Knowledge of the elastic properties of prints during printing processes is essential in printing presses. A computational inverse technique is presented to determine the elastic properties of materials. An effective technique for identification of elastic properties of prints consisting of the paper and several layers of ink and varnish is based on experimental data of modal vibration testing and finite element modelling. The aim of finite element modelling and optimization is to guess the material properties obtaining the same vibration frequencies and modes while test specimen is loaded in the same way as on printing press. Proposed technique can be used for the printing process modelling as non-destructive method during the initial design stage

A. Kilikevičius

J. Sidaravičius

P. Ragauskas

S. Grigaliūnienė

V. Turla

English

Vibroengineering PROCEDIA

  ©VIBROENGINEERING. VIBROENGINEERING PROCEDIA. SEPTEMBER 2013. VOLUME 1. ISSN 2345-0533 1 
Research of Elastic Parameters of Paper and Prints 
S Grigaliūnienė, V Turla, J Sidaravičius, P Ragauskas and A Kilikevičius 
RESEARCH OF ELASTIC PARAMETERS OF PAPER AND PRINTS.  
S GRIGALIŪNIENĖ, V TURLA, J SIDARAVIČIUS, P RAGAUSKAS AND A KILIKEVIČIUS 
S Grigaliūnienė1, V Turla2, J Sidaravičius3, P Ragauskas4 and A Kilikevičius5 
1, 2, 3, 5 Vilnius Gediminas Technical University, 28 Basanavičiaus str., LT-10225 Vilnius 
4 Vilnius Gediminas Technical University, 11 Sauletekio al., LT-10105 Vilnius 
 
E-mail: simona.grigaliuniene@vgtu.lt 
Abstract. Knowledge of the elastic properties of prints during printing processes is essential in printing presses. 
A computational inverse technique is presented to determine the elastic properties of materials. An effective 
technique for identification of elastic properties of prints consisting of the paper and several layers of ink and 
varnish is based on experimental data of modal vibration testing and finite element modelling. The aim of finite 
element modelling and optimization is to guess the material properties obtaining the same vibration frequencies 
and modes while test specimen is loaded in the same way as on printing press. Proposed technique can be used 
for the printing process modelling as non-destructive method during the initial design stage. 
1. Introduction 
Today printing industry continues to grow, and a lot of effort is put into the development of new and 
improved technologies and products. With this increased growth the need for quality assessment also 
increases, for example to evaluate if new technologies outperform existing technologies, or to compare 
different products in order to find the best one [1]. 
Composite material concept can be applied both for paper and printouts. Compared to 
homogeneous material, properties of composite materials are not only different, but have advantage in 
most cases [3-5].  
Elasticity parameters are important not during the printing process. The main characteristics 
outlining elasticity parameters of the product are Poisson's ratio and modulus of elasticity. Important is 
that values of these parameters are different for paper casting directions – longitudinal and transverse 
[6], therefore, the paper is considered as orthotropic material. 
Paper elasticity parameters described and studied in a number of publications [6-9]. Most of them 
describes comparison of theoretical and experimentally measured or calculated values of elasticity 
parameters. Theoretical and experimental results reviewed in [2] showed that in terms of the transverse 
direction of the paper casting, elasticity parameter values becomes greater compared with a printed 
paper than just plain paper. 
In this paper properties identification technology of the printouts is described, which is based on 
vibration tests and numerical material model [10-11]. In abovementioned works elastic properties of 
composite materials are identified. Paper is considered as single-layered, covered with paint and/or 
lacquered – multi-layered composite material. 
2. Problem formulation 
Proposed elastic material parameters identification technology involves vibration testing carried out on 
an experimental research equipment [12] and mathematical material model. Sample eigen-frequencies 
and the corresponding mode shapes are obtained from vibration test. In the mathematical model elastic 
properties are alternated until the mathematical model eigen-frequencies correspond with vibration 
testing frequencies. Then it is assumed that chosen in such a way elastic parameters correspond to the 
real values. Obtained elastic properties are for the whole specimen but not of the particular layer of the 
specimen. 
Frequencies of paper specimen were obtained from natural experiment. During numerical analysis of 
                                                     
