Accounting for large membrane strains in Q4GS and T3GS elements in EUROPLEXUS.
Date: 2016-05-12
Institutions: Joint Research Centre
Subjects: accident prevention, materials technology, research report, resistance of materials, simulation, software

large  membrane
Accounting 
strains  in  Q4GS  and  T3GS  elements
in EUROPLEXUS 

for 

Folco Casadei 

Vegard Aune 

Georgios Valsamos 

Martin Larcher 

2016 

EUR 27836 EN

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
                                                                    
 
 
 
 
 
large  membrane
Accounting 
strains  in  Q4GS  and  T3GS  elements
in EUROPLEXUS 

for 

 
 
 
 
This publication is a Technical report by the Joint Research Centre, the European Commission’s in-house science 
service. It aims to provide evidence-based scientific support to the European policy-making process. The scientific 
output expressed does not imply a policy position of the European Commission. Neither the European 
Commission nor any person acting on behalf of the Commission is responsible for the use which might be made 
of this publication. 

JRC Science Hub 
https://ec.europa.eu/jrc 

JRC101010 

EUR 27836 EN 

ISBN 978-92-79-57731-4 (PDF) 

ISSN 1831-9424 (online) 

doi:10.2788/888282  

© European Union, 2016 

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How to cite: Authors; title; EUR; doi 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Accounting for large membrane strains in Q4GS and T3GS elements
in EUROPLEXUS

F. Casadei1, V. Aune2, G. Valsamos3, and M. Larcher3

1Retired from JRC ELSA
2Structural Impact Laboratory (SIMLab), Centre for Research-based Innovation (CRI)
and Department of Structural Engineering, Norwegian University of Science and Technology,
Rich. Birkelands vei 1A, NO-7491 Trondheim, Norway
3European Laboratory for Structural Assessment (ELSA), Institute for the Protection and Security of the Citizen (IPSC)
Joint Research Centre (JRC), 21027 Ispra, Italy

February 19, 2016

Contents

1 Introduction

2 Updating the shell element thickness

2.1 Calculating the new thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2

Implementation notes

3 Numerical examples

3.2 Test cases with linear material

3.1 Test cases with VPJC material

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Q4GSS3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 T3GSS3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Q4GSS1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Q4GSS3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Q4GSS4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . .
3.3.1 Q4GSS2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Q4GSS5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3 Test cases with elsastic perfectly-plastic material

4 Conclusions and future work

References

Appendix — Input ﬁles

List of input ﬁles

List of Tables

2

2
2
4

4
4
4
4
4
5
5
6
6
6
6

6

6

8

11

1
2
3

Calculations with 3D shell elements and VPJC material. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . .
Solutions of the uniaxial stress problem with elastic material
. . . . .
Solutions of the uniaxial stress problem with elastic perfectly plastic material

4
5
6

List of Figures

1

Total driving force in cases Q4GSS3 and T3GSS3.

. . . . . . . . . . . . . . . . . . . .

5

1

1

Introduction

This short note presents the updating of element thickness due to large membrane strains recently
introduced in some shell elements (Q4GS and T3GS) of the EUROPLEXUS code (EPX).

EUROPLEXUS [1] is a computer code jointly developed by the French Commissariat `a l’Energie
Atomique (CEA DMT Saclay) and by EC-JRC. The code application domain is the numerical simula-
tion of fast transient phenomena such as explosions, crashes and impacts in complex three-dimensional
ﬂuid-structure systems.

The Cast3m [2] software from CEA is used as a pre-processor to EPX when it is necessary to

generate complex meshes.

The development proposed here solves a problem highlighted in a previous report, see [3], where
it had been noted that some of EPX’s shell elements do not update the thickness when the element
is subjected to large membrane strains. As a consequence, membrane forces (but also bending and
transverse shear components) are incorrectly evaluated when large membrane strains are present.

2 Updating the shell element thickness

In reference [3] the implementation of the VPJC modiﬁed Johnson-Cook material model described
in [4] was checked by simple displacement-driven one-element tests. The imposed diplacements were
such that (very) large membrane strains were induced in the elements.

It was noted that some shell elements failed (at least partly) to give the expected (analytical)
solution. The computed stresses and strains were correct, but the nodal forces were wrong due to the
fact that the element thickness was not updated as a consequence of the large membrane deformations.
For one of these elements (JRC’s COQI triangular plate/shell) the problem was identiﬁed in the
element formulation itself. Although the thickness of this element is updated as a consequence of large
membrane strains, the element formulation itself is such that large membrane strains are not properly
accounted for. Therefore, it was concluded that COQI elements should not be used whenever the
expected membrane strains exceed a few percent.

For another set of elements (CEA’s Q4GS, T3GS, Q4GR, QPPS, DKT3 and DST3) the problem
consists in the fact that the update of element thickness was not implemented in the element routine
(with the notable exception of Q4GS when used in conjunction with the hyperelastic material HYPE).
The existing bibliography on these elements formulation was then inspected in order to devise a
possible solution. It turns out that the DKT3 and DST3 elements are not really suited to be used in
conjunction with non-linear materials, see e.g. reference [6], and this despite the fact that EPX does
allow their use with materials such as VMIS ISOT (elasto-plastic). Since large (membrane) strains
are almost necessarily accompanied by non-linear material behaviour in practical applications, it was
decided not to update these element routines.

The same conclusion was applied to the QPPS element (because it is rarely used) and to the Q4GR
(this element is underintegrated and necessitates of anti-hourglass treatment by means of empirical
parameters, therefore its use is discouraged in recent applications, in favour of Q4GS).

The two remaining elements, Q4GS and T3GS, are the most general and most frequently used
shell elements of EPX, for the quadrilateral and triangular shape, respectively, and can be used in
mixed meshes being fully compatible with each other. Therefore, it was considered essential to extend
at least these two heavy-duty shell elements to the treatment of large membrane strains.

The existing documentation for the Q4GS is reference [5], and for T3GS it is reference [6].

2.1 Calculating the new thickness

For the two shell elements considered here (Q4GS and T3GS), the element thickness is contained in
the global array TH(1), while the element excentricity is contained in TH(2).

These values are always the initial values, as provided by the user in the input ﬁle, with the only
exception of the Q4GS element used in conjunction with the HYPE (hyperelastic) material, where
the value of TH(1) (but curiously not TH(2)) is updated as a consequence of through-the-thickness

2

strain. In the modiﬁcations prepared in the present work, care has been taken so as not to modify
the behaviour of Q4GS when used in conjunction with HYPE.

When a shell undergoes large membrane strains, its thickness varies in general. The new thickness
can be computed from the through-the-thickness total strain (cid:15)z, whose value is computed and returned
by (most) material routines as a consequence of imposing a zero-stress condition along the thickness
(σz = 0). Of course, the change in shell thickness has an inﬂuence on membrane, bending and
transverse shear forces.

