American Institute of Aeronautics and Astronautics

1

Numerical Analysis of Dynamically Loaded Advanced

Stiffened Aerospace Composite Structures with

Bonded/Fastened Joints

Shivashankar Binnamangala¹ and Javid Bayandor²

¹School of Aerospace, Mechanical and Manufacturing Engineering

Royal Melbourne Institute of Technology, Melbourne, Victoria, Australia

²CRashworthiness for Aerospace Structures and Hybrids (CRASH) Lab

Center for Intelligent Material Systems and Structures, Department of Mechanical Engineering

Virginia Tech, Blacksburg, Virginia, U.S.A.

This paper discusses a numerical methodology for better understanding of low velocity

impact behaviour on pre-strained aircraft composite structural joints. An adhesively

bonded/mechanically fastened aircraft joint was explicitly analysed in accordance with

relevant previous experimental studies on aerospace grade composites when subjected to

realistic operational loads of an aircraft. A detailed finite element analysis model was

constructed and tested for possible numerical instabilities. Good agreements were obtained

for force-time histories when predicted analysis data were compared to available

experimental results. An extension of impact analysis was carried out for two low velocity

impact energies for biaxial tension, biaxial compression and zero pre-strain cases. Results

are presented on the effect of pre-strain on peak contact force, absorbed energy and damage

size. The paper continues by providing a comprehensive comparisons of the numerical

results to the experimental investigation of impact loading on a pre-strained aircraft

composite structural joint.

Nomenclature

σi = material strength in i axis Psi

σj = material strength in j axis Psi

σij = in-plane (plane i and j) shear stress Psi

Xt = longitudinal tensile strength of fibre Psi

Xc = longitudinal compressive strength of fibre Psi

Yt = transverse tensile strength of fibre Psi

Yc = transverse compressive strength of fibre Psi

Sc = in-plane shear strength (plane a and b) of fibre. Psi

σn = normal stress of the adhesive Psi

σs = shear stress of the adhesive Psi

E = Young’s modulus Psi

με = microstrain

I. Introduction

The quest for light weight yet strong materials for various aircraft structural applications has led to increased use

of polymer matrix composites. Realisation of the full potential of aircraft composite structures demands the design

of efficient joints as joint efficiencies in composites are significantly less than that of metals10

. The particular

reasons for lower optimised joint design in composite structures are high stress concentration around loaded holes,

anisotropic properties, low transverse strength, unpredictable crack propagation patterns, and sensitivity to

environmental conditions. Recognition of these drawbacks in composite laminates from material level to structural

level requires the understanding of energy absorption mechanism during impact, impact damage resistance and post-

impact damage tolerance.

49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition4 - 7 January 2011, Orlando, Florida

AIAA 2011-167

Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

American Institute of Aeronautics and Astronautics

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Generally, impact damages on aircraft are classified as low, medium and high velocity impacts. A low-velocity

impact (LVI) with sufficient energy will cause a barely visible/visible damage in composite structures which may

lead to catastrophic failure. An initial pre-strain of composite structures subjected to LVI will further complicate the

behaviour of the structures. This complicated damage entails matrix cracking, delamination, fibre fracture or local

deformation/crushing at the surface. Thus LVI is considered to be one of the potential threats to aerospace

composite structures which has to be addressed during the design phase.

Furthermore the certification requirements of aircraft composite structural joints under dynamic loading

conditions necessitate costly and time consuming experimental trials and conservative designs. Such certification

processes for increased passenger safety demand a numerical methodology to fully capture the intricacies of the

dynamic events, while allowing for easy integration into the design tools.

A. Outline of Sections

A general overview of this paper is presented in this section.

Background: this section briefly describes the literature survey conducted to address the issues related to the

present analysis work.

Initial simulation: this section illustrates an initial simulation and validation performed to a relevant previous

experimental study.

FE Model and Simulation: using validated model a detailed methodology is explained to perform the present

simulation.

Result and Discussion: discussion of results of present simulation is elucidated in this section.

Conclusion: Concluding remarks about the present numerical investigation is covered under this part.