1 Corresponding author 
RESEARCH OF ELASTIC PARAMETERS OF PAPER AND PRINTS.  
S GRIGALIŪNIENĖ, V TURLA, J SIDARAVIČIUS, P RAGAUSKAS AND A KILIKEVIČIUS 
2 ©VIBROENGINEERING. VIBROENGINEERING PROCEDIA. SEPTEMBER 2013. VOLUME 1. ISSN 2345-0533  
the paper dynamics the known in advance properties of paper were taken: length of the paper, width, 
thickness, Poisson's ratio, modulus of elasticity and density. 
The elastic properties identification is formulated as an optimization problem, where the 
discrepancies between mathematical model of specimen and the experimental vibration data are 
minimized. The problem could be stated as follows: 
Minimize ( )
2
1
∑
=







 −
=
n
i
NE
i
NE
i
FEM
i
f
ff
XF , subject to 
iii
xxx ≤≤ , mi ,...,3,2,1= , 
where F  is the objective function of the design variables [ ]
m
xxxxX ,...,,,
321
= . Variable m  is the 
number of design variables 
i
x . The eigenfrequency from vibration test denoted as NE
i
f  (NE – natural 
experiment); from finite mathematical model is represented as FEM
i
f  (FEM – finite element method). 
The number of natural frequencies in objective function is n . The second power makes the objective 
function always positive. Line under and over in design variable represent lower and upper bounds. 
The paper is modeled as an orthotropic material; therefore it can be described by six independent 
elastic parameters: 
 
)/2(1EG ,GG
 , , ,EE ,E
232231312
231312321
ν+==
νν=ν=
  (1) 
However, in order to simplify the three-dimensional identification problem to the two dimensional 
one, the following assumptions are introduced: 
 
231312231312321
GGG ,  ,EE ,E ==ν=ν=ν=   (2) 
3. Experiment 
Sample POP1 is plain paper without any coating. Selecting such material helps verify reliability of 
results of more complex specimens. Only several natural frequencies were introduced into 
identification since determination of all sequence is complicated. The natural and numerical 
experiment eigen-frequencies has significant mismatch, caused by poor identification of natural 
frequencies of specimen. Nevertheless comparison of eigenfrequencies of identified and calculated 
eigenfrequencies suggests that the mathematical model of material is developed properly, i.e. 
mathematical model meets real specimen and one can be used in further experiments with more 
complex specimens. In the Table 1 are presented identified and known elastic parameters of paper and 
the percentage difference between them. 
 
Table 1. Identified elastic parameters. 
Elastic parameters 
POP1 
Reference Identified Δ, % 
1
E , GPa 1.1E+09 1.22E+09 21.54 
2
E , GPa 0.34E+9 3.34E+08 14.3 
12
v  0.40 0.39076 2.31 
23
v  0.14 - - 
Objective function - 0.0354506 - 
 
Identification and analysis of elastic parameters of sample POP1 shows, that material properties of 
paper were identified with poor accuracy, since high order eigenfrequencies has less sensitivity to 
change of elastic properties in mathematical model that first ones. This and comparison of results of 
previous work [12] suggests, that only first several modes of spectrum must be introduced into 
RESEARCH OF ELASTIC PARAMETERS OF PAPER AND PRINTS.  
S GRIGALIŪNIENĖ, V TURLA, J SIDARAVIČIUS, P RAGAUSKAS AND A KILIKEVIČIUS 
 ©VIBROENGINEERING. VIBROENGINEERING PROCEDIA. SEPTEMBER 2013. VOLUME 1. ISSN 2345-0533 3 
identification. 
Sample POP2 is fully covered with the ink and varnish paper. Only several natural frequencies 
were introduced into identification since determination of some is complicated. 
In the Table 2 are presented identified and known elastic parameters of sample and the percentage 
difference between them. It must be noted that in column “Reference” are presented elastic properties 
of plain paper, since ones of printout are not known. 
 
Table 2. Identified elastic parameters. 
Elastic parameters 
POP2 (100% covered) 
Reference Identified Δ, % 
1
E , GPa 1.0E+09 1.43E+09 43.3 
2
E , GPa 0.39E+9 1.48E+09 280 
12
v  0.40 0.0659 83.525 
23
v  0.14 - - 
Objective function - 0.001254469 - 
 