Shell elements possess a number of Gauss integration points, which are located on laminas (surfaces
parallel to the mean surface of the shell). When non-linear materials are used, several laminas
and therefore several Gauss points through the thickness are used to achieve accurate numerical
integration, because the stress proﬁle through the thickness is non-linear in general. A ﬁber is deﬁned
as a straight line, initially normal to the shell mid-surface (lamina). As a consequence of deformation,
the ﬁber is assumed to remain straight (so that the strain proﬁle along a ﬁber is linear), but it may
become no longer normal to the laminas if Reissner-Mindlin shell theory (thick shells) is adopted (this
is the case for Q4GS and T3GS), as opposed to Poisson-Kirchhoﬀ (thin shells) theory.

Note incidentally that in EPX stress and strain values for shells may be organized either ﬁber-ﬁrst,

or lamina-ﬁrst (the latter is the case for both Q4GS and T3GS), depending on element type.

As concerns lamina integration, the Q4GS adopts a 2 × 2 (i.e., 4 points) rule in each lamina, while
the T3GS uses a single point in each lamina. The number of Gauss points through the thickness (i.e
along a ﬁber) depends upon the material. A single point (analytical integration) is used with “linear”
materials (e.g. the linear elastic material LINE or a global formulation such as GLRC), while several
points (5 by default, but their number can be varied by the user) are used if a non-linear material
(and/or a layered shell model with varying material layer by layer) is adopted. Each Gauss point has
its own set of stress, strain and hardening variable components.

At the beginning of the element routine, in order to update the element thickness, a weighted

average (cid:15)z of the through-the-thickness strain (cid:15)z is evaluated along each ﬁber i:

(cid:15)zi =

nf(cid:80)

f =1

(cid:15)zif Wf

nf(cid:80)

f =1

Wf

(1)

where i indicates the particular ﬁber chosen, f are the integration points (from 1 to nf ) along the
ﬁber (i.e., through the thickness) and Wf is the integration weight associated with each integration
point.

By denoting h0 the initial thickness of the element (as provided by the user), the current thickness

hi of the ﬁber i under consideration is is estimated as:

From this, an average current thickness h for the whole element is estimated, according to:

hi = h0 exp((cid:15)zi)

h =

1
nl

nl(cid:88)

l=1

hl

where l are the integration points (from 1 to nl) over the lamina (i.e. in the element plane).

The element excentricity κ is scaled in the same proportion as the thickness:

κ =

h
h0

κ0

(2)

(3)

(4)

where κ0 indicates the initial element excentricity as provided by the user.

The estimated current thickness h and current excentricity κ are then used in the rest of the
routine instead of the initial ones in order to compute the element strain increments, new stresses and
nodal forces. Note, however, that the values of thickness and excentricity in the TH array are never

3

modiﬁed (except in the case of HYPE material already noted above) and remain therefore the initial
values provided by the user.

2.2 Implementation notes

The thickness (and excentricity) update proposed in the previos Section is applied in the Q4GS and
T3GS elements only when the element is integrated through the thickness, i.e. when more than one
Gauss point is used along a ﬁber. Recall that this is the case for non-linear materials. In fact, for
linear materials it would probably not make sense to update the thickness, since in such cases the
membrane strains should be small anyway.

With the proposed modiﬁcation, all standard benchmark tests pass for the T3GS element, while
for Q4GS (which is used much more frequently) some benchmarks do not pass the qualiﬁcation (this
is perhaps normal, if non-negligible membrane strains occur in such cases).

In order to avoid perturbing the results of existing tests and applications, it has been decided to
implement the proposed modiﬁcation in the form of an option. A new optional keyword OPTI LMST
(for Large Menbrane STrains) is implemented. This option activates the thickness update in elements
Q4GS and T3GS, provided these elements use a non-linear material. In case of linear material (and
also in case of the HYPE material, for the Q4GS), the option has no eﬀect and the results obtained
should be identical to previous solutions (without the option).

3 Numerical examples

3.1 Test cases with VPJC material

We ﬁrst check the problematic cases of reference [3] with Q4GS and T3GS by adding the new option
to see whether the results in terms of nodal forces are correct. All such tests use the VPJC material.
The performed tests are summarized in Table 1. Two sets of cases were considered, one involving
linear elastic material and the other involving elastic perfectly-plastic material. The test geometry
is similar to the one considered in the previous section (a single 4-node shell element subjected to
imposed displacements) but the ﬁnal length of the element is twice the initial one (instead of three
times the initial one).

Case
Analytical
Q4GSS3
T3GSS3

Mesh
—

(cid:15)x
−0.54931
Q4GS −0.54894
T3GS −0.54894

(cid:15)y

(cid:15)z

1.0986 −0.54931
1.0986 −0.54025
1.0986 −0.54025

σy
10.116 × 108
10.116 × 108
10.116 × 108

Fy
3.3720 × 108
3.3777 × 108
3.3777 × 108

Table 1: Calculations with 3D shell elements and VPJC material.

3.1.1 Q4GSS3

This test is similar to the homonymous case of reference [3] but the OPTI LMST is added. As shown in
Table 1, the total driving force Fy resulting from the imposed displacement is now correct.

The time variation of the driving force is depicted in Figure 1(a).

3.1.2 T3GSS3

This test is similar to the homonymous case of reference [3] but the OPTI LMST is added. As shown in
Table 1, the total driving force Fy resulting from the imposed displacement is now correct.

The time variation of the driving force is depicted in Figure 1(b).

3.2 Test cases with linear material

Next, we check the Q4GS element in conjunction with other materials. In particular, we refer to the
tests already considered, and which failed at least partially, in reference [7]. In all such tests, the new
option OPTI LMST is added.

4

(a) Case Q4GSS3

(b) Case T3GSS3

Figure 1: Total driving force in cases Q4GSS3 and T3GSS3.

The test geometry is similar to the one considered in the previous section (a single 4-node quadri-
lateral subjected to imposed displacements), but the ﬁnal length of the element is only twice instead
of three times the initial one.

Two sets of tests are considered, one involving linear elastic material and the other involving

elastic perfectly-plastic material. The performed tests for the ﬁrst set are summarized in Table 2.

Case

Element Material

Analytical
Q4GSS1
Q4GSS3
Q4GSS4

N/A
Q4GS
Q4GS
Q4GS

N/A
VM23 (elastic)
LINE
VMIS PARF (elastic)

Comments

Static solution

‘Linear’ case

(cid:15)x

0.69315
0.69314
0.69314
0.69314

(cid:15)y

-0.20794
-0.20793
-0.20791
-0.20791

(cid:15)z

-0.20794
-0.20795
N/A (0.0)
−4.0 × 10−15

σx
1.3863 × 1011
1.3863 × 1011
1.3863 × 1011
1.3863 × 1011

Fx
9.1461 × 1010
9.1462 × 1010
11.261 × 1010
11.261 × 1010

Table 2: Solutions of the uniaxial stress problem with elastic material

3.2.1 Q4GSS1

This test is similar to the homonymous case of reference [7] but the OPTI LMST is added. As shown in
Table 2, the total driving force Fx resulting from the imposed displacement is now correct.

This is due to the fact that the used material model to represent an elastic behaviour is VM23
(a nominally an elasto-plastic law), with parameters set in such a way that the elastic limit is not
exceeded. In this way, the code does perform numerical integration through the element thickness
and the LMST option has a chance to work (as it does, indeed).

This is a useful practical “trick” in order to perform an elastic (but large strain) calculation with

Q4GS.

