II-7 Simms Multibody Modelling for Impact Biomechanics Delhi 2013

Introduction to Multibody Modelling for

Impact Biomechanics Applications

Dr Ciaran Simms FTCD

[email protected]

Delhi

December 2013

Ciaran Simms Multibody Methods

mailto:[email protected]

Mechanical dummies

Mathematical

modelling

Virtual crash

environment

CANNOT GENERALLY CRASH TEST HUMANS…NEED MODELLING METHODS

Volunteers

Animals

Cadavers

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pSgtztx

2

2

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Model Complexity

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Need to decide your research question to determine

appropriate model complexity

Make everything as simple as possible, but no

simpler (Einstein)

More complex models have more outputs, but also

more inputs – often increased uncertainity


Particle models can predict pedestrian trajectories

MIXED SINGLE SEGMENT MOMENTUM AND PARTICLE MODELS TO

ESTIMATE IMPACT SPEED FROM PROJECTION DISTANCE

But what about effects of vehicle shape?

Simms & Wood, Springer 2009


Models based on conservation of Momentum

Accounts for geometry and inertia and captures principal

kinematics even with a single segment model WITHOUT

knowledge of vehicle stiffness.


Momentum based models

Can assume plastic contacts and rigid body relations and then

do not need specific contact stiffnesses to proceed – good for

general analysis, also essence of PC Crash

Assume step changes in velocity components when contacts

occur: hence no injury predictions

HOWEVER, for force time history modelling need an ordinary

differential equation approach

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ORDINARY DIFFERENTIAL EQUATION FORMULATION

xX

z

B – vehicle contact on leg

C – vehicle contact on head

D – feet contact with ground

FC


How to get velocities & displacements from this kind of model ?

eg spring mass system, stiffness

Initial conditions:

Newton II:

Euler integration

Similar approach to get displacements (normally

coupled solutions to two 1st order ODEs used)

Time marching solution using initial conditions

ii txktx

knownxx

0,0

txtx ,

iiiii tttxtxtx

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k

k


Multibody Modelling

To capture body articulation, need to be able to

combine a number of links with kinematic joints and

add joint stiffnesses

Need to be able to handle hysteresis and damping

and non-linearity in contacts

Can then get force time and acceleration time

behaviour of all components

Assumption that all links remain rigid 9


ONE/TWO SEGMENT ORDINARY DIFFERENTIAL EQUATION FORMULATION



MULTIBODY MODELS: eg MADYMO – commercial code to make using these models easier

CAN PREDICT FORCES, ACCELERATIONS, but essentially

what you put in is what you get out!

Model itself is not so interesting, it is what it can tell you...


Madymo Pedestrian impact simulations


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Rigid

Body

Dynamics

• Tree structure

• Rigid bodies

• Surfaces

• Contacts

• Integration

Adapted from TNO Madymo

So how does it work?


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Multibody systems mathematically simulate the motion of multiple

rigid bodies connected by joints to form multiple systems

Force models and contact interactions are applied to the rigid bodies

and the motions caused by these forces are calculated with

numerical integration methods

working with FORCES and DISPLACEMENTS, NOT with STRESS

and STRAIN (as used in FE models)

lumped parameter models (like a free body diagram)

Multibody approach



Tree Structure

unique sequence of bodies and kinematic joints

2 systems 3 systems, resp., 7 bodies1 body and 5 bodies

1 system with 12 bodies

A System is one or more chains of one or more rigid bodies Adapted from TNO Madymo


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Rigid Body

A rigid body has constant mass & rotational inertia but no geometrical properties of its own

Connected to other bodies within a multibody system by joints

Can be connected to other bodies with springs and dampers

Planes, ellipsoids, etc can be connected to a rigid body

Define mass, inertia and centre of gravity wrt local coordinate system

Positions and orientations of rigid bodies are computed



Rigid Body Relations

Two points on a rigid body have a relative velocity

defined by the distance between them and the

angular velocity of the body

Can be expressed in vector format as:

16 ABBAAB

ABBAAB

ABAB

rvv

rv

vvv

/

//

/

B

A

Bv

Av

Ar

BA


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Multibody Surfaces

Surfaces for contact evaluations and visualising

– PLANES

– ELLIPSOIDS

– CYLINDERS

FE Mesh may also describe an arbitrary surface, but

this is a ‘null’ material and no strain-stress calculation

is performed



(Hyper-) Ellipsoids

A (hyper-)ellipsoid is defined by

The location of the centre

The degree n

The semi-axes a, b and c

The orientation of the semi-axis

xe

a

n

ye

b

n

ze

c

n

1

ye

2D ellipsoid 3D ellipsoid

ze

xe

x y

z

ze

ye

z

y

cb b

c

a

n = 2

n = 8



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Integration Method and Time Step

Numerical integration of the system’s

differential equation’s of motion

Usually Runge Kutta or Euler integration

Euler:

Forward integration is conditionally stable:

need to check timestep small enough

iiiii tttxtxtx

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Timestep importance

Spring mass system: period T = 0.2 ps



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Contact between multibody surfaces.