II. Background

A large number of studies have been performed on effects of impact loading on composite structural joints. To

date, majority of the research undertaken in LVI on composite joints has been experimental and mainly focused on

impacting unstressed or in a small number of cases, biaxial stressed coupons.

Pillai (2001) and Bhamare (2006) conducted experimental and numerical LVI testing on adhesively bonded

composite laminates. The joint model was modelled in accordance with ASTM D7136 standard. From their research

it was found that the smaller the size of the impactor higher the fibre cracking and matrix cracking which leads to

catastrophic failure. Further impactor with larger diameter induced more impact force on the test coupons which

leads to larger internal damage.

Bayandor et al. (2003) did drop weight testing and FE analysis on composite laminates. They used three different

analysis tools which are common in the field of LVI damage of composite materials: LS-Dyna, Pam-Shock and

MSC-Dytran. The master/slave contact interfaces were modelled as the panel and the impactor for the master and

the slave, respectively. Contact force generated through FE simulation was in good agreement with experimental

results.

Li, et al. (2001) conducted experiments on the quasi-static and dynamic loading behaviours of riveted joints.

Different failure modes for various joint designs under different loading rates were identified. The joint strength

under dynamic load was found to be lower than that of the quasi-static loading.

Further, Mitrevski et al. (2006), Chiu et al. (1996), and Whittingham et al. (2004) all experimentally investigated

the effect of pre-strain on the response of composite laminated plates subjected to LVI. Applied pre-strains were

between 1000με to 3000με (operational strains which may be experienced by an aircraft). The results indicated

various behaviours, from little or no effect to reduction of impact resistance of the composite laminates.

In complement, these papers present important findings, however there is a need for further research to develop a

numerical methodology to understand how pre-strain affects the damage tolerance and structural integrity of

composite structures.

III. Initial Simulation

For initial simulation and validation of numerical study of this paper, an adhesively bonded composite lap joint

model was created according to the study of Bhamare (2006) which was according to ASTM D 7136 standard. All

finite element analysis (FEA) was carried out using a dynamic FEA code, LS Dyna. To avoid modeling errors,

models were tested for stability and robustness. The test was conducted by discarding all the load cases and

increasing the termination time to 100 cycles. In the post-process result, energy issues and non zero response

magnitude are verified to conform the stability of the model.

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1. Geometry and Boundary Conditions:

Figure 1 represents the geometry and boundary conditions of the model. Laminates were of 6in * 4in * 0.16in

with an overlap of 3in and was modelled with shell elements. impactor diameter was 1” and was modelled with solid

rigid elements. All the highlighted nodes (Figure 1) of the model were fixed in all the direction to reflect the

clamping surfaces of experimental study of Bhamare (2006).

2. Meshing and Material Properties:

Ply orientation of laminates were of [00/90

0/0

0/90

0]s. At impact region fine mesh was adopted, and in overlap

region, top laminate was meshed finer than bottom laminate and the impactor (Figure 1). This fine mesh was

required to avoid nodes penetration between interacting surfaces. The laminates were of glass epoxy composites

(Newport E-glass fabric 7781-NB321) and they were bonded together using Hysol EA 9394 adhesive (using contact

card). Some of the properties are given in Table 1.

Figure 1 Geometry and boundary condition of initial simulation model

Note: SPC’s 123 represents translational constraints in X, Y, Z directions respectively and SPC’s 456 represents

rotational constraints in X, Y, Z directions respectively

“ represents inch

Table 1 Laminates and adhesive properties3, 11, 16, and 12

Newport E glass

fabric 7781-NB321

CYCOM 970

Density 0.065 lb/in3

0.0567 lb/in3

Young’s modulus (E11=E22) 3.57 x 106Psi 7.9 x 10

6Psi

Longitudinal tensile strength, Xt 87000Psi 107000Psi

Transverse tensile strength, Yt 12000Psi 15000Psi

Longitudinal compressive strength, Xc 71000Psi 114000Psi

Transverse compressive strength, Yc 15000Psi 21760Psi

Shear strength (xy axis), Sc 15000Psi 18500Psi

Adhesive HYSOL 9394

Allowable Normal stress (peel stress) 20lbs/in

Allowable shear stress 4200Psi

6”