3.2.2 Q4GSS3

This test is similar to the homonymous case of reference [7] but the OPTI LMST is added. Note that
this case is diﬀerent from case Q4GSS3 (actually, BM STR VPJC Q4GSS3) presented in the previous
Section, although they have the same “short” name. The material for this test is the LINE material.
Therefore, as already mentioned in the previous Sections, the element is not integrated through the
thickness and the LMST option should have no eﬀect.

Indeed, the results of the calculation in terms of driving force are as false as in reference [7]. Note
also that the through-the-thickness strain (cid:15)z is not computed by the LINE material routine (it is
zero). Therefore, the result would be wrong anyway, even if the code would take into account the
LMST option for this material.

5

EUROPLEXUS16 FEBRUARY  2016 DRAWING  7Q4GSS3-1- FY_SUM                 TIME [S]0.00.51.01.52.0TOT. FORCE [N]-1.E+08     0. 1.E+08 2.E+08 3.E+08 4.E+08 5.E+08 6.E+08 7.E+08 8.E+0811111EUROPLEXUS16 FEBRUARY  2016 DRAWING  7T3GSS3-1- FY_SUM                 TIME [S]0.00.51.01.52.0TOT. FORCE [N]-1.E+08     0. 1.E+08 2.E+08 3.E+08 4.E+08 5.E+08 6.E+08 7.E+08 8.E+08111113.2.3 Q4GSS4

This test is similar to the homonymous case of reference [7] but the OPTI LMST is added. The material
for this test is the VMIS PARF material, i.e. an elastic perfectly-plastic law, but with an elastic limit
high enough so that it is never reached during this test (so that the law is elastic in practice). The
shell element routine does integrate the element through the thickness in this case, so the LMST option
has a chance to work.

Nevertheless, the results of the calculation in terms of driving force are as false as in reference [7].
This is due to the fact that the through-the-thickness strain (cid:15)z is not correctly computed by the VMIS
PARF material routine (it is practically zero). However, this is a problem of the material routine and
not of the shell element routine.

3.3 Test cases with elsastic perfectly-plastic material

The performed tests for the second set of tests from reference [7] (i.e.
perfectly-plastic material model) are summarized in Table 3.

those assuming an elastic

Case

Element Material

Comments

Analytical
Q4GSS2
Q4GSS5

N/A
Q4GS
Q4GS

N/A
VM23
VMIS PARF

Static solution

(cid:15)x

0.69315
0.69314
0.69314

(cid:15)y

-0.34657
-0.34699
-0.34699

(cid:15)z

-0.34657
-0.14835
−1.8 × 10−14

σx
4.0000 × 108
4.0000 × 108
4.0000 × 108

Fx
2.0000 × 108
2.4375 × 108
2.8273 × 108

Table 3: Solutions of the uniaxial stress problem with elastic perfectly plastic material

3.3.1 Q4GSS2

This test is similar to the homonymous case of reference [7] but the OPTI LMST is added. The
VM23 material model is used with suitably chosen parameters to represent an elastic perfectly-plastic
material behaviour.

As it can be seen from Table 3, the computed driving force is still false (although the found value
is diﬀerent from the one in reference [7], which did not use the LMST option). This seems to be due to
the fact that the through-the-thickness strain (cid:15)z is wrongly computed by the routine SGDI in these
circumstances. The value of this strain is largely underestimated, as it appears from Table 3.

This problem will have to be further investigated.

3.3.2 Q4GSS5

This test is similar to the homonymous case of reference [7] but the OPTI LMST is added. The VMIS
PARF material model is used, which would be the obvious choice in this case.

As seen in Table 3, the computed value of the driving force is wrong. This is because, as already
noted in test Q4GSS4 commented above, the VMIS PARF routine fails to compute the correct value
of (cid:15)z (which is returned as nearly zero).

4 Conclusions and future work

The new option LMST allows to to update the element thickness in Q4GS and T3GS shell elements
whenever a non-linear material model is used.

This works if the material routine correctly estimates the through-the-thickness strain (cid:15)z resulting

from the plane stress assumption in the shell element formulation.

The problems observed in a previous report with the VPJC material model are corrected by the

new option.

For other material models such as VM23 and VMIS, some problems persist (and will have to be
corrected in a fortcoming development) but these are due to the material routine and not to the shell
element routine.

6

References

[1] EUROPLEXUS User’s Manual, on-line version: http://europlexus.jrc.ec.europa.eu.

[2] Cast3m Software: http://www-cast3m.cea.fr/.

[3] F. Casadei, V. Aune, G. Valsamos, M. Larcher. Testing of the Johnson-Cook material model
VPJC in EUROPLEXUS. JRC Technical Report, PUBSY No. JRC98848, EUR Report 27594
EN, in publication, 2016.

[4] V. Aune, F. Casadei and G. Valsamos. Formulation and Implementation of a Viscoplastic Mate-
rial Model in ABAQUS/Explicit and EUROPLEXUS. Application of the Cutting Plane Algorithm
to Determine the Structural Response in Fast Transient Dynamics. NTNU/JRC Report (2015),
in publication.

[5] A. Letellier. Contribution `a la mod´elisation des impacts d’oiseaux sur les aubes des r´eacteurs

d’avions. CEA Report DRN/DMT 96.439 (also PhD Thesis, Universit´e d’Evry), 1996.

[6] D. Markovic. Implementation d’un nouvel ´el´ement ﬁni de coque ´epaisse (T3GS) dans Europlexus.

EDF Report H-T62-2008-00080-FR, 2008.

[7] F. Casadei, V. Aune, G. Valsamos, M. Larcher. Description of the elasto-plastic material routine

SGDI. JRC Technical Report, PUBSY No. JRC97557, EUR Report 27434 EN, 2015.

7

Appendix — Input ﬁles

All the input ﬁles used in the previous Sections are listed below.

bm str vpjc q4gss3.epx

TOUS GVALSAMOS 15/12/10 20:09:15 #2978

BM_STR_VPJC_Q4GSS3

$
Q4GSS3
ECHO
!CONV WIN
LAGR TRID
GEOM LIBR POIN 4 Q4GS 1 TERM

-0.5 -0.5 0.0
1 2 3 4

0.5 -0.5 0.0

0.5

0.5

0.0

-0.5 0.5

0.0

COMP EPAI 1.0 LECT 1 TERM
MATE VPJC RO

0.33

7850.0
YOUN 2.1E11
NU
ELAS 3.70E8
QR1 2.364E8
CR1 39.3
QR2 4.081E8
CR2 4.5
PDOT 5.E-4
C
TQ
CP
TM
M
DC
WC
LECT 1 TERM

! We assume adiabatic conditions

0.0
0.9
452.0
1800.0
0.0
1.0
15.95E8 ! Large WC : no failure (realistic value is 4.73E8)

