Evaluation of Finite Element Modelling Techniques of Printed Circuit Boards under Dynamic and Static Loading and Validation with Experimental Data

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2021 IEEE 27th International Symposium for Design and Technology in Electronic Packaging (SIITME)
27-30 Oct 2021, Timișoara, Romania
Evaluation of Finite Element Modelling Techniques
of Printed Circuit Boards under Dynamic and Static
Loading and Validation with Experimental Data
Iulia – Eliza Ținca
Dept. of Mechatronics, University
Politehnica Timișoara
ADAS, Continental Automotive
Timișoara, Romania
eliza.tinca@student.upt.ro
Ciprian Bleoju
Dept. of Mechanics and Strength of
Materials, Politehnica University
QL, Continental Automotive
Timișoara, Romania
ciprian.bleoju@student.upt.ro
Iulian – Ionuț Ailinei
Dept. of Mechanics and Strength of
Materials, University Politehnica
Timișoara
QL, Continental Automotive
Timișoara, Romania:
iulian.ailinei@student.upt.ro
Arjana Davidescu
Dept. of Mechatronics, University
Politehnica Timișoara , Romania
arjana.davidescu@upt.ro
Andrei-Marius Silaghi
Dept. of Measurements and Optical
Electronics, University Politehnica
Timișoara
QL, Continental Automotive
Timișoara, Romania:
andrei.silaghi@upt.ro
Liviu Marșavina
Dept. of Mechanics and Strength of
Materials, Politehnica University
Timișoara, Romania
liviu.marsavina@upt.ro
Abstract—When modeling the Printed Circuit Boards (PCBs)
for structural analysis, we usually trade complexity for inaccuracy
due to the PCB composite nature and data unavailability. This
paper presents an extensive survey of innovative Finite Element
(FE) techniques for numerical modeling of the PCBs in static and
dynamic conditions. We aim for an optimal FE modeling
approach that captures the global effects and correct stiffness
behavior. We use ANSYSTM Workbench, ANSYSTM Material
Designer, and ANSYSTM Sherlock and analyze the FE model with
OptiSLangTM. In addition, we model a PCB assembly as well.
Keywords—FEA, PCB, Physical Validation, Virtual Prototype
I. INTRODUCTION
Industry and literature best practices often consider the
assumption that isotropic homogenous material properties are
enough for PCB FE modeling [1] [2] [3]. However, this
approach no longer complies with accuracy requirements in
day-to-day practice. Furthermore, the development of new
computer-aided engineering (CAE) tools [4] opens new
possibilities to capture the heterogeneous orthotropic behavior
of the PCB [5]. Within this paper, we discuss in detail these
commercially proposed workflows. Our objective is to
determine an optimal material approach and finite element
model for PCBs under static and dynamic loading, capturing
global effects and correct stiffness behavior. First, to
determine the physical response of the PCB stiffness, we
conducted one dynamic and one static experiment for both
bare boards and assembled PCBs (PCBA). Secondly, we
simulated the experiments through FE Analysis (FEA) using
different modeling techniques. Lastly, we run sensitivity
analyses on both dynamic and static setups to study the effect
of PCB orthotropy and FE model robustness.
II. EXPERIMENTAL SETUP
We conduct the experiments on an eight conductor layer,
172x133x1.6mm PCB, weighing 103.2g. The population
amounts to 1422 parts, and the PCBA weighs 160.5g.
In the dynamic experiment, an electrodynamic shaker
generates the forced harmonic motion to excite the test
specimens. Piezo-electric accelerometers measure the
acceleration response during the test. The vibration profile is
a broadband sine sweep, ranging from 10[Hz] to 1000[Hz],
with a constant acceleration of 1G, having a logarithmic
sweep rate of 0.5 octaves/minute over the entire spectrum. Fig.
1 shows the complete vibration test setup, where the specimen
under test, PCB (1), is clamped by the fixture (2). The drive
acceleration sensor (3) controls the shaker's moving element,
and (4) are the sensors that measure the acceleration response
in the center of the PCB (4a) and on edge (4b).