9”

3” 4”

Highlighted nodes: SPC’s: 123456 3”

Adhesive represented by

contact card (invisible)

Impactor diameter 1”

SPC’s: 12 Laminates

Thickness 0.16”

5”

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3. Failure criteria:

Tsai-Wu is the most popular failure criteria for polymer matrix composites7, thus a material card based on this

criteria was used. Tsai-Wu represents improved criteria than any other criterions in terms of more terms in

predicting equation and better agreement with experimental data. The criteria for three dimensional stresses in

material strengths notation is:

Fi+σi+Fijσiσj=1,….,6 (1)

Where: Fi and Fij are material strengths.

Further, in the material card, reduction of tensile and compressive strength of composite material after

compressive failure of matrix can be accounted8. In order to achieve this, maximum strain for matrix was assumed

as 4% and reduction factor for tensile strength and compressive strength after matrix failure were assumed as 0.7

and 3 respectively8. That is once the matrix fails in compression, longitudinal tensile strength of the fibre reduces to

70% and longitudinal compressive strength of fibre reduces to 3 * transverse compressive strength of the fibre.

4. Adhesive representation using contact card:

Contacts are used to identify nodes penetration in to the contacting surfaces15

. For adhesive representation, a

contact card with failure criteria was used. This failure criterion is limited by a perfectly plastic yield condition.

In tension: yield condition is 13

22

NLFS

sn (2)

In compression: yield condition is 13

2

NLFS

s (3)

Where: NLFS is Plastic yield stress of the adhesive joint.

If above yield condition crosses 1 then failure occurs.

In impact analysis, it was assumed that all combination of stresses (tension, compression and shear) were

experienced. And thus tension yield condition was used to account all the stresses (von Mises) and from the above

equations, failure stress is given by NLFS= 22 3 sn .

From Ref 2, shear strength and peel strength of adhesive Hysol 9394 is 4200Psi and 5lbs/in respectively.

Thus, n is calculated as 33.33*3

)33(*5

int_

int_*_

areajo

perimeterjostrengthpeeln lb/in

2

Note: only edges across the joint excluding constraint region were considered as joint perimeter.

Thus, failure stress/criteria of the joint is (NLFS)= 7247322 sn lb/in

2

5. Load Cases (LC):

Two LVI energies 88.5lb-in (10J) and 221.25lb-in (25J) without any pre-strain were considered in this analysis.

Maximum impact force of the joint was compared with the study of Bhamare (2006).

6. Simulation:

As mentioned before, an explicit nonlinear FE analysis code, LS-Dyna was used. Time interval of 10kHz was

adopted in the analysis.

7. Maximum impact force comparison:

Table 2 compares the maximum impact force of the joint analysis for the two impact energies.

Table 2 maximum impact force of the joint

Impact energy case Initial

simulation

Vinay Vasanth Bhamare Error *, %

FE model Experimental

88.5lb-in 1583lbs 1053lbs 1302 lbs -6.2

221.25lb-in 1893lbs 1896lbs 1867lbs -1.4

The possible cause for the above error could be due to some of the estimated material properties and

approximated strength reduction factor of fibres. Damage front was not simulated (crushing process), i.e. Young’s

modulus and strengths of neighbourhood elements of failed elements. Further friction involved in the clamping of

laminates in the experimental work was not considered. Overall a reasonable agreement between experimental and

numerical study was reached.

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IV. Finite Element Model and Simulation

Using the above validated adhesively bonded composite model, an extension of impact analysis was carried out

on pre-strained joint. Impact analysis on pre-strained mechanically fastened composite joint was also conducted

using different model geometry. In the following sections all the FE processing methodology of adhesively bonded

composite joints with pre-strain and mechanically fastened composite joints with pre-strain are described.

B. Adhesively bonded composite joints with pre-strain:

In adhesively bonded composite joints with pre-strain models, except load cases and boundary conditions, all the

other FE methodology and the parameters were the same as Initial Simulation (section III). Different load cases

were generated with the combination of pre-strain and LVI energies.

