Explicit FEM Applied to Impact Biomechanics pProblems

D. CroninIRCOBI 2011

Introduction93,986 solid elements20,903 shell elements1,129 beam elements256 material definitions

• Impact BiomechanicsI th t d f h b d t i t l di

256 material definitions.

[Yuen 2010]

– Is the study of human body response to impact loading, and injury resulting from mechanical interaction [Schmitt 2010]

• Explicit FE allows us to consider complex geometryExplicit FE allows us to consider complex geometry, nonlinear materials and contact in transient problems

[Watson 2010]FMVSS 214 (54 kph) side impact test[Vehicle model courtesy of NCAC]

Conclusion

• Nobody believes the model except the• Nobody believes the model, except the modeler…

• Everybody believes the experiment except theEverybody believes the experiment, except the experimentalist…

What’s the answer?

• What do we really need?– Understanding or a design tool

• Diminishing returns for effort

100%

? 70 80%

Quality

? 70-80%

EffortWeeks Months Years …

Introduction - Why pursue modeling?y p g

• Models can allow us to:I t t i t l lt– Interpret experimental results

– Investigate response to impact (sensitivity studies) – Consider new designs for protection and safety– Consider new designs for protection and safety

• Models must be developed with a specific intentModels must be developed with a specific intent or hypothesis in mind. – Models are an approximate representation of a physical y

phenomenon, bounded by their assumptions and have a finite life.

[Fice 2010]

Model Construction

Pre processing Solver Post processingPre-processing Solver Post-processing

Geometry -> Mesh

Validation

Material properties(93,986 solid elements)

Convergence(Verification)

Boundary conditionsResponse

Boundary conditions

(301,800 solid elements)

Model Requirements

Model Scale

Model RequirementsA balanced approach is required!

• Material properties• Constitutive models Response

Kinetic/KinematicInjury

Model Scale

Material Geometry/a e aProperties

Geo e y/Anatomy

• Model refinement• Relevant anatomical

Loading(BC’s)

structures

• Force, Deformation or related quantities•Representative • Coupling

Model Requirements - Geometry

• Model design must be reasonable, and meet i t

q y

requirements:– Prediction goals

Relevant material properties– Relevant material properties– Continuum-based approach– Computation cost Detailed (3 D) local

http://www.nlm.nih.gov/research/visible/visible_human.html

Computation cost

Mathematical ModelDetailed 2-D blast model

Detailed (3-D) localmodel

L bd ll l d

8Multibody model

Lobdell lumped mass model

[Yuen 2010]

Model Requirements - Geometryq y

Meshing 100.0

• Discretization:– 1D, 2D shell, 3D solid

10.0

Volum

e Missing

• Element size and quality• Strain rate

1.0

% Mass or V

• Element formulation 0.1

0.0 0.2 0.4 0.6 0.8 1.0

Element Size/ Curve Radius  (‐)

MaterialProperties

G tL di GeometryLoading 

Response Injury

Forb

es 2

005

Tetrahedral elements – limitations

Model Requirements – Loading (BCs)q g ( )

• Model requirements – Progressive complexity

Watson, IJCR 2011Yuen, WCB 2010Campbell, ESV 2009Yuen IRCOBI 2008

MaterialProperties

GeometryLoading 

Yuen, IRCOBI 2008Forbes, IJC 2006Forbes, WCB 2006Forbes, IUTAM 2005 Response Injury

Side impact vehicle testSide sled testPendulum impact

Material PropertiesMaterialProperties

GeometryLoading p

• Generally regarded as the most challengingResponse Injury

Generally regarded as the most challenging area with the highest degree of uncertainty

• Most biological materials exhibit non-linear gresponse and are sensitive to strain rate.