! Zero M : no temperature-induced softening

FONC NUM 1 TABL 2 0.0 1.0 ! Constant function in time

LINK COUP

2.0 1.0

VITE 2 -0.5 FONC 1 LECT 1 2 TERM ! Relative velocity 1 m/s
VITE 2

0.5 FONC 1 LECT 3 4 TERM

INIT VITE 2 -0.5 LECT 1 2 TERM
0.5 LECT 3 4 TERM

VITE 2

ECRI COOR DEPL VITE ACCE FINT FEXT FLIA FDEC CONT EPST ECRO FREQ 10000

FICH ALIC FREQ 100
OPTI NOTE PAS UTIL LOG 1000

LMST ! To activate thickness update in Q4GS element with VPJC material

CALC TINI 0 TFIN 2.0 PASF 2.E-5 NMAX 100000
SUIT
Post-treatment
ECHO
RESU ALIC GARD PSCR
SORT GRAP
AXTE 1.0 ’Time [s]’
COUR 1 ’dy_1’ DEPL COMP 2 NOEU LECT 1 TERM
COUR 2 ’dy_2’ DEPL COMP 2 NOEU LECT 2 TERM
COUR 3 ’dy_3’ DEPL COMP 2 NOEU LECT 3 TERM
COUR 4 ’dy_4’ DEPL COMP 2 NOEU LECT 4 TERM
COUR 5 ’fy_1’ FLIA COMP 2 NOEU LECT 1 TERM
COUR 6 ’fy_2’ FLIA COMP 2 NOEU LECT 2 TERM
COUR 7 ’fy_3’ FLIA COMP 2 NOEU LECT 3 TERM
COUR 8 ’fy_4’ FLIA COMP 2 NOEU LECT 4 TERM
COUR 11 ’s1_1’ CONT COMP 1 ELEM LECT 1 TERM
COUR 12 ’s2_1’ CONT COMP 2 ELEM LECT 1 TERM
COUR 13 ’s3_1’ CONT COMP 3 ELEM LECT 1 TERM
COUR 14 ’s4_1’ CONT COMP 4 ELEM LECT 1 TERM
COUR 15 ’s5_1’ CONT COMP 5 ELEM LECT 1 TERM
COUR 16 ’s6_1’ CONT COMP 6 ELEM LECT 1 TERM
COUR 21 ’e1_1’ EPST COMP 1 ELEM LECT 1 TERM
COUR 22 ’e2_1’ EPST COMP 2 ELEM LECT 1 TERM
COUR 23 ’e3_1’ EPST COMP 3 ELEM LECT 1 TERM
COUR 24 ’e4_1’ EPST COMP 4 ELEM LECT 1 TERM
COUR 25 ’e5_1’ EPST COMP 5 ELEM LECT 1 TERM
COUR 26 ’e6_1’ EPST COMP 6 ELEM LECT 1 TERM
COUR 32 ’se_1’ ECRO COMP 2 ELEM LECT 1 TERM
COUR 33 ’ep_1’ ECRO COMP 3 ELEM LECT 1 TERM
COUR 50 ’fy_sum’ FLIA COMP 2 ZONE LECT 3 4 TERM
TRAC 1 2 3 4 AXES 1.0 ’DISPL. [M]’ YZER
TRAC 5 6 7 8 AXES 1.0 ’FORCE [N]’ YZER
TRAC 11 12 13 14 15 16 AXES 1.0 ’STRESS [PA]’ YZER
TRAC 21 22 23 24 25 26 AXES 1.0 ’STRAIN [-]’ YZER
TRAC 14 AXES 1.0 ’STRESS [PA]’ XAXE 24 1.0 ’STRAIN [-]’ YZER
TRAC 32 AXES 1.0 ’EQ. STRESS [PA]’ XAXE 33 1.0 ’EQ PL STRAIN [-]’ YZER
TRAC 50 AXES 1.0 ’TOT. FORCE [N]’ YZER
QUAL EPST COMP 1 LECT 1 TERM REFE -0.54931E+00 TOLE 1.E-2 ! EPS-XX
EPST COMP 2 LECT 1 TERM REFE 0.10986E+01 TOLE 1.E-3 ! EPS-YY
EPST COMP 4 LECT 1 TERM REFE -0.54931E+00 TOLE 1.E-2 ! EPS-ZZ
CONT COMP 2 LECT 1 TERM REFE 0.10116E+10 TOLE 1.E-2 ! SIG-YY
0.33720E+09 TOLE 1.E-2 ! FY-SUM
COUR 50

REFE

SUIT
Q4GSS3A
ECHO

CONV WIN
OPTI PRIN
RESU ALIC GARD PSCR
SORT VISU NSTO 1
PLAY
CAME
!

0.00000E+00

0.00000E+00
1.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00

1 EYE
Q
VIEW 0.00000E+00 0.00000E+00 -1.00000E+00
RIGH 1.00000E+00 0.00000E+00 0.00000E+00
UP
1.00000E+00 0.00000E+00
FOV

0.00000E+00
2.48819E+01

7.90569E+00

!NAVIGATION MODE: ROTATING CAMERA

8

!CENTER : 0.00000E+00 0.00000E+00 0.00000E+00
!RSPHERE: 1.58114E+00
!RADIUS : 7.90569E+00
!ASPECT : 1.00000E+00
: 6.16644E+00
!NEAR
!FAR
: 1.10680E+01
SCEN GEOM NAVI FREE
REFE FRAM
INIT WIRE

VECT SCCO FIEL VITE SCAL USER PROG 0.035 PAS 0.035 0.49 TERM
TEXT VSCA
COLO PAPE
SLER CAM1 1 NFRA 1
FREQ 10
TRAC OFFS FICH AVI
GOTR LOOP 99 OFFS FICH AVI CONT NOCL DEFO REND
GO
TRAC OFFS FICH AVI CONT DEFO REND
ENDPLAY
FIN

NOCL NFTO 101 FPS 15 KFRE 10 COMP -1 DEFO REND

BEGIN DESCRIPTION

A bi-unit quadrilateral shell is subjected to an imposed elongation up to 3
times the initial length along one of the axes (by an imposed
constant velocity).

The material is VPJC and the purpose is to test the material model
under large strains. The effects of strain rate and of
temperature are neglected (m=0, C=0).

The result is compared with an analytical solution, showing
good agreement.

END DESCRIPTION

bm str vpjc t3gss3.epx

TOUS GVALSAMOS 15/12/10 20:09:15 #2978

$ BM_STR_VPJC_T3GSS3
T3GSS3
ECHO
!CONV WIN
LAGR TRID
GEOM LIBR POIN 4 T3GS 2 TERM

-0.5 -0.5 0.0
1 2 3
3 4 1

0.5 -0.5 0.0

0.5

0.5

0.0

-0.5 0.5

0.0

COMP EPAI 1.0 LECT 1 2 TERM
MATE VPJC RO

0.33

7850.0
YOUN 2.1E11
NU
ELAS 3.70E8
QR1 2.364E8
CR1 39.3
QR2 4.081E8
CR2 4.5
PDOT 5.E-4
C
TQ
CP
TM
M
DC
WC
LECT 1 2 TERM

! We assume adiabatic conditions

0.0
0.9
452.0
1800.0
0.0
1.0
15.95E8 ! Large WC : no failure (realistic value is 4.73E8)