8. Boundary conditions:

In order to facilitate pre-strain on the laminates, one of the edge was fixed (translation only) in all the direction.

Then depending on the loading type and direction, other edge constraints were developed, see Figure 2 and Table 3.

9. Load Cases (LC):

To obtain various load cases, impacts were applied to models with zero strain, biaxial tension and biaxial

compression pre-strain. Strain rates between 1500με to 2000με were considered. In addition to GFRP laminate,

CFRP laminate was also considered. Different load cases were obtained based on laminate types, impact energies,

and pre-strains. Table 3 and Figure 2 represent all the load cases and the corresponding boundary conditions of this

analysis.

Table 3 Load cases of adhesively bonded joint

Load

Cases

Laminate

type

Loads Boundary conditions

Remarks Impact

energy, lb-in

X pre-

strain, με

Y pre-

strain, Psi

Fixed X

end

Fixed

Y end

Movable

X end

LC1

GFRP 88.5

0 0 123 N/A 123

See Figure 2 for

representation

of boundary

conditions

LC2 2000 1500 123 2 23

LC3 -2000 -1500 123 2 23

LC4

GFRP 221.25

0 0 123 N/A 123

LC5 2000 1500 123 2 23

LC6 -2000 -1500 123 2 23

LC7

CFRP 88.5

0 0 123 N/A 123

LC8 2000 1500 123 2 23

LC9 -2000 -1500 123 2 23

LC10

CFRP 221.25

0 0 123 N/A 123

LC11 2000 1500 123 2 23

LC12 -2000 -1500 123 2 23

Note: Negative sign above represents a

compressive strain.

X pre-strain and Y pre-strain were

applied via movable X end and movable Y

end respectively, whereas impact energy

was through the impactor, see Figure 2. X

pre-strain and Y pre-strain in the laminates

were created by applying a constant

displacement at the movable X end and

movable Y end correspondingly.

Fixed X end Movable X end

Impactor

Fixed Y end

Movable Y end

Figure 2 Representation of boundary conditions of adhesively

bonded composite joint with pre-strain

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C. Mechanically fastened composite joint with pre-strain:

As mentioned earlier, mechanically fastened composite joint with pre-strain was modelled with solid elements.

Owing to huge computational time in solving solid elements, only two load cases were considered for CFRP

laminate only.

10. Geometry and Boundary Conditions:

Geometry of the model was exactly similar to the study of Li et. al. (2000), see Figure 3. Laminates were of

7.36in * 1.57in * 0.083in with an overlap of 1in. Impactor parameters were similar to Initial Simulation section.

Fastener was modelled along with a washer to represent HI-LOK Universal rivet of shank diameter of 0.15” (4 mm).

Universal head of rivets were modelled as a cylindrical headed fastener. A radial clearance of 0.004” (0.1mm) was

included, to account for maximum allowable clearance in aircraft industry. In Figure 3, constraints were applied at

fixed X end and movable X end depending on the load case see Table 4.

11. Meshing and Material Properties:

Ply orientation of laminates were of [00/90

0/0

0/90

0]s. At and around the joint region and impact zone, fine mesh

was adopted. The materials of laminates, fastener, and washer were CFRP, titanium, typical steel. Properties of these

materials were extracted from Ref 4, and Ref 12.

12. Failure criteria:

Once again Tsai-Wu failure criterion was used in the analysis. However there was no strength reduction factor

considered.

13. Representation of surfaces interaction using contact card:

A typical contact card was used to represent interactions between all the contact surfaces like rivets to washer,

washer to laminates, between laminates and rivets to laminates.

14. Load Cases (LC):

Due to high computational time in handling unstable elements during impact and also huge time in solving solid

elements, only two load cases were considered, see Table 4.

Table 4 Load cases of mechanically fastened composite joint with pre-strain

Load

Cases

Laminate

type

Loads Boundary conditions Remarks

Impact energy,

lb-in

X pre-

strain,

Psi

Fixed X end Movable X

end

LC13 CFRP

16.43 0 123456 123456 See Figure 3 for

representation of boundary

conditions LC14 16.43 600 123456 23456

Only uniaxial X pre-strain was considered and applied via movable X end and impact energy was through the

impactor, see Figure 3.