In the static 3-point bending test, the PCB in Fig. 2 (1)
stands on two supporting edges of the testing jig (2) and (3),
and a longitudinal element (4) applies a rate-controlled
displacement of 2 mm/min conducted according to [6], [7].
The tensile test machine records the force-displacement
response of the tested sample.
Fig. 1. The sine sweep vibration test setup
Fig. 2. The 3-points bending test setup

2021 IEEE 27th International Symposium for Design and Technology in Electronic Packaging (SIITME)
27-30 Oct 2021, Timișoara, Romania
III. FINITE ELEMENT ANALYSIS
A. CAE Tools
The FEAs use the ANSYSTM Mechanical solver through
Workbench and Sherlock interfaces. Sherlock is an automated
design analysis tool, which integrates various analytical and
FEA procedures. Sherlock creates the PCB materials,
geometry, and mesh, based on Electronic Computer-Aided
Design (ECAD) input files and Bill of Materials (BOM). The
semi-analytically generated lumped material properties
depend on the percentage of metal, resin and laminate
materials found in each layer [8]. In our work, we also use the
Material Designer tool for numerical material
homogenization. The application determines the material
properties of a unit cell by performing three tensile and shear
tests by applying a macroscopic strain and assembles the
stiffness matrix using the reaction forces [9].
B. PCB Modeling Techniques for Bare Board
The modeling techniques discussed here consider the
different materials described in Table I. Material formulations
imply different approaches for the geometric construction of
the board, depending on the representation of the conductive
layers. Table II shows a summary of the reviewed techniques.
Approaches 1 and 2 define the range of the results, one being
the most flexible and two the most rigid idealization of the
PCB. Although approach 3 is inexpensive, Sherlock includes
a laminate library, making it affordable to select the specified
laminate material in approaches 4 – 7. A lumped approach
considers a homogenous section of the board. On the other
hand, a lumped layered approach considers a layered section
of the board consisting of homogenous dielectric and
conductor layers as in Fig. 3. In approaches 1 and 2, we
consider materials A and B to find an accurate but inexpensive
method. In approach 3, with Material Designer, we create a
homogenized lumped material – D, which we assign to a solid
homogenous board. In approaches 4 through 7, Sherlock
creates the PCB based on materials A and C. In approaches 6
and 7, material assignment depends on the discretization of the
board. Conclusively, in a mapped trace approach, depending
on element size, several materials are generated based on the
unique combinations of laminate and conductor materials
covered by the mesh element. Fig. 4 shows the top side of the
board for the 6th and seventh approaches.
C. FEA Considerations
1) Dynamic analysis. The PCB clamping on the shaker is
idealized through rectangular mount pads, with the bottom
nodes constrained in all directions. Virtual accelerometers
placed in the FEA model in similar locations to those used on
the PCB during physical tests measure the peak acceleration
as in Fig. 5, ACC_center and ACC_edge.
2) Static analysis. The test setup is simplified to two
supporting edges and a push element, as shown in Fig. 6. In
approaches 1, 2, and 3, we use the double symmetry planes, A
and B, in Fig. 6 for efficiency purposes. Mesh element
formulation is linear, SOLID185, four elements through-
thickness for homogenous sections. Finally, in approaches 4 –
7, the board model is imported from Sherlock without any
simplifications, as in Fig. 7.
D. Electronic Component Population Modeling
Using Sherlock, we add the population to the bare board.
Based on the commercial part number, Sherlock identifies the
parts in Sherlock Part Library and imports their properties.
Sherlock models the parts as monolithic blocks connected to
the PCB by computationally inexpensive constraint equations
(linear couplings). Finally, we solve the dynamic analysis in
Sherlock and the static analysis in Workbench.