! Zero M : no temperature-induced softening

FONC NUM 1 TABL 2 0.0 1.0 ! Constant function in time

LINK COUP

2.0 1.0

VITE 2 -0.5 FONC 1 LECT 1 2 TERM ! Relative velocity 1 m/s
VITE 2

0.5 FONC 1 LECT 3 4 TERM

INIT VITE 2 -0.5 LECT 1 2 TERM
0.5 LECT 3 4 TERM

VITE 2

ECRI COOR DEPL VITE ACCE FINT FEXT FLIA FDEC CONT EPST ECRO FREQ 10000

FICH ALIC FREQ 100
OPTI NOTE PAS UTIL LOG 1000

LMST ! To activate thickness update in T3GS element with VPJC material

CALC TINI 0 TFIN 2.0 PASF 2.E-5 NMAX 100000
SUIT
Post-treatment
ECHO
RESU ALIC GARD PSCR
SORT GRAP
AXTE 1.0 ’Time [s]’
COUR 1 ’dy_1’ DEPL COMP 2 NOEU LECT 1 TERM
COUR 2 ’dy_2’ DEPL COMP 2 NOEU LECT 2 TERM
COUR 3 ’dy_3’ DEPL COMP 2 NOEU LECT 3 TERM
COUR 4 ’dy_4’ DEPL COMP 2 NOEU LECT 4 TERM
COUR 5 ’fy_1’ FLIA COMP 2 NOEU LECT 1 TERM
COUR 6 ’fy_2’ FLIA COMP 2 NOEU LECT 2 TERM
COUR 7 ’fy_3’ FLIA COMP 2 NOEU LECT 3 TERM
COUR 8 ’fy_4’ FLIA COMP 2 NOEU LECT 4 TERM
COUR 11 ’s1_1’ CONT COMP 1 ELEM LECT 1 TERM
COUR 12 ’s2_1’ CONT COMP 2 ELEM LECT 1 TERM
COUR 13 ’s3_1’ CONT COMP 3 ELEM LECT 1 TERM

COUR 14 ’s4_1’ CONT COMP 4 ELEM LECT 1 TERM
COUR 15 ’s5_1’ CONT COMP 5 ELEM LECT 1 TERM
COUR 16 ’s6_1’ CONT COMP 6 ELEM LECT 1 TERM
COUR 21 ’e1_1’ EPST COMP 1 ELEM LECT 1 TERM
COUR 22 ’e2_1’ EPST COMP 2 ELEM LECT 1 TERM
COUR 23 ’e3_1’ EPST COMP 3 ELEM LECT 1 TERM
COUR 24 ’e4_1’ EPST COMP 4 ELEM LECT 1 TERM
COUR 25 ’e5_1’ EPST COMP 5 ELEM LECT 1 TERM
COUR 26 ’e6_1’ EPST COMP 6 ELEM LECT 1 TERM
COUR 32 ’se_1’ ECRO COMP 2 ELEM LECT 1 TERM
COUR 33 ’ep_1’ ECRO COMP 3 ELEM LECT 1 TERM
COUR 50 ’fy_sum’ FLIA COMP 2 ZONE LECT 3 4 TERM
TRAC 1 2 3 4 AXES 1.0 ’DISPL. [M]’ YZER
TRAC 5 6 7 8 AXES 1.0 ’FORCE [N]’ YZER
TRAC 11 12 13 14 15 16 AXES 1.0 ’STRESS [PA]’ YZER
TRAC 21 22 23 24 25 26 AXES 1.0 ’STRAIN [-]’ YZER
TRAC 14 AXES 1.0 ’STRESS [PA]’ XAXE 24 1.0 ’STRAIN [-]’ YZER
TRAC 32 AXES 1.0 ’EQ. STRESS [PA]’ XAXE 33 1.0 ’EQ PL STRAIN [-]’ YZER
TRAC 50 AXES 1.0 ’TOT. FORCE [N]’ YZER
QUAL EPST COMP 1 LECT 1 TERM REFE -0.54931E+00 TOLE 1.E-2 ! EPS-XX
EPST COMP 2 LECT 1 TERM REFE 0.10986E+01 TOLE 1.E-3 ! EPS-YY
EPST COMP 4 LECT 1 TERM REFE -0.54931E+00 TOLE 1.E-2 ! EPS-ZZ
CONT COMP 2 LECT 1 TERM REFE 0.10116E+10 TOLE 1.E-2 ! SIG-YY
0.33720E+09 TOLE 1.E-2 ! FY-SUM
COUR 50

REFE

SUIT
T3GSS3A
ECHO

CONV WIN
OPTI PRIN
RESU ALIC GARD PSCR
SORT VISU NSTO 1
PLAY
CAME
!

0.00000E+00

0.00000E+00
1.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00

1 EYE
Q
VIEW 0.00000E+00 0.00000E+00 -1.00000E+00
RIGH 1.00000E+00 0.00000E+00 0.00000E+00
UP
1.00000E+00 0.00000E+00
FOV

0.00000E+00
2.48819E+01

7.90569E+00

0.00000E+00

!NAVIGATION MODE: ROTATING CAMERA
!CENTER : 0.00000E+00 0.00000E+00
!RSPHERE: 1.58114E+00
!RADIUS : 7.90569E+00
!ASPECT : 1.00000E+00
: 6.16644E+00
!NEAR
!FAR
: 1.10680E+01
SCEN GEOM NAVI FREE
REFE FRAM
INIT WIRE

VECT SCCO FIEL VITE SCAL USER PROG 0.035 PAS 0.035 0.49 TERM
TEXT VSCA
COLO PAPE
SLER CAM1 1 NFRA 1
FREQ 10
TRAC OFFS FICH AVI
GOTR LOOP 99 OFFS FICH AVI CONT NOCL DEFO REND
GO
TRAC OFFS FICH AVI CONT DEFO REND
ENDPLAY
FIN

NOCL NFTO 101 FPS 15 KFRE 10 COMP -1 DEFO REND

BEGIN DESCRIPTION

A bi-unit quadrilateral shell is subjected to an imposed elongation up to 3
times the initial length along one of the axes (by an imposed
constant velocity).

The material is VPJC and the purpose is to test the material model
under large strains. The effects of strain rate and of
temperature are neglected (m=0, C=0).

The result is compared with an analytical solution, showing
good agreement.

