis ...
(CFL), which states that “in any time-marching computer simulation, the time step must be less than the time for some significant action to occur, and preferably considerably less." In a crash simulation, the fastest significant actions are the acoustic signals that travel inside the structural material.
The solid elastic stress wave speed amounts to
:
where
is the initial elastic modulus (before
plastic deformation
In engineering, deformation (the change in size or shape of an object) may be ''elastic'' or ''plastic''.
If the deformation is negligible, the object is said to be ''rigid''.
Main concepts
Occurrence of deformation in engineering application ...
) of the material and
is the mass density. The largest stable time step for a given material is therefore
:
,
where
is the smallest distance between any two nodes of the numerical crash simulation model.
Since this distance can change during a simulation, the stable time step changes and must be updated continually as the solution proceeds in time. When using
steel
Steel is an alloy of iron and carbon that demonstrates improved mechanical properties compared to the pure form of iron. Due to steel's high Young's modulus, elastic modulus, Yield (engineering), yield strength, Fracture, fracture strength a ...
, the typical value of the stable time step is about one
microsecond
A microsecond is a unit of time in the International System of Units (SI) equal to one millionth (0.000001 or 10−6 or ) of a second. Its symbol is μs, sometimes simplified to us when Unicode is not available.
A microsecond is to one second, ...
when the smallest discrete node distance in the mesh of the finite element model is about 5 millimeters. It needs then more than 100,000 time intervals to solve a crash event that lasts for one tenth of a second. This figure is exceeded in many industrial crash models demanding optimized crash solvers with High-Performance Computing (
HPC) features, such as
vectorization and
parallel computing
Parallel computing is a type of computing, computation in which many calculations or Process (computing), processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time. ...
.
See also
*
Finite element method in structural mechanics The finite element method (FEM) is a powerful technique originally developed for the numerical solution of complex problems in structural mechanics, and it remains the method of choice for analyzing complex systems. In FEM, the structural system is ...
*
Finite element analysis
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical models, mathematical modeling. Typical problem areas of interest include the traditional fields of structural ...
*
Crash test
A crash test is a form of destructive testing usually performed in order to ensure safe design standards in crashworthiness and crash compatibility for various modes of transportation (see automobile safety) or related systems and compon ...
References
{{Reflist
*Haug, E. (1981) "Engineering safety analysis via destructive numerical experiments", EUROMECH 121, Polish Academy of Sciences, Engineering Transactions 29(1), 39–49.
*Haug, E., T. Scharnhorst, P. Du Bois (1986) "FEM-Crash, Berechnung eines Fahrzeugfrontalaufpralls", VDI Berichte 613, 479–505.
Automotive safety
Simulation
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