Observed discrepancies in Table 2 should be not considered as really existing. It is seen that 
applying a uniform coating on paper turns it from orthotropic to isotropic material, i.e. in plane 
properties of the material in perpendicular and transverse directions become similar. This was also 
proved in previous paper [12]. It can be assumed, that identification of elastic characteristics of such 
sample could be sufficiently accurate since elastic parameters of isotropic material are identified with 
sufficient accuracy, as it has been shown with sample POP1. 
In this case, it can be assumed that it is necessary to take into account possible changes in 
orthotropy direction. This was theoretically proved in previous paper [12]. Elastic parameters of such 
sample can be determined as accurately as any orthotropic material. It was already proven during the 
test of sample POP1. 
Sample POP3 not completely covered with ink and completely covered with varnish paper. In the 
Table 3 are presented identified and known elastic parameters of paper and the percentage difference 
between them. In column “Reference” elastic properties of plain paper are presented. 
Discrepancies in Table 3 should be not considered as really existing since properties of such print is 
not known. It is seen that applying a uniform coating on paper turns it from orthotropic to isotropic 
material, i.e. value of Young's modulus 
1
E  becomes smaller than 
2
E . 
 
Table 3. Identified elastic parameters. 
Elastic parameters 
POP3 (14% covered) 
Reference Identified Δ, % 
1
E , GPa 1.0E+09 5.87e+009 487 
2
E , GPa 0.39E+09 4.87e+010 12387 
12
v  0.40 0.0632 84.2 
23
v  0.14 - - 
Objective function - 0.0264487 - 
4. Conclusions 
The possibility to determine the elastic constants of printouts using the combination of finite element 
modeling and genetic algorithm was shown on previous paper [12]. The repeatability and accuracy of 
the proposed inverse determination method is verified. The investigation of the two samples of 
RESEARCH OF ELASTIC PARAMETERS OF PAPER AND PRINTS.  
S GRIGALIŪNIENĖ, V TURLA, J SIDARAVIČIUS, P RAGAUSKAS AND A KILIKEVIČIUS 
4 ©VIBROENGINEERING. VIBROENGINEERING PROCEDIA. SEPTEMBER 2013. VOLUME 1. ISSN 2345-0533  
printouts also proves that the elastic properties identification technique is appropriate. 
Theoretical and practical experiments reviewed in [1] claims that the elastic properties of printout 
changes in the way that from orthotropic material prints turn to isotropic because ink effects paper 
structure. This was once more confirmed by the present and previous [12] works and proves reliability 
of the proposed technology for the identification of elastic properties of printouts. 
It was stated that amount and sequence of eigenfrequencies used in identification process must be 
composed according identification results. This will be analysed in future investigations. 
References 
[1] M Pedersen, N Bonnier, J Y Hardeberg and F Albregtsen 2011 Image quality metrics for 
evaluation of print quality Proc. of SPIE-IS&T Electronic Imaging SPIE 7867(786702) 
[2] A Kabelkaitė 2009 Investigation of influence of the running direction of paper and cardboard 
and defects of material to the eigenmodes of vibrations Doctoral dissertation (Kaunas) 
[3] S Markulytė, J Sidaravičius and V Turla 2012 Paper and prints as composite materials Science – 
Future of Lithuania 4(6) 528–532 
[4] T A Schaedler, A J Jacobsen, A Torrents, A E Sorensen, J Lian, J R Greer, L Valdevit and W B 
Carter 2011 Ultralight Metallic Microlattices Science 334(6058) 962–965 
[5] A R Ranjbartoreh, B Wang, X Shen and G Wang 2011 Advanced mechanical properties of 
graphene paper Journal of applied physics 109(014306) 
[6] K Niskannen 2008 Paper physics. Second ed., Finnish Paper Engineers 
[7] J. van Beeck 2008 Paper: a closer study. Bachelor final project (Eindhoven) 
[8] T Yokoyama and K Nakai 2007 Evaluation of in-plane orthotropic elastic constants of paper 
and paperboard In proceeding of: 2007 SEM Annual Conference & Exposition on 
Experimental and Applied Mechanics 
[9] P L Ridgway, R E Russo, E Lafond, T Jackson and C Habeger 2003 Laser Ultrasonic System 
for On-Line Measurement of Elastic Properties of Paper Journal of Pulp and Paper Science 
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[11] P Ragauskas and R Belevičius 2009 Identification of material properties of composite materials 
Aviation (Vilnius, Lithuania) 13(4) 109 
[12] P Ragauskas, S Grigaliūnienė, J Sidaravičius and V Turla 2013 Identification of the Prints 
Elastic Parameters using Vibrational Methods Mechatronical Systems and Materials 
 


Research of Elastic Parameters of Paper and Prints

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Research of Elastic Parameters of Paper and Prints

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