An action and reaction force is applied on the corresponding

bodies depending on the surface penetration

Contact force consists of

Elastic force Fe(l)

Damping force Fd

Friction force Ff

Freaction

Faction

Ff

Fe

Fd

λ

Multibody contacts



Relative Velocity in a Contact

Velocity used for calculation of damping and friction force is

the relative velocity of the contacting bodies at the point of

application of the contact force

P

Vnorm

V

Vplane



Elastic Force

user defined force-penetration loading (L)

and unloading (U) function

Can measure experimentally and use as

input

Hysteresis can be specified, often very

important for realistic kinematics

Dynamic amplification factor can account

for dependency of the elastic force on the

rate of the penetration



Elastic force is found from observed penetration between surfaces in contact at a given timestep

p1

l

p2

ellipsoid

plane

p1

p2

ellipsoid

plane

ellipsoid 2

l1l2

l



Newton-Euler Equations of Motion

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𝑭 = 𝑮

(linear)

𝑴 = 𝑯 = 𝐼 𝝎 + 𝝎 ×𝑯

(angular)

In MADYMO, these equations of Motion are solved for

systems of rigid bodies using the Principle of Virtual Power


A study of pedestrian head translation, rotation and impact velocity: The influence of vehicle speed,

pedestrian speed and pedestrian gait

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Case study 1: Ciaran Simms Multibody Methods

• Influence of vehicle speed, pedestrian speed and pedestrian gait on

pedestrian post impact kinematics have not been quantified - MADYMO

• Transverse translation influences injury severity due to variations in local

vehicle stiffness

• Head rotation is related to pedestrian stance at impact which influences the

overall kinematics

• Head impact velocity influences head injuries


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Baseline simulation Transverse Offset

Pedestrian Gait cycle Head rotation about

vertical axis


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Typical MADYMO Pedestrian Animation – SIDE VIEW


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Typical MADYMO Pedestrian Animation – TOP VIEW


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Transverse offset varies cyclically with pedestrian gait

Modelling Results: Transverse Offset Ciaran Simms Multibody Methods

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Modelling Results: Transverse Offset

Transverse Offset depends also on vehicle speed


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Modelling Results: Transverse Offset

Transverse offset reduces

with vehicle speed Transverse offset increases

with pedestrian speed


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Modelling Results: Head Rotation

Head Rotation reduces with

vehicle speed

Head Rotation increases

with vehicle speed


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Modelling Results: Head Rotation

Positive and Negative Regions of Pedestrian Head Rotation


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Modelling Results: head impact velocity

Head impact speed is a linear function of vehicle speed

Largely independent of pedestrian speed


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Modelling Results: Analysis

Transverse Offset is a linear function of ratio of Pedestrian to Vehicle speed


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Modelling Results: Head rotation

Head Rotation is a linear function of ratio of Pedestrian to Vehicle speed


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• Transverse Offset, Head rotation and head impact

speed vary cyclically and significantly with gait

• First quantification of the influences of pedestrian

speed and stance on transverse offset and head

rotation, both of which may sometimes be available in

individual pedestrian accident cases.

Study conclusions Ciaran Simms Multibody Methods

The Influence of Vehicle Shape on Pedestrian Ground Contact

Mechanisms

Presented to IRCOBI conference Krakow 2011

CK Simms1, Tom Ormond1 & DP Wood2

1Centre for Bioengineering, Trinity College, Dublin, Ireland 2Denis Wood Associates, Dublin, Ireland

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Case study 2: Ciaran Simms Multibody Methods

• Injuries from the vehicle contact and ground contact phases.

• High variability of ground contact injuries.