END DESCRIPTION

q4gss1.epx

Q4GSS1
ECHO
!CONV WIN
TRID LAGR
GEOM LIBR POIN 4 Q4GS 1 TERM

0 0 0
1 2 3 4

1 0 0

1 1 0

0 1 0

COMP EPAI 1.0 LECT 1 TERM
MATE VM23 RO 8000 YOUN 2.E11 NU 0.3 ELAS 2.E11

TRAC 1 2.E11 1.0
LECT 1 TERM
LINK COUP BLOQ 1 LECT 1 4 TERM

VITE 1 1.0 FONC 1 LECT 2 3 TERM

FONC NUM 1 TABL 2 0.0 1.0
1.0 1.0

INIT VITE 1 1.0 LECT 2 3 TERM
ECRI COOR DEPL VITE ACCE FINT FEXT FLIA FDEC CONT EPST ECRO FREQ 5000

FICH ALIC FREQ 50

OPTI NOTE PAS UTIL CSTA 0.5E0

LMST

CALC TINI 0 TFIN 1.0 PASF 2.E-5 NMAX 50000
SUIT
Post-treatment
ECHO

RESU ALIC GARD PSCR
SORT GRAP
AXTE 1.0 ’Time [s]’
COUR 1 ’dx_1’ DEPL COMP 1 NOEU LECT 1 TERM
COUR 2 ’dx_2’ DEPL COMP 1 NOEU LECT 2 TERM
COUR 3 ’dx_3’ DEPL COMP 1 NOEU LECT 3 TERM
COUR 4 ’dx_4’ DEPL COMP 1 NOEU LECT 4 TERM
COUR 5 ’fx_1’ FLIA COMP 1 NOEU LECT 1 TERM
COUR 6 ’fx_2’ FLIA COMP 1 NOEU LECT 2 TERM
COUR 7 ’fx_3’ FLIA COMP 1 NOEU LECT 3 TERM
COUR 8 ’fx_4’ FLIA COMP 1 NOEU LECT 4 TERM
COUR 11 ’s1_1’ CONT COMP 1 ELEM LECT 1 TERM
COUR 12 ’s2_1’ CONT COMP 2 ELEM LECT 1 TERM
COUR 13 ’s3_1’ CONT COMP 3 ELEM LECT 1 TERM
COUR 14 ’s4_1’ CONT COMP 4 ELEM LECT 1 TERM
COUR 15 ’s5_1’ CONT COMP 5 ELEM LECT 1 TERM
COUR 16 ’s6_1’ CONT COMP 6 ELEM LECT 1 TERM
COUR 21 ’e1_1’ EPST COMP 1 ELEM LECT 1 TERM
COUR 22 ’e2_1’ EPST COMP 2 ELEM LECT 1 TERM
COUR 23 ’e3_1’ EPST COMP 3 ELEM LECT 1 TERM
COUR 24 ’e4_1’ EPST COMP 4 ELEM LECT 1 TERM
COUR 25 ’e5_1’ EPST COMP 5 ELEM LECT 1 TERM
COUR 26 ’e6_1’ EPST COMP 6 ELEM LECT 1 TERM
COUR 50 ’fx_sum’ FLIA COMP 1 ZONE LECT 2 3 TERM
TRAC 1 2 3 4 AXES 1.0 ’DISPL. [M]’ YZER
TRAC 5 6 7 8 AXES 1.0 ’FORCE [N]’ YZER
TRAC 11 12 13 14 15 16 AXES 1.0 ’STRESS [PA]’ YZER
TRAC 21 22 23 24 25 26 AXES 1.0 ’STRAIN [-]’ YZER
TRAC 11 AXES 1.0 ’STRESS [PA]’ XAXE 21 1.0 ’STRAIN [-]’ YZER
QUAL EPST COMP 1 LECT 1 TERM REFE 0.69315E+00 TOLE 1.E-2 ! EPS-XX
EPST COMP 2 LECT 1 TERM REFE -0.20794E+00 TOLE 1.E-3 ! EPS-YY
EPST COMP 4 LECT 1 TERM REFE -0.20794E+00 TOLE 1.E-2 ! EPS-ZZ
CONT COMP 1 LECT 1 TERM REFE 0.13863E+12 TOLE 1.E-2 ! SIG-XX
0.91461E+11 TOLE 1.E-2 ! FX-SUM
COUR 50

REFE

FIN

q4gss2.epx

Q4GSS2
ECHO
!CONV WIN
TRID LAGR
GEOM LIBR POIN 4 Q4GS 1 TERM

0 0 0
1 2 3 4

1 0 0

1 1 0

0 1 0

COMP EPAI 1.0 LECT 1 TERM
MATE VM23 RO 8000 YOUN 2.E11 NU 0.3 ELAS 4.E8

TRAC 2 4.E8 2.E-3

4.E8 1.E0

LECT 1 TERM
LINK COUP BLOQ 1 LECT 1 4 TERM

VITE 1 1.0 FONC 1 LECT 2 3 TERM

FONC NUM 1 TABL 2 0.0 1.0
1.0 1.0

INIT VITE 1 1.0 LECT 2 3 TERM
ECRI COOR DEPL VITE ACCE FINT FEXT FLIA FDEC CONT EPST ECRO FREQ 5000

FICH ALIC FREQ 50

OPTI NOTE PAS UTIL CSTA 0.5E0

LMST

CALC TINI 0 TFIN 1.0 PASF 2.E-5 NMAX 50000
SUIT
Post-treatment
ECHO
RESU ALIC GARD PSCR
SORT GRAP
AXTE 1.0 ’Time [s]’
COUR 1 ’dx_1’ DEPL COMP 1 NOEU LECT 1 TERM
COUR 2 ’dx_2’ DEPL COMP 1 NOEU LECT 2 TERM
COUR 3 ’dx_3’ DEPL COMP 1 NOEU LECT 3 TERM
COUR 4 ’dx_4’ DEPL COMP 1 NOEU LECT 4 TERM
COUR 5 ’fx_1’ FLIA COMP 1 NOEU LECT 1 TERM
COUR 6 ’fx_2’ FLIA COMP 1 NOEU LECT 2 TERM
COUR 7 ’fx_3’ FLIA COMP 1 NOEU LECT 3 TERM
COUR 8 ’fx_4’ FLIA COMP 1 NOEU LECT 4 TERM
COUR 11 ’s1_1’ CONT COMP 1 ELEM LECT 1 TERM
COUR 12 ’s2_1’ CONT COMP 2 ELEM LECT 1 TERM
COUR 13 ’s3_1’ CONT COMP 3 ELEM LECT 1 TERM
COUR 14 ’s4_1’ CONT COMP 4 ELEM LECT 1 TERM
COUR 15 ’s5_1’ CONT COMP 5 ELEM LECT 1 TERM
COUR 16 ’s6_1’ CONT COMP 6 ELEM LECT 1 TERM
COUR 21 ’e1_1’ EPST COMP 1 ELEM LECT 1 TERM
COUR 22 ’e2_1’ EPST COMP 2 ELEM LECT 1 TERM
COUR 23 ’e3_1’ EPST COMP 3 ELEM LECT 1 TERM
COUR 24 ’e4_1’ EPST COMP 4 ELEM LECT 1 TERM
COUR 25 ’e5_1’ EPST COMP 5 ELEM LECT 1 TERM
COUR 26 ’e6_1’ EPST COMP 6 ELEM LECT 1 TERM
COUR 50 ’fx_sum’ FLIA COMP 1 ZONE LECT 2 3 TERM
TRAC 1 2 3 4 AXES 1.0 ’DISPL. [M]’ YZER
TRAC 5 6 7 8 AXES 1.0 ’FORCE [N]’ YZER
TRAC 11 12 13 14 15 16 AXES 1.0 ’STRESS [PA]’ YZER
TRAC 21 22 23 24 25 26 AXES 1.0 ’STRAIN [-]’ YZER
TRAC 11 AXES 1.0 ’STRESS [PA]’ XAXE 21 1.0 ’STRAIN [-]’ YZER
QUAL EPST COMP 1 LECT 1 TERM REFE 0.69315E+00 TOLE 1.E-2 ! EPS-XX
EPST COMP 2 LECT 1 TERM REFE -0.34657E+00 TOLE 1.E-3 ! EPS-YY
EPST COMP 4 LECT 1 TERM REFE -0.34657E+00 TOLE 1.E-2 ! EPS-ZZ
CONT COMP 1 LECT 1 TERM REFE 0.40000E+09 TOLE 1.E-2 ! SIG-XX
0.20000E+08 TOLE 1.E-2 ! FX-SUM
COUR 50

