1

Multi-scale analysis for structural design on engine exhausted heat recovery system using

thermoelectric element

Kazunari KAWAHARA1, Satoshi ISHIKAWA1, Katsuya MINAMI2

[1]IDAJ Co., Ltd. and [2] Honda R&D Co., Ltd.

Abstract: In order to apply thermoelectric generator (TEG) into engine exhausted heat recovery

system, the thermoelectric module needs to be compact balancing between structural durability

and thermal transfer characteristics. However, the manufacturing process of the thermoelectric

module, which can be classified into two categories, is highly complicated. The first process is to

bond the Cu electrodes onto the top and bottom surfaces of thermoelectric element, while certain

residual stress and deformation are observed in itself. The second process is the module

manufacturing which assembles large numbers of the bonded single elements with residual stress

on the exhausted plate. Regarding the structural design, the arrangement and shape of the

elements is very important to secure the strength and thermal efficiency, also to prevent damage

and crack on the system. In this paper, we explored the multi-scale analysis for the whole

manufacturing process of thermoelectric module by using Abaqus/Standard. The first process was

analyzed on micro scale with fine mesh for acquiring precise results, subsequently the results were

mapped onto the second process as macro scale analysis by an automatic mapping tool which we

developed in this study. These analyses of processes could help us to minimize the residual stress

and the design of the bonding arrangement. Furthermore the deformation and stress state under

actual operation of the system were analyzed, and those results showed the enhanced efficiency of

the electrical generation. Our proposed method contributed to new structural design concept to

resolve the above mentioned issues.

Keywords: Thermoelectric Generator, Multi-scale Analysis, Stress Mapping, Residual Stress.

1. Introduction

An efficiency improvement for automobile fuel consumption and an energy regeneration

technology are strongly demanded in the recent market. With thermal efficiency improvement and

a friction loss reduction technology, a thermal management technology attracts attention for the

energy regeneration. The exhaust loss reaches approximately 40% of fuel energy, and effective

utilization of this energy is expected. Exhaust heat recirculation systems, which warm up the

engine coolant using the exhaust heat, have been already released on market to enhance real-world

fuel economy and cabin heater performance in winter season. However the energy regeneration

technology from engine exhaust heat to electric energy does not lead to mass-production for a

passenger car at a point of view of system size and the cost effectiveness “(Minami, 2017).”

2

Moreover the manufacturing process of the thermoelectric module which can be classified into

two categories is highly complicated. The first process is to bond the Cu electrodes onto the top

and bottom surfaces of thermoelectric element, while certain residual stress and deformation are

observed in itself. The second process is the module manufacturing which assembles large

numbers of the bonded single elements with residual stress on the exhausted plate.

Among these environments, a new structural concept of thermoelectric generator that can recycle

the engine exhaust heat was proposed from Honda, and this concept was verified and specified

into the design through the finite element analysis using Abaqus/Standard. The analysis procedure

consists of two steps in accordance with the real manufacturing process. The first process was

analyzed on micro scale with fine mesh for acquiring precise results; subsequently, the results

were mapped onto the second process as macro scale analysis by an automatic mapping tool

developed in this study. In addition to these, the deformation and stress state under actual

operation of the system were analyzed, and those results showed the enhanced efficiency of the

electrical generation. From the standpoint of numerical analysis, in case of usage of same fine

mesh as first process, the analysis model of manufacturing process and actual operation required

considerable calculation time and memory. For this reason, we developed the mapping tool to

transfer the residual stress and plastic strain from micro scale model to macro scale model.

Our proposed method contributes to new structural design concept to highly balance between

thermal efficiency and structural strength.

2. Analysis Methodology

As stated before, the manufacturing process has two steps, one is bonding process of

thermoelectric element, and the other is fabricating of the thermoelectric module with a large

number of the bonded thermoelectric elements on plates. In case of fine meshing for the second

process, the analysis model would require a large scale number of degree of freedom with

considerable CPU time and memory. Therefore the analysis methodology consisted of micro scale

and macro scale. In section 2.1, we describe the micro scale analysis which was bonding process

of thermoelectric element with electrode. In section 2.2, the manufacturing process of the

thermoelectric module with over 50 thermoelectric elements is figured using macro scale analysis.