• Vehicle Shape is important for ground related pedestrian injuries:

• Ground contact head injuries more frequent for high Bonnet Leading Edges

• Ground contact injuries from newer cars less significant

• Ground contact: Passenger cars (ground contact is 7% of head injuries)

Light Trucks and Vans (ground contact is 39% of head injuries)


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Research approach

What is the kinematic explanation why high-fronted vehicles

result in more severe head/ground injuries for pedestrians than

collisions with conventional cars?

Research question

Multibody models (Madymo) to include effects of vehicle

speed, vehicle shape & pedestrian size and gait stance.

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Madymo Simulation Setup

Cars and SUV models created in Madymo

Contact surfaces & characteristics for bumper,

BLE, bonnet top and windscreen.

The midsize male/small female

Walking pedestrian struck from the side, leading

leg or trailing leg struck first

Vehicle impact speed 25-35 km/h

72 simulations performed

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Results

Mechanism 1: 46% of cases: a wrap trajectory, rotation (90o< α< 180o)

with the head hitting the ground first, followed by the body.

Angle of impact with ground correlates with HIC score (r2= 0.56).

Six Mechanisms of ground contact accounted for 94% cases

Distinguished by amount & direction of rotation of the body at ground contact

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Results

Mechanism 2:14% of cases: Rotation (0o< α< 90o) insufficient to raise

body above the head before ground contact occurs

Body strikes the ground first followed by the head

Mechanism 3:12% of cases: Rotation (180o< α< 270o).

Head strikes ground first, then body

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Results Mechanism 4:15% of cases: Whole body rotation (α> 270o) occurs &

body contacts the ground first, then head

Mechanism 5: BLE sufficiently above the pedestrian centre of gravity

(α<90o). Pedestrian pushed forward, body contacts ground first.

Mechanism 6: shoulder contacts ground first - head protection

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HIC score by mechanism type

HIC score strongly depends on Mechanism

HIC for Mechanism 1 & 2 >> HIC for Mechanisms 3-6.

Mech 1

(90o<α<180o)

Mech 2

(0o<α<90o)

Mech 3

(180o<α< 270o)

Mech 4

(α>270o)

Mech 5

(α<90o)


Impact mechanism by vehicle type

Instances of Mechanism 1 increase with increasing vehicle size (bonnet

height) as far as midsized SUV (BLE height of about 1 m)

Mechanism 4 (α>270o) only occurs with cars, Mechanism 5 (α<90o) only

occurs with large SUV model.

Mech 1

(90o<α<180o)

Mech 2

(0o<α<90o)

Mech 4

(α>270o)

Mech 5

(α<90o)

Mech 3

(180o<α< 270o)


Results/Discussion

Comparative study: focus on trends, no validation data

Average HIC for different vehicles versus normalized bonnet height showed r2

values of .74 for midsized male.

HIC from ground independent of vehicle speed (r2= 0.04).

For Mechanism 1 (46% of cases), angle of body impact with the ground

correlated with HIC score (r2= 0.56) and angle of impact also decreased with

bonnet height (r2= 0.37).

Simple Explanation: High HIC occurs when impact angle is low

and rotation < 180° so that body rotation causes head to move

towards ground

Direct influence of body angle on HIC new

Lower bonnets cause more body rotation, so that by time of ground contact

body is rotating away from ground.

For large SUV, reduced rotation means very few Mechanism 1 cases, but

many Mechanism 2 cases


Conclusions

For speed range 25-35 km/h, variations in normalised bonnet height accounts

for up to 74% of variation in ground HIC.

Most common & worst scenario is wrap trajectory where head hits ground first

with body rotating head towards the ground – then ground HIC depends on

body angle and direction of body rotation.

The angle of impact with the ground is correlated with the HIC (r2= 0.56) and

bonnet leading edge height (r2= 0.37).

When the body is rotating away from the ground at ground contact, HIC is

reduced - more likely to occur for car impact than for SUV impact cases

Since impact angle decreases with bonnet height, these findings help to

explain why high-fronted vehicles result in more significant head injuries in

ground contact.


Conclusions for MB modelling

Multibody models are fast

and efficient for whole body

simulations

Can predict all structural

parameters like linear and

angular acceleration,

bending moments and force

These are easily related to

common injury criteria

Need to be aware of model

limitations and validation

extent

No means to evaluate tissue

stress and strain

Contacts are chief modelling

challenge

Despite popularity and

potential of FE modelling,

relative simplicity of MB

models will ensure their

continued usage in the

future for fundamental

insights – don’t give up on

this method

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II-7 Simms Multibody Modelling for Impact Biomechanics Delhi 2013

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