REFE

FIN

q4gss3.epx

9

Q4GSS3
ECHO
!CONV WIN
TRID LAGR
GEOM LIBR POIN 4 Q4GS 1 TERM

0 0 0
1 2 3 4

1 0 0

1 1 0

0 1 0

COMP EPAI 1.0 LECT 1 TERM
MATE LINE RO 8000 YOUN 2.E11 NU 0.3

LECT 1 TERM
LINK COUP BLOQ 1 LECT 1 4 TERM

VITE 1 1.0 FONC 1 LECT 2 3 TERM

FONC NUM 1 TABL 2 0.0 1.0
1.0 1.0

INIT VITE 1 1.0 LECT 2 3 TERM
ECRI COOR DEPL VITE ACCE FINT FEXT FLIA FDEC CONT EPST ECRO FREQ 5000

FICH ALIC FREQ 50

OPTI NOTE PAS UTIL CSTA 0.5E0

LMST ! This should have no effect with LINE material ...

CALC TINI 0 TFIN 1.0 PASF 2.E-5 NMAX 50000
SUIT
Post-treatment
ECHO
RESU ALIC GARD PSCR
SORT GRAP
AXTE 1.0 ’Time [s]’
COUR 1 ’dx_1’ DEPL COMP 1 NOEU LECT 1 TERM
COUR 2 ’dx_2’ DEPL COMP 1 NOEU LECT 2 TERM
COUR 3 ’dx_3’ DEPL COMP 1 NOEU LECT 3 TERM
COUR 4 ’dx_4’ DEPL COMP 1 NOEU LECT 4 TERM
COUR 5 ’fx_1’ FLIA COMP 1 NOEU LECT 1 TERM
COUR 6 ’fx_2’ FLIA COMP 1 NOEU LECT 2 TERM
COUR 7 ’fx_3’ FLIA COMP 1 NOEU LECT 3 TERM
COUR 8 ’fx_4’ FLIA COMP 1 NOEU LECT 4 TERM
COUR 11 ’s1_1’ CONT COMP 1 ELEM LECT 1 TERM
COUR 12 ’s2_1’ CONT COMP 2 ELEM LECT 1 TERM
COUR 13 ’s3_1’ CONT COMP 3 ELEM LECT 1 TERM
COUR 14 ’s4_1’ CONT COMP 4 ELEM LECT 1 TERM
COUR 15 ’s5_1’ CONT COMP 5 ELEM LECT 1 TERM
COUR 16 ’s6_1’ CONT COMP 6 ELEM LECT 1 TERM
COUR 21 ’e1_1’ EPST COMP 1 ELEM LECT 1 TERM
COUR 22 ’e2_1’ EPST COMP 2 ELEM LECT 1 TERM
COUR 23 ’e3_1’ EPST COMP 3 ELEM LECT 1 TERM
COUR 24 ’e4_1’ EPST COMP 4 ELEM LECT 1 TERM
COUR 25 ’e5_1’ EPST COMP 5 ELEM LECT 1 TERM
COUR 26 ’e6_1’ EPST COMP 6 ELEM LECT 1 TERM
COUR 50 ’fx_sum’ FLIA COMP 1 ZONE LECT 2 3 TERM
TRAC 1 2 3 4 AXES 1.0 ’DISPL. [M]’ YZER
TRAC 5 6 7 8 AXES 1.0 ’FORCE [N]’ YZER
TRAC 11 12 13 14 15 16 AXES 1.0 ’STRESS [PA]’ YZER
TRAC 21 22 23 24 25 26 AXES 1.0 ’STRAIN [-]’ YZER
TRAC 11 AXES 1.0 ’STRESS [PA]’ XAXE 21 1.0 ’STRAIN [-]’ YZER
TRAC 50 AXES 1.0 ’TOT. FORCE [N]’ YZER
QUAL EPST COMP 1 LECT 1 TERM REFE 0.69315E+00 TOLE 1.E-2 ! EPS-XX
EPST COMP 2 LECT 1 TERM REFE -0.20794E+00 TOLE 1.E-3 ! EPS-YY
EPST COMP 4 LECT 1 TERM REFE -0.20794E+00 TOLE 1.E-2 ! EPS-ZZ
EPST COMP 4 LECT 1 TERM REFE 0.00000E+00 TOLE 1.E-2 ! EPS-ZZ
CONT COMP 1 LECT 1 TERM REFE 0.13863E+12 TOLE 1.E-2 ! SIG-XX
0.91461E+11 TOLE 1.E-2 ! FX-SUM
COUR 50

REFE

!

FIN

q4gss4.epx

Q4GSS4
ECHO
!CONV WIN
TRID LAGR
GEOM LIBR POIN 4 Q4GS 1 TERM

0 0 0
1 2 3 4

1 0 0

1 1 0

0 1 0

COMP EPAI 1.0 LECT 1 TERM
MATE VMIS PARF RO 8000 YOUN 2.E11 NU 0.3 ELAS 2.E11

LECT 1 TERM
LINK COUP BLOQ 1 LECT 1 4 TERM

VITE 1 1.0 FONC 1 LECT 2 3 TERM

FONC NUM 1 TABL 2 0.0 1.0
1.0 1.0

INIT VITE 1 1.0 LECT 2 3 TERM
ECRI COOR DEPL VITE ACCE FINT FEXT FLIA FDEC CONT EPST ECRO FREQ 5000

FICH ALIC FREQ 50

OPTI NOTE PAS UTIL CSTA 0.5E0

LMST

CALC TINI 0 TFIN 1.0 PASF 2.E-5 NMAX 50000
SUIT
Post-treatment
ECHO
RESU ALIC GARD PSCR
SORT GRAP
AXTE 1.0 ’Time [s]’
COUR 1 ’dx_1’ DEPL COMP 1 NOEU LECT 1 TERM
COUR 2 ’dx_2’ DEPL COMP 1 NOEU LECT 2 TERM