Moreover, the actual operation analysis is explained in section 2.3.

2.1 Micro scale analysis for single thermoelectric element

2.1.1 Manufacturing process

At first, the process of bonding the Cu electrode with the ceramic had to be analyzed. Figure 1

shows the schematic depiction of the thermoelectric element consisting of Cu electrodes, metal

deposition layers and a ceramic. The ceramic, two Cu electrodes and two metal deposition layers

are depicted by red, yellow and orange squares respectively. This unit was formed with the

bonding jig under the thermal and mechanical loading process as shown in Figure 2. The metal

deposition layers were very thin as compared with Cu electrodes, and the material behavior of

these layers was complicated. Hence, the bonding process of these layers was treated with the

capability of contact condition. The detail processes are described below with Figure 2 and 3.

3

(a) The element which was put between two bonding jig was heated from the room

temperature (300 [K]) to 823 [K]. The deposition layers were modeled as normal contact

condition as same as between the Cu electrode and the bonding jig.

(b) The mechanical loading was applied on the upper bonding jig as pressure load

117.6[MPa] as shown in blue line in Figure 2 under keeping the temperature condition

823[K].

(c) To treat the bonding process, the contact condition on the deposition layers was changed

to the rigid tie condition under keeping the temperature and pressure load.

(d) The pressure was unloaded under high temperature, and the contact condition on the jig

was released.

(e) Finally the element was cooled from 823[K] to the room temperature.

CeramicDeposition

layer

Bonding Jig

Bonding Jig

Cu Electrode

Cu Electrode

(a)

(b)

(c)

(e)

(d)

823 [K]

RT

Pressure

117.6 [MPa]

Figure 1. Schematic of Figure 2. Process time table. thermoelectric element.

(a) Heating

RT –> 823 [K]

(b) Loading

823 [K]

117.6 [MPa]

(c) Bondig

823 [K]

117.6 [MPa]

(d) Unloading

823 [K]

0 [MPa]

(e) Cooling

823[K] –> RT

Contact Contact ContactRigid

TieRigid

Tie

Rigid

Tie

Figure 3. Bonding processes.

2.1.2 Material

The ceramic was treated as an elastic material that had temperature dependency, and the material

of Cu electrode also had the temperature dependency of elastic modulus. Table 1 shows the

Young’s modulus and Poisson’s ratio only in the room temperature. The Cu electrode was dealt

with a plastic material as shown in Figure 4. Regarding the following macro analysis of heat

transfer, the material data of heat conductivity and specific heat had temperature dependency too.

4

Table 1. Elastic modulus in room temperature.

Material Young’s modulus [MPa] Poisson’s ratio

Ceramic 175200 0.28 Cu electrode 96320 0.343

Figure 4. Stress-strain relation with temperature dependency.

2.1.3 Analysis model

The micro scale model was made with quarter model as shown in Figure 5. The red part was the

ceramic, the orange parts were the Cu electrodes, and the blue and gray parts indicated the

bonding jigs as rigid parts. The finite element model was constructed out of 16020 C3D8R

elements and 18943 nodes based on the proper symmetry boundary conditions. The thermal loads

were applied as Figure 2, and the pressure load was applied on the upper rigid gray part. Not to

mention, four contact conditions were applied between the ceramic and the electrodes and the

electrodes and the bonding jigs.

Figure 5. Fine mesh for micro scale analysis.