Fig. 3. PCB section lumped (left) and lumped layered (right)
Fig. 4. Mapped (left) and mapped layered (right) top side of the PCB
Fig. 5. Dynamic analysis model
Fig. 6. Double-symmetry static analysis model in approaches 1, 2 and 3
Fig. 7. Complete static analysis model in approaches 4 - 7
ACC_edge
ACC_center

2021 IEEE 27th International Symposium for Design and Technology in Electronic Packaging (SIITME)
27-30 Oct 2021, Timișoara, Romania
TABLE I. MATERIAL PROPERTIES
Identifier
Material
Density
[kg/m3]
Elastic Modulus
[MPa]
Poisson’s Ratio
Description
A
Copper
8900
110000
0.34
General material
B
FR4
1840
Ex = 20400
Ey = 18400
Ez = 15000
νxy = 0.11
νyz = 0.09
νxz = 0.14
General material
C
Laminate
1900
Ex = Ey = 24804
Ez = 3450
νxy = νyz = νyz = 0.15
According to PCB specifications
D
Lumped – Ansys Material Designer
3348.8
Ex = 37194
Ey = 17307
Ez = 35710
νxy = 0.183
νyz = 0.068
νxz = 0.252
Based on A and B
E
Lumped – Sherlock Uniform
3348.8
Ex = Ey = 42895
Ez = 9920
νxy = νyz = νyz = 0.30
Based on A and C
TABLE II. SIMULATION APPROACHES
Approach
Description
Analysis
PCB
Traces
Material
Method
1
FR4
Static
Bare
Lumped
B
ANSYSTM
Workbench
2
FR4 and Copper
Static
Bare
Lumped Layered
A, B
3
FR4 and Copper
Static, Dynamic
Bare, Assembled
Lumped
D
ANSYSTM
Workbench / Material
Designer
4
Uniform
Static, Dynamic,
Sensitivity
Bare, Assembled
Lumped
E
ANSYSTM
Workbench /
Sherlock
5
Layered
Static, Dynamic
Bare, Assembled
Lumped Layered
16 orthotropic materials
derived from A and C
6
Uniform Elements
Static, Dynamic
Bare, Assembled
Mapped
170 isotropic materials
derived from A and C
7
Layered Elements
Static, Dynamic
Bare, Assembled
Mapped Layered
5 isotropic materials
derived from A and C
IV. SENSITIVITY ANALYSIS
We use the Metamodel of Optimal Prognosis (MOP)
method in OptiSLang. This method determines the essential
input variables contributing to the selected output through a
quality measure, the Coefficient of Prognosis (CoP).
Reference [10] describes the method in detail, noting "if the
sum of the single indices is significantly larger as the total CoP
value, such interaction terms have significant importance."
Prolonged exposure to time-varying loads is the second
cause of failure for EC [11]. The board-level strain generated
by vibration is proportional to the interconnect strain; hence,
it is part of the models used to predict the time-to-failure of
EC. Therefore, the accuracy of the life prediction models
depends on the accuracy of the FE model. To better
understand the effect of material modeling, we study the
influence of PCB stiffness over the 1st natural frequency.
Through the sensitivity analysis of the static FE model, we
want to guarantee that it gives the structure's response based
on the PCB's properties and that the noise from FE
idealizations is minimal. Therefore, the MOPs use the 4th
modeling approach and parameters in Table III.
TABLE III. THE METAMODEL OF OPTIMAL PROGNOSIS PARAMETERS
Analysis
Parameters
Response
Dynamic
3x Young's modulus (X, Y, Z)
3x Shear modulus (XY, YZ, XZ)
1st Natural
frequency
Static
3x Young's modulus (X, Y, Z)
3x Shear modulus (XY, YZ, XZ)
3x Poisson’s ratio (XY, YZ, XZ)
Force
reaction, Z
1x PCB Length, L
1x PCB Width, W
1x PCB Thickness, t
2x Coefficients of friction
4x Mesh settings
V. RESULTS AND DISCUSSION
A. Sensitivity Analysis
In-plane Young's and shear moduli contribute most to the
1st natural frequency. At the same time, the reaction force in
the static analysis comes from geometry parameters and X
Young's modulus, as in Fig. 8. The total CoP is close to 100%
in both cases, suggesting that the analysis included enough
design points. The geometry and boundary conditions drive
the structure's response, while the PCB in-plane anisotropy
has a lower influence. In the static analysis, FE model
parameters do not influence the response, suggesting a robust
FE model.