COUR 3 ’dx_3’ DEPL COMP 1 NOEU LECT 3 TERM
COUR 4 ’dx_4’ DEPL COMP 1 NOEU LECT 4 TERM
COUR 5 ’fx_1’ FLIA COMP 1 NOEU LECT 1 TERM
COUR 6 ’fx_2’ FLIA COMP 1 NOEU LECT 2 TERM
COUR 7 ’fx_3’ FLIA COMP 1 NOEU LECT 3 TERM
COUR 8 ’fx_4’ FLIA COMP 1 NOEU LECT 4 TERM
COUR 11 ’s1_1’ CONT COMP 1 ELEM LECT 1 TERM
COUR 12 ’s2_1’ CONT COMP 2 ELEM LECT 1 TERM
COUR 13 ’s3_1’ CONT COMP 3 ELEM LECT 1 TERM
COUR 14 ’s4_1’ CONT COMP 4 ELEM LECT 1 TERM
COUR 15 ’s5_1’ CONT COMP 5 ELEM LECT 1 TERM
COUR 16 ’s6_1’ CONT COMP 6 ELEM LECT 1 TERM
COUR 21 ’e1_1’ EPST COMP 1 ELEM LECT 1 TERM
COUR 22 ’e2_1’ EPST COMP 2 ELEM LECT 1 TERM
COUR 23 ’e3_1’ EPST COMP 3 ELEM LECT 1 TERM
COUR 24 ’e4_1’ EPST COMP 4 ELEM LECT 1 TERM
COUR 25 ’e5_1’ EPST COMP 5 ELEM LECT 1 TERM
COUR 26 ’e6_1’ EPST COMP 6 ELEM LECT 1 TERM
COUR 50 ’fx_sum’ FLIA COMP 1 ZONE LECT 2 3 TERM
TRAC 1 2 3 4 AXES 1.0 ’DISPL. [M]’ YZER
TRAC 5 6 7 8 AXES 1.0 ’FORCE [N]’ YZER
TRAC 11 12 13 14 15 16 AXES 1.0 ’STRESS [PA]’ YZER
TRAC 21 22 23 24 25 26 AXES 1.0 ’STRAIN [-]’ YZER
TRAC 11 AXES 1.0 ’STRESS [PA]’ XAXE 21 1.0 ’STRAIN [-]’ YZER
QUAL EPST COMP 1 LECT 1 TERM REFE 0.69315E+00 TOLE 1.E-2 ! EPS-XX
EPST COMP 2 LECT 1 TERM REFE -0.20794E+00 TOLE 1.E-3 ! EPS-YY
EPST COMP 4 LECT 1 TERM REFE -0.20794E+00 TOLE 1.E-2 ! EPS-ZZ
CONT COMP 1 LECT 1 TERM REFE 0.13863E+12 TOLE 1.E-2 ! SIG-XX
0.91461E+11 TOLE 1.E-2 ! FX-SUM
COUR 50

REFE

FIN

q4gss5.epx

Q4GSS5
ECHO
!CONV WIN
TRID LAGR
GEOM LIBR POIN 4 Q4GS 1 TERM

0 0 0
1 2 3 4

1 0 0

1 1 0

0 1 0

COMP EPAI 1.0 LECT 1 TERM
MATE VMIS PARF RO 8000 YOUN 2.E11 NU 0.3 ELAS 4.E8

LECT 1 TERM
LINK COUP BLOQ 1 LECT 1 4 TERM

VITE 1 1.0 FONC 1 LECT 2 3 TERM

FONC NUM 1 TABL 2 0.0 1.0
1.0 1.0

INIT VITE 1 1.0 LECT 2 3 TERM
ECRI COOR DEPL VITE ACCE FINT FEXT FLIA FDEC CONT EPST ECRO FREQ 5000

FICH ALIC FREQ 50

OPTI NOTE PAS UTIL CSTA 0.5E0

LMST

CALC TINI 0 TFIN 1.0 PASF 2.E-5 NMAX 50000
SUIT
Post-treatment
ECHO
RESU ALIC GARD PSCR
SORT GRAP
AXTE 1.0 ’Time [s]’
COUR 1 ’dx_1’ DEPL COMP 1 NOEU LECT 1 TERM
COUR 2 ’dx_2’ DEPL COMP 1 NOEU LECT 2 TERM
COUR 3 ’dx_3’ DEPL COMP 1 NOEU LECT 3 TERM
COUR 4 ’dx_4’ DEPL COMP 1 NOEU LECT 4 TERM
COUR 5 ’fx_1’ FLIA COMP 1 NOEU LECT 1 TERM
COUR 6 ’fx_2’ FLIA COMP 1 NOEU LECT 2 TERM
COUR 7 ’fx_3’ FLIA COMP 1 NOEU LECT 3 TERM
COUR 8 ’fx_4’ FLIA COMP 1 NOEU LECT 4 TERM
COUR 11 ’s1_1’ CONT COMP 1 ELEM LECT 1 TERM
COUR 12 ’s2_1’ CONT COMP 2 ELEM LECT 1 TERM
COUR 13 ’s3_1’ CONT COMP 3 ELEM LECT 1 TERM
COUR 14 ’s4_1’ CONT COMP 4 ELEM LECT 1 TERM
COUR 15 ’s5_1’ CONT COMP 5 ELEM LECT 1 TERM
COUR 16 ’s6_1’ CONT COMP 6 ELEM LECT 1 TERM
COUR 21 ’e1_1’ EPST COMP 1 ELEM LECT 1 TERM
COUR 22 ’e2_1’ EPST COMP 2 ELEM LECT 1 TERM
COUR 23 ’e3_1’ EPST COMP 3 ELEM LECT 1 TERM
COUR 24 ’e4_1’ EPST COMP 4 ELEM LECT 1 TERM
COUR 25 ’e5_1’ EPST COMP 5 ELEM LECT 1 TERM
COUR 26 ’e6_1’ EPST COMP 6 ELEM LECT 1 TERM
COUR 50 ’fx_sum’ FLIA COMP 1 ZONE LECT 2 3 TERM
TRAC 1 2 3 4 AXES 1.0 ’DISPL. [M]’ YZER
TRAC 5 6 7 8 AXES 1.0 ’FORCE [N]’ YZER
TRAC 11 12 13 14 15 16 AXES 1.0 ’STRESS [PA]’ YZER
TRAC 21 22 23 24 25 26 AXES 1.0 ’STRAIN [-]’ YZER
TRAC 11 AXES 1.0 ’STRESS [PA]’ XAXE 21 1.0 ’STRAIN [-]’ YZER
QUAL EPST COMP 1 LECT 1 TERM REFE 0.69315E+00 TOLE 1.E-2 ! EPS-XX
EPST COMP 2 LECT 1 TERM REFE -0.34657E+00 TOLE 1.E-3 ! EPS-YY
EPST COMP 4 LECT 1 TERM REFE -0.34657E+00 TOLE 1.E-2 ! EPS-ZZ
CONT COMP 1 LECT 1 TERM REFE 0.40000E+09 TOLE 1.E-2 ! SIG-XX
0.20000E+08 TOLE 1.E-2 ! FX-SUM
COUR 50

REFE

FIN

10

List of input ﬁles

B
bm str vpjc q4gss3.epx . . . . . . . . . . . . . . . . . . . . . . . . 8
bm str vpjc t3gss3.epx . . . . . . . . . . . . . . . . . . . . . . . . . 8

Q
q4gss1.epx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
q4gss2.epx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
q4gss3.epx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
q4gss4.epx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
q4gss5.epx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

11

 
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JRC Mission 

As the Commission’s  
in-house science service,  
the Joint Research Centre’s  
mission is to provide EU  
policies with independent,  
evidence-based scientific  
and technical support  
throughout the whole  
policy cycle. 

Working in close  
cooperation with policy  
Directorates-General,  
the JRC addresses key  
societal challenges while  
stimulating innovation  
through developing  
new methods, tools  
and standards, and sharing  
its know-how with  
the Member States,  
the scientific community  
and international partners. 

Serving society  
Stimulating innovation  
Supporting legislation 

doi:10.2788/888282 

ISBN 978-92-79-57731-4 

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