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Figure 3 Mechanically fastened composite joint model with pre-strain

Note: “ represents inch

V. Result and Discussion

D. Adhesively bonded composite joints with pre-strain:

15. Force-time histories:

Force-time histories obtained in this analysis for the various load cases are shown in Figure 4. The peak force

highlighted in the figure is smoothed values (maximum value of the trendline of the curves). Among all the impact

cases, the peak force generally behaves as: Fbiaxial tensile>Fzero strain>Fbiaxial compression. However there was only a very

trivial difference between zero strain and pretension cases.

Figure 4 Peak force of adhesively bonded composite joints with pre-strain

Note: Poly(LC-) is the polynomial trendline to the LC-

Washer, Ø0.31” x 0.04”

7.36” 1”

Impactor diameter 1”

SPC’s: 12

Laminates

Thickness 0.083”

Fixed X end Movable X end

0.63” 2.58”

00 plies (red color)

900 plies (green color)

Rivet

Head: Ø0.27” x0.06”

Shank: Ø0.15” Radial clearance of 0.004” (black thick line)

1.57”

Section AA

A A

Peak force of CFRP

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0.0164 0.0169 0.0174 0.0179 0.0184

Time (s)

Pe

ak

fo

rce

(lb

s)

LC7

LC8

LC9

LC10

LC11

LC12

Poly. (LC7)

Poly. (LC8)

Poly. (LC9)

Poly. (LC10)

Poly. (LC11)

Poly. (LC10)

Peak force of GFRP

0

500

1000

1500

2000

2500

3000

0.0188 0.0193 0.0198 0.0203 0.0208 0.0213 0.0218 0.0223 0.0228

Time (sec)

Pea

k f

orc

e (l

bs)

LC1

LC2

LC3

LC4

LC5

LC6

Poly. (LC1)

Poly. (LC2)

Poly. (LC3)

Poly. (LC4)

Poly. (LC5)

Poly. (LC6)

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According to previous studies3,

15, and 17, the peak force is proportional to the flexural stiffness of the composite

laminate. The pretension model was subjected to in-plane tension that can reduce the flexure deflection, i.e.

pretension model has higher flexure stiffness. On contrary, the precompression model has the lowest flexure

stiffness. Hence, the peak force of the precompression model was lower than those for other load cases.

In Figure 4, a high drop in the curves immediately after the peak force is evident. This indicates a considerable

deflection in the laminates; i.e. reduction of normal resistive force from the laminate and thereby large absorption of

impact energy. As expected, CFRP models (LC7 to LC12) posed more resistant against the impact energy, hence

inducing larger normal forces.

16. Damage area:

Most of the damage sourced at the impact zone and around the boundary constraints. The damage then very

quickly travelled in all directions. As expected, matrix damage -most critical in 900 plies, was the first failure mode

to form. However, fibre damage patterns among all the load cases were similar. Fibre damage in tension for LC10 to

LC12 is shown in Figure 5. As can be seen, relatively high fibre damage is sustained. This is caused by large

bending of the joints.

Figure 5 LC10 to LC12: fibre damage (tensile)

Note: the above model is rotated 600 about X axis and impactor is not shown for better view

Maximum fibre damage occurred at the top most ply (00 ply), damage areas were 0.0473in

2, 0.066in

2 and

0.0578in2 for load cases LC10, LC11 and LC12, respectively, see Figure 5. From this, it is clear that tensile stress

LC10 LC11 LC12

0.11”

0.43”

0.11”

0.6”

0.17”

0.34”

Damage area at 1st ply

1st ply= 0

0

2nd

ply= 900

3rd

ply= 00

4th

ply= 900

5th

ply= 900

6th

ply= 00

7th

ply= 900

8th

ply= 00

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dominated the damage area. According to Chiu (1996), sequence of damage area can be stated as: Abiaxial tensile>Azero

strain>Abiaxial compression. However in the present study, damage area of the zero strain model was the lowest. The

rationale for more damaged area in pre-compression case than the zero strain case can be stated as follows:

Immediately after being subjected to impact energy, the pre-compression joint was damaged and bent with a large

deflection. Since the compressive stress was not yet released, the specimen remained under postbuckling. Therefore,

the initial damage in the pre-compression model continued to enlarge due to the postbuckling-induced-delamination

and subsequent delamination buckling, resulting in fibre failure.