0 0.05 0.1 0.15 0.2 0.25

Tru

e S

tres

s

Plastic Strain [-]

300[K]

373[K]

573[K]

773[K]

973[K]

5

2.2 Macro scale analysis for modules manufacturing

2.2.1 Mapping system

To clarify the mapping system, a quarter model of the thermoelectric module is depicted in Figure

6 at the beginning of this section. Figure 6 (a) shows the quarter analysis model, and Figure 6 (b)

is a section picture that shows the fin shape clearly. Figure 6 (c) shows the arrangement of 54

thermoelectric elements in this model, and an enlarged drawing of element is shown in Figure 6

(d). The difference of the mesh size between Figure 5 and Figure 6 (d) is remarkable. If the fine

mesh was applied on each thermoelectric element, this module analysis would have a large

number of degrees of freedom. Therefore, the results of residual stress and plastic strain which

analyzed in section 2.1 were mapped onto each elements of macro scale model by our developed

tool. Figure 7 shows the system flow of mapping tool. The Excel sheet included the information of

arrangement of the thermoelectric element, such as the number of X, Y row and pitch, the set

name of elements and the center coordinate of tip, etc. Our tool referred to the results of the micro

analysis and the base exhaust plate input file, after it generated automatically the Abaqus

command ‘*INITIAL CONDITIONS’ as shown in Figure 8.

Figure 6. Exhaust plate model for macro scale analysis.

(a) Quarter model (b) Cross-sectional view

(c) Arrangement of

thermoelectric element (d) Enlarged drawing

Exhaust gas zone

Cooling fin zone

6

Example of Arrangement

Excel sheet of Arrangement data

Single element

Abaqus odb file

Extract & mapping

Program

Abaqus inp file

including *INITIAL

CONDITIONS

Data of

Arrangement of

elements

Exhaust plate

input file

　

Figure 7. System flow of mapping.

Figure 8. Example of INITIAL CONDITIONS in input file.

2.2.2 Manufacturing process

In this study, we examined two analysis types following the real manufacturing process. One is a

diffusion bonding which is a solid state welding technique capable of joining between similar or

different metals, and the other is a brazing bonding which is a metal-joining process in which two

or more metal items are joined together by melting. At first, the diffusion bonding is explained in

the next section.

** SET PART : PLATE_COPPER_HI-1 **

*INITIAL CONDITIONS, TYPE=STRESS

264595, 42.706, 3.111, -24.081, 11.296, 13.014, -7.271

264596, 47.739, -3.510, -6.896, 16.605, 6.769, -7.619

264597, 135.077, 2.515, -6.271, 0.781, 6.836, -1.316

264598, 135.236, -1.817, -2.519, 2.712, 3.630, -4.176

*INITIAL CONDITIONS, TYPE=PLASTIC STRAIN

264595, 3.303E-05,-1.213E-05,-2.090E-05, 6.693E-06, 1.002E-05,-4.052E-06

264596, 7.953E-05,-1.124E-04, 3.289E-05, 3.229E-05, 4.096E-06, 8.570E-06

264597, 2.732E-03,-1.231E-03,-1.501E-03, 3.860E-05, 3.409E-04,-7.628E-05

264598, 2.702E-03,-1.480E-03,-1.223E-03, 1.605E-04, 1.768E-04,-2.008E-04

7

2.2.2.1 Diffusion bonding

Figure 9 shows the schematic depiction of one part of the module. The residual stress and plastic

strain of Cu electrode and ceramic were mapped from the micro analysis. Two deposition layers in

this process are depicted by yellow squares. The bonding process of these layers was treated with

the capability of contact condition as same as the micro scale analysis. The module was formed

with the bonding jig under thermal and mechanical loading process as shown in Figure 10. The

detail processes are described below.

(a) The temperature of thermostatic chamber rose from the room temperature to 823 [K].

The deposition layers were modeled as normal contact condition as same as between the

Copper 1 and the bonding jig.

(b) The mechanical loading was applied on the upper bonding jig as pressure load

117.6[MPa] under keeping the temperature condition 823[K].

(c) To treat the bonding process, the contact condition on the deposition layers was changed

to the rigid tie condition under keeping the temperature and pressure condition.