** Need to know the expected strain and strain ratep

[Mattucci 2011]

Model Requirements –Materials (Macro)Materials (Macro)

(~100-500 1/s)[Moulton 2010]

(~0.01-10 1/s)

From ASM, Volume 8, Mechanical Testing and Evaluation (~300-3000 1/s)Cronin SEM 2011Cronin SEM 2010Campbell, SEM 2007

Servohydraulic Pendulum ImpactDrop TowerEM Test Frame

Split Hopkinson Pressure Bar Apparatus

Ca pbe , S 00Ouellet, Exp Mech 2006Doman, Exp Mech 2006VanSligtenhorst, JoB 2006Ouellet, PASS 2004Motuz, SAV 2003VanSligtenhorst, ASME BED 2003Salisbury, Plasticity 2002

Material PropertiesMaterialProperties

GeometryLoading p• Properties need to be expressed in a

th ti l / i l f

Response Injury

mathematical / numerical form (~200 models in LS-Dyna)

• Experimental method should be directed t d th d l i ttowards the model requirements.

• A constitutive equation relates stress and strain, accounting for:accounting for:– Deviatoric stress – Volumetric responseVolumetric response

Bovine muscle tissue (1500s-1)

Prediction of injuryMaterialProperties

GeometryLoading j y

• A question of scale…Response Injury

A question of scale…• Requires model calibration

Model Scale

MechanicalResponse

Global Injury Load-based [vehicle g’s]

Model Scale

Global BioChest wall comp.velocity,acceleration

Injuryacceleration, work/energy

ExperimentalistsEpidemiologistsS i ti t

Local Bio Local organ andtissue injury criteria

ScientistsMedicalEngineers…

Model Response 8

10

12

ssur

e (b

ar)

No Hole

Hole Area: 6.25%

Hole Area: 25%p

Model convergence 2

4

6

k W

all P

eak

Pre

s

Richardson Extrapolations

g• Mesh size depends on:

– Loading and Boundary

0

2

0.0 0.5 1.0 1.5

Bac

k

Element Size (mm)g yConditions

– Material properties and failureC t t d l– Contact models

– Assessment metric

• Evaluation Methods– Single/multiple parameter 40

6080

100

Angle

 (deg)

– Single/multiple parameter– Corridor (ISO)– Cross-correlation (CORA)

‐20020

0 100 200 300He

ad A

Time (ms)

Deng (1999) Model

Response - V&VASME V&V 10-2006, “Guide for Verification and Validation in Computational Solid Mechanics”

p

• Verification and Validation (V&V) forms ( )the basis for model development …a continuous process

• Key principles:Verification (assess code and numerical– Verification (assess code and numerical errors) must precede validation (comparison of model to experiments)Validation should be pursued in a hierarchical– Validation should be pursued in a hierarchical fashion (simple to complex)

– Validation is specific to a particular model and applicationapplication

– Uncertainty assessmentFice, 2010

Solution uniquenessq

• The problem follows a unique time-response pathThe problem follows a unique time response path• It is possible for the solution to diverge from this

pathp– Numerical round-off– Material failure / Contact failure– Parameter estimation for non-linear materials

Response

t

Material Failure and Damageg

• We are often interested inWe are often interested in response to impact, and the subsequent damage – Hard tissue damage and failure

• Often addressed using elastic-plastic material model withplastic material model with element erosion

D d/ f il f ft– Damage and/or failure of soft tissues

• CDM for structural (gross) failure• Developing area for physiological

response[DeWitt 2010]

What’s current and next?

CurrentCurrent• Multi-physics (Fluid/gas-structure)• Continuum Damage MechanicsContinuum Damage Mechanics• Meshless and other (EFG, SPH)

Next• Crack propagation (XFEM)• Crack propagation (XFEM)• Improved CDM approaches

M t i l ti d tit ti• Material properties and constitutive modeling

Summaryy

• A model should be developed based on aA model should be developed based on a hypothesis, with appropriate specifications.

• Focus on balance (geometry, materials, bc’s)(g y, , )• ! Mesh refinement must be sufficient !• V&V is an ongoing process (multiple scales)V&V is an ongoing process (multiple scales).

• Modeling is a technique that can give us insight• Modeling is a technique that can give us insight.

• Take small steps and ask simple questions to• Take small steps and ask simple questions to get reasonable answers.