17. Absorbed energy:

Energy absorbed by all of the models was calculated from the initial kinetic energy minus the rebound kinetic

energy of the impactor. The results are shown in Table 5.

Table 5 Absorbed energy of adhesively bonded composite joints with pre-strain

Load cases LC1 LC2 LC3 LC4 LC5 LC6 LC7 LC8 LC9 LC10 LC11 LC12

Absorbed

energy, lb-in 88.0 87.8 88.3 220.1 219.4 220.5 85.2 85.0 86.8 217.5 217.0 219.4

Absorbed impact energy was varied by less than 4% among all the cases. Variation of the absorbed energy in

zero strain and pretension cases was less than pre-compression cases. This could be the result of the secondary

deflection and postbuckling of the pre-compression models (explained in the next section), making the pre-

compression laminates respond in a significantly different manner. Once again CFRP models were more resilient as

expected, while CFRP proved to be stiffer than GFRP.

E. Mechanically fastened composite joint with pre-strain:

Simulation analyses were conducted to capture all the fastener movements and subsequent progressive damage.

Due to the joint clearance, zero pre-strained model deflected more than the pre-strained model.

Figure 6 and 7 illustrate stress distribution and progressive damage in and around the zero strained and uniaxial

pre-strained mechanical fastened composite joints, respectively. In the impact scenario, the joint resulted in bending

of laminates and fasteners, longitudinal penetration of fastener head, fastener rotation and bearing damage on the

laminates.

As expected, the top laminate experienced more local bending stress. The clearance between the hole and the

fastener provided a space for the fastener to kink clearly, resulting in more concentrated stress within the vicinity of

the hole. The local stress concentration subjected the adjacent plies to induced stress and damage.

Figure 6 Progressive damage and stress distribution in a zero strained mechanically fastened composite joint

(A, B and C are impact stages, starting from immediately before to after impact).

Top laminate Bottom laminate

Global stress distribution Local stress distribution with and without fastener

Section line at the fastener

A

B

C

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Rivet rotation was another important failure observed that occurred due to the unsymmetrical load feature of the

single-lap joint. The rotated rivet, applied a localised compressive force on the laminate, which together with the

tensile force from impact lead to a considerable damage in the contact area of the laminate with fastener (Figure 7).

These failures were more evident in the cases of pre-strained specimens. In Figure 7, a progressive damage

involving a gradual increase of contact area, fastener rotation, local bending and eventually high local stresses

around the fastener can be observed

Figure 7 Progressive damage and stress distribution in a pre-strained mechanically fastened composite joint

(A, B, C and D are impact stages, starting from immediately before to after impact).

Local stress distribution with and without fastener

Fastener rotation

High stresses

Increased contact area

Section line

A B

C D

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VI. Conclusion

Finite element models of adhesively bonded joints and mechanically fastened joints of an aircraft structure were

developed to accurately simulate the nonlinear behaviour of impact loading on pre-strained joints. A good

agreement was achieved for initial simulations of impact onto specimens with no pre-strain. An extension of the

dynamic simulation developed was then applied to zero strain, biaxial compression and biaxial tension pre-strained

joints. It was found that pre-loading of the composite joints subject to impact events generally resulted in reduced

damage tolerance. Exceptions were a number of cases under pre-compression.

The modelling technique developed offers a potential for more accurate failure prediction in dynamic loading

conditions. Constructing detailed composite joint models can be extremely time consuming. However, the prospects

of considerably reducing experimental trials, while developing technical design expertise in controlled failure

sequencing of aerospace structural components, cannot be disregarded.

Acknowledgments

The authors would like to thank Dr. Bayandor’s Dynamic Damage Modelling research team for their invaluable

suggestions and constructive criticism. In particular, the authors wish to greatly acknowledge Mr. Minki Kim for

providing modelling insights and assistance throughout this study.

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