B. Static and Dynamic analysis
Table IV summarizes all results and the error to the
experimental values shown in Fig. 9 and Fig. 10.
The acceleration response of the PCB over the frequency
spectrum, measured on edge, correlates to the simulation
results within 10% for the bare board in all approaches. For
the PCBA, all approaches overestimate the first frequency.
However, edge acceleration correlates within 1%, and in the
center, the predicted acceleration is 10-15% lower due to
increased stiffness of the component in the vicinity.
The static response of the bare board is within ±20%.
Reduced integration elements lower the stiffness by 7%
resulting in better correlation, but they may be inconvenient to
use in ANSYSTM. For the PCBA, the homogenized
approaches 3 and 4 correlate as for the bare board. There is a
50% increase in stiffness for the layered sections compared to
the bare board. The strain varies 10% for a homogenized
section and up to 23% for a layered section for bare board and
PCBA.

2021 IEEE 27th International Symposium for Design and Technology in Electronic Packaging (SIITME)
27-30 Oct 2021, Timișoara, Romania
Fig. 8. CoPs for Dynamic (left) and Static (right) setups
Fig. 9. Experimental and numerical dynamic results
Fig. 10. Experimental and numerical static results
TABLE IV. NUMERICAL ANALYSIS RESULTS
Approach
PCB
1st NF
[Hz]
Error
[%]
RF
[N]
Error
[%]
Strain
[%]
1
B
n/a
n/a
45.40
-41
0.18
2
B
n/a
n/a
136.41
76
0.24
3
B
150.18
-2
83.17
7
0.18
4
B
155.19
1
98.08
27
0.18
5
B
169.26
10
77.09
0
0.12
6
B
154.24
1
61.49
-21
0.16
7
B
167.92
10
79.85
3
0.16
3
A
150
27
90.95
6
0.34
4
A
160.15
36
110.28
28
0.31
5
A
175
48
135.05
57
0.40
6
A
159.20
35
113.15
31
0.38
7
A
172.40
46
130.55
52
0.38
a. B – bare PCB,
b. A – assembled PCB
VI. CONCLUSIONS
A homogenized section provides a consistent response in
both static and dynamic setups than a layered section. A
uniform section in Sherlock – approach 4 is computationally
inexpensive, while Material Designer does not require
sophisticated inputs. With fine-tuning, perfect calibration for
bare board is achievable.
Population modeling and PCB strain validation remain
topics for further study. In addition, the mapped layers
approach remains of interest because of its capability to
represent the local response of the PCB in a thermo-
mechanical analysis.
ACKNOWLEDGMENT
The research project nr. CS 30/BC72/2016 between
University Politehnica from Timișoara (Department of
Measurements and Optical Electronics) and Continental
Automotive Timișoara (Qualification Laboratory
Department) funded the study.
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79%
15% 5%
100
%
0%
25%
50%
75%
100%
Ex Ey Gxy Total
67%
27% 17% 16%
97%
0%
25%
50%
75%
100%
LEx W t Total
0
10
20
30
40
0 100 200 300 400 500
Acceleration [G]
Frequency [Hz]
TEST_PCB_bare SIM_PCB_bare_6
TEST_PCBa SIM_PCBa_4
NFPCB,measured =153.3Hz
NFPCBA,measured =117.3Hz
0
30
60
90
120
150
180
0 1 2 3 4 5
Force [N]
Displacement [mm]
TEST_PCB_bare SIM_PCB_bare_3
TEST_PCBa SIM_PCBa_3
RFPCB,measured,3mm =77.4N
RFPCBA,measured,3mm =86.2N