(d) The pressure was unloaded under high temperature, and the contact condition on the jig

was released.

(e) Finally the temperature of thermostatic chamber was cooled from 823[K] to the room

temperature as an exponential function.

Bonding Jig

CeramicDeposition

layer

Copper 2

Copper 3

Alumina

Fin case

Copper 1Contact area

300

450

600

750

900

0 2000 4000 6000

Tem

per

atu

re [

K]

Process Time [s]

Pressure 117.6 [MPa]

(a)

(b)

(c)

(d)(e)

Figure 9. Schematic of Figure 10. Process time table thermoelectric element. of diffusion bonding.

8

2.2.2.2 Brazing bonding

The process of brazing bonding is as almost same as the diffusion bonding, but the pressure is

much smaller than the diffusion bonding. The detail processes are described below with Figure 11.

(a) The mechanical loading was applied on the upper bonding jig as pressure load

0.98[MPa] under the room temperature. The deposition layers were modeled as normal

contact condition as same as between the Copper 1 and the bonding jig.

(b) The temperature of thermostatic chamber rose from the room temperature to 1063[K]

which was higher temperature than the diffusion process.

(c) To treat the bonding process, the contact condition on the deposition layers was changed

to the rigid tie condition under keeping the temperature and pressure load.

(d) The temperature of thermostatic chamber was cooled from 1063[K] to the room

temperature non-linearly.

(e) Finally the pressure was unloaded under the room temperature, and the contact condition

on the jig was released.

300

600

900

1200

0 3000 6000 9000

Tem

per

atu

re [

K]

Process Time [s]

(a)(e)Pressure 0.98 [MPa]

(b)

(c)

(d)

Figure 11. Process time table of brazing bonding.

2.3 Analysis model for actual operation

2.3.1 Analysis model

The structural analysis assembly was modeled in quarter model of the thermoelectric generator as

shown in Figure 12. The finite element model was constructed out of 595006 C3D8R elements

and 837475 nodes based on the proper symmetry boundary conditions. Naturally, the residual

stress and plastic strain were mapped from the macro analysis of the manufacturing process on

each thermoelectric element for example Figure 12 (d).

9

Figure 12. Quarter model of Thermoelectric generator.

2.3.2 Loading and thermal conditions

The key points of strength analysis in actual operation were the initial stress, the temperature

condition and the operation pressure in the cooling and the exhaust gas zone. Therefore, the steady

state analysis of the temperature was carried out first, and the elastic-plastic thermal analysis

including initial stress was executed successively. The blue arrow pressure shown in Figure 13

was applied on the outer case structure, the green arrows were the pressure on the cooling plate,

and also the pink arrows indicated the internal pressure as the air pressure. As for those pressure

levels, an actual work condition was assumed. Moreover, two boundary conditions of exhaust gas

pressure, 1atm and 4atm, were investigated.

Exhaust gas zone

Cooling zone

Figure 13. Quarter model of Thermoelectric generator.

(a) Quarter model

(d) Initial stress on thermoelectric element

(b) Cooling fin

(c) Exhaust gas zone

10

3. Results

3.1 Micro scale analysis results of single thermoelectric element

Figure 14 shows the transition results of each process. The absolute principal stress contour plots

are shown in the second line, the red and blue shows the tension and the compressive stress

respectively. The plastic strain plots of Cu electrode are shown in the third line, the red indicates

the high plastic strain, and the blue is zero. Alphabetical order in the first line refers to Figure 2.

In the heating process (a), there were no stresses both the electrode and ceramic, because the

single thermoelectric element was in the free expansion condition. At the end of the loading (b),

both the electrode and ceramic were subjected to the compressive stress, and the edge on the

electrode suffered plastic strain. The connecting faces between the electrode and ceramic were

bonded by applying the rigid tie condition after the loading, for this reason the tension stress

occurred around the edge of the ceramic after the unloading process (d). Furthermore in the

naturally cooling process (e), the high tension stress and plastic strain existed around the edge

because of the thermal expansion difference between the electrode and the ceramic.

(a) Heating (b) Loading (d) Unloading (e) Cooling

Pri

ncip

al S

tress (

Ab

s)

Pla

sti

c s

train

Figure 14. Results of single element bonding analysis.

3.2 Mapping results from Micro to Macro model

For the sake of the accurate analysis of module manufacturing, the residual stress and plastic strain

in the micro analysis needed to be mapped onto the macro analysis correctly. Figure 15 shows the

stress mapping results. Figure 16 shows the path plots along the red arrow in Figure 15, and Figure

16 (a) is the principal stress on the ceramic, also 16 (b) shows the principal stress on the electrode,

while 16 (c) is the plastic strain on the electrode. The mapping was executed correctly, however

11

the slight difference was observed at the end of ceramic as shown in Figure 16 (a). This difference

was caused from the averaging of mesh sizes. Therefore, the fine mesh at the end of the element

was taken in order to reduce the error.

Results of

micro analysis

Initial conditions for macro analysis

Mapping

Figure 15. Result of mapping from micro element to macro module.

Figure 16. Path plots of Micro and Macro analysis.

3.3 Macro scale analysis results of module manufacturing

3.3.1 Results of the diffusion bonding

Figure 17 shows the transition results of the absolute principal stress in each process, and the red

and blue shows the tension and the compressive stress respectively. The stress of the ceramic was

higher than it of the electrode during the processes due to the high elastic module of the ceramic.

Figure 18 shows the transition of the plastic strain, and the red shows the high plastic strain and

the blue indicates the zero.

The stress distribution of the element inherited from the initial stress of micro analysis after the

heating process (a) because of the free expansion condition. At the end of the loading (b), the

compressive stress occurred at the edge of the ceramic, and the edge on the electrode suffered

plastic strain. The connecting faces between the electrode and ceramic were bonded after the

loading. As a consequence, the stress distribution after the unloading process (d) was as same level

as the heating process, on the other hand the plastic strain became larger by the effect of bonding.

Finally the end of the cooling process (e), the large tension stress occurred in the ceramic and

0 0.5 1

Prin

cip

al st

ress

Results of Micro analysis

Initial stress for Macro

analysis

0

0 0.5 1

Pri

nci

pa

l st

ress

Results of Micro analysis

Initial stress for Macro

analysis

0 0.5 1

Pla

stic

str

ain

Results of Micro analysis

Initial stress for Macro

analysis

(a) stress on ceramic (b) stress on Cu electrode (c) plastic strain on Cu electrode

0

12

electrode, besides the electrode had the largest plastic strain because of the thermal expansion

difference between the electrode and the ceramic. In addition, in each arranged thermoelectric

elements, the highest stress occurred on a thermoelectric element in the outside which was marked

by a red circle in the second line fourth row in Figure 17.

(a) Heating (b) Loading (d) Unloading (e) Cooling

Figure 17. Principal stress of diffusion bonding of module.

(a) Heating (b) Loading (d) Unloading (e) Cooling

Figure 18. Plastic strain of diffusion bonding of module.

3.3.2 Results of the brazing bonding

Figure 19 shows the transition results of the absolute principal stress in each process, and Figure

20 shows the transition of the plastic strain.

The value of the pressure load of the brazing bonding was much smaller than the diffusion

bonding, thus the stress distribution of the element corresponded with the initial stress of micro

analysis after the loading process (a). The stress lowered during the heating (b) on account of the

temperature dependency of the elasticity. The connecting faces between the electrode and ceramic

were bonded after the heating, and the thermoelectric element had an effect of the difference of

thermal expansion. In this reason, the level of stress became larger after the cooling (d), and the

plastic strain also became larger especially at the bonding face to the cooling plate. The stress and

strain after the unloading process were as same as the cooling process because the value of the

13

pressure was small. Finally the highest stress was found on an element in a red circle in the second

line fourth row in Figure 19.

(a) Loading (b) Heating (d) Cooling (e) Unloading

Figure 19. Principal stress of brazing bonding of module.

(a) Loading (b) Heating (d) Cooling (e) Unloading

Figure 20. Plastic strain of brazing bonding of module.

3.4 Results of actual operation

Figure 21 shows the temperature of steady state and the absolute principal stress of the quarter

analysis model in the actual driving.

Figure 22 illustrates the principal stress of the representative thermoelectric element in each

analysis cases, and the contour range was the same in all figures. The position of the maximum

stress in the brazing bonding was the same as the diffusion bonding as shown in Figure 22 (a) and

(b) in the third line. But the stress level of the diffusion was much larger than the brazing, even in

the large exhaust gas pressure condition in Figure 22 (c) and (d).

Figure 23 illustrates the absolute principal stress path plot along the blue and black arrows in (a).

Figure 23 (b) is the path plot at the edge of the cooling side depicted in blue lines (a), while Figure

23 (c) is the path plot at the exhaust gas side depicted in black lines (a). The red line of the path

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plots is the result of the diffusion bonding, and the other green line is the brazing bonding.

Obviously the stress of the diffusion was much larger than the brazing at the cooling side as shown

in Figure 23 (b), on the contrary the stress difference was not found at the exhaust gas side as

Figure 23 (c).

Figure 21. Results of Thermoelectric generator.

(a) Diffusion 1atm (b) Brazing 1atm (c) Diffusion 4atm (d) Brazing 4atm

Figure 22. Principal stress of representative thermoelectric element on module.

(a) Plot position (b) Stress on the cooling side (c) Stress on the exhaust gas side

Figure 23. Path plots of the principal stress along the electrode.

(a) Temperature (b) Absolute Principal stress

Diffusion

Brazing

Diffusion

Brazing

0

15

4. Discussion and Conclusion

The focus of this study was to simulate new structural design of the thermoelectric generator from

manufacturing process to actual system operation, and to optimize the manufacturing condition

and design specification. FEM analysis such as Abaqus/Standard was powerful tool for the design

validation. However if we constructed the precise FEM model on each thermoelectric elements,

the analysis would require a large quantity of computer resource. Therefore, to accomplish our

objective, we developed the multi-scale analysis system with the mapping tool from micro model

to macro model. We analyzed the micro process which was the bonding process of single

thermoelectric element, and investigated the difference between the diffusion bonding and the

brazing bonding during the manufacturing process by the macro scale analysis, furthermore the

actual operation was analyzed with each bonding process. Our study provided the following

important findings.

The micro analysis for the single thermoelectric element could make the stress transition

clear in the bonding processes as shown in Figure 14.

Figure 16 showed that the residual stress and plastic strain from micro to macro were

transferred precisely by using ‘*INITIAL CONDITIONS’. Moreover our tool enabled the

variable arrangement design of the thermoelectric elements on the exhaust plate.

The difference between the diffusion bonding and the brazing bonding was clarified by

the macro analysis as shown in the third line fourth row in Figure 17 and 19. The tension

stress was found both the electrode and the ceramic in the diffusion bonding; on the

contrary, the tension stress on the electrode was small in the brazing bonding.

The most important finding was to reveal the large difference of the stress along the

electrode on the cooling side in the actual operation as shown in Figure 23 (b). This result

elucidated the advantage of the brazing bonding.

In conclusion, we developed the multi-scale analysis system on Abaqus/Standard and analyzed the

manufacturing process and the actual system operation. This analysis system could help us to

optimize the design of the thermoelectric generator with balancing system durability and thermal

efficiency.

5. References

1. Minami, K., Matsumoto, M., and Mori, M., “Structural Design Approach on Engine

Exhausted Heat Recovery System using Thermoelectric Element”, Journal of Society of

Automotive Engineers of Japan, Vol. 71, No. 10, 2017.

2. Abaqus Users Manual, Version 6.12-1, Dassault Systèmes Simulia Corp., Providence, RI.