WO2006135298A1

WO2006135298A1 - Device and method for use in producing packages

Info

Publication number: WO2006135298A1
Application number: PCT/SE2006/000421
Authority: WO
Inventors: John Dexborg
Original assignee: Tetra Laval Holdings & Finance S.A.
Priority date: 2005-06-15
Filing date: 2006-04-10
Publication date: 2006-12-21
Also published as: CN1880173A; CN100548810C; RU2008101545A; RU2388666C2; BRPI0611587B1; BRPI0611587A2; TR200708434T1

Abstract

A device (14) for holding a tube portion (62) during sealing for obtaining an upper transverse seal (64) of the tube, the portion being arranged between the upper and a lower transverse seal (66) of the tube, is provided. It is arranged to control a cross section of a first part (62a) of the portion, by directly contacting it, to have a first extension (72) in a first direction (x) essentially perpendicular to a longitudinal tube direction (67). It is characterized in being arranged to control a cross section of a second part (62b) of the portion, by directly contacting it, to have a second extension (74) in the first direction, the first part being arranged between the lower transverse seal and the second part, the second part being arranged between the upper transverse seal and the first part, and the first extension being larger than the second extension.

Description

DEVICE AND METHOD FOR USE IN PRODUCING PACKAGES

Technical Field of the Invention

The present invention relates to a device and a method for holding a portion of a tube of packaging material during sealing for obtaining an upper transverse seal of the tube, the portion being arranged between the upper transverse seal and a lower transverse seal of the tube, wherein the device is arranged to control a cross section of a first part of the portion, by being in direct contact with it, so as to have a first tube extension in a first direction essentially perpendicular to a longitudinal direction of the tube. Background Art

Within packaging technology, use has long been made of packages for packing and transporting products such as milk, juice and other beverages. A large group of these packages is produced from a laminated packaging material comprising a core layer of, for example, paper or paper- board and an outer, liquid-tight coating of thermoplastic material on at least that side of the core layer which forms the inside of the package. Sometimes the material also includes a gas barrier, for example in the form of an aluminum layer .

Such packaging containers are often produced in that a web of packaging material is formed into a tube by sealing the longitudinal overlapping . edges of the web. The tube is continuously filled with a product and then transversally sealed and formed into cushions . The sealing is made along narrow, transverse, mutually spaced apart, sealing zones. The transverse sealing of the tube takes place in a per se known manner substantially at right angles to the longitudinal direction of the tube and constantly in the same plane. The sealed-off portions of the tube thus containing contents are thereafter separated from the tube by means of incisions in these sea- ling zones . This technology of forming a tube from a web is well known per se and will not be described in detail.

In a known machine for producing packages like the ones described above, the transverse sealing of the tube is effected by arranging the tube between two opposing jaws. The jaws each comprises a sealing bar, the tube being squeezed flat between these sealing bars to heat the thermoplastic material in the sealing zone and obtain the seal. To make sure that the final cushion shaped package contains the right volume of product, each of the jaws further comprises a plate, or a so-called volume flap. In connection with the sealing, these volume flaps are positioned with a predetermined mutual distance. In this position, the flaps apply a pressure onto the tube to squeeze it and give it a thickness equal said predetermined mutual distance in a direction perpendicular to a longitudinal axis of the tube.

In connection with this known way of obtaining a transverse seal of a tube, the packaging material may be subjected to considerable stress. In turn, this may cause unwanted deformation of the tube wall, .such as indentations, especially in the areas between the volume flaps extending along the longitudinal axis of the tube. If such a deformation occurs in the area of the sealing zone, the resulting seal may be negatively affected. For example, instead of getting a plain seal consisting of two layers of the packaging material, a seal with double- folded corners, which means four layers of packaging material, may be obtained. This may, in some situations, lead to channels in the seals and, accordingly, leaking packages . Summary of the Invention

An object of the present invention is to provide a device and a method for holding a tube of packaging material during transverse sealing of the same for obtaining a package, which- device and method, at least partly, eliminate any limitations of prior art. The basic concept of the invention is to stabilize the form of the package during the transverse sealing to reduce the stress in the packaging material in the sealing zone to such an extent that unwanted deformation of the resulting seal can be avoided. This can be achieved by deliberately deforming the package in an area outside the sealing zone prior to sealing to control the location of package deformation.

The device and the method for achieving the object above are defined in the appended claims and discussed below.

A device for holding a portion of a tube of packaging material during sealing for obtaining an upper transverse seal of the tube, the portion being arranged between the upper transverse seal and a lower transverse seal of the tube, according to the present invention, is arranged to control a cross section of a first part of the portion, by being in direct contact with it, so as to have a first tube extension in a first direction essentially perpendicular to a longitudinal direction of the tube. The device is characterized in that it further is arranged to control a cross section of a second part of the portion, by being in direct contact with it, so as to have a second tube extension in the first direction, the first part being arranged between the lower transverse seal of the tube and the second part of the portion, the second part being arranged between the upper transverse seal of the tube and the first part of the portion, and the first tube extension being larger than the second tube extension. One advantage with the present invention is that already existing devices for holding a tube of packaging material during transverse sealing of the same can be modified so as to embody the inventive way of holding the tube. For example, the volume flaps in the initially discussed known machine could be reconstructed so as to act on the tube differently in different areas of a future package.

Said portion is arranged to form a piece of a final package limited by the upper and lower transverse seals.

By actively controlling the cross section of the first and second parts so as to obtain the above-described first and second extensions, an intentional deformation of the package material can be produced in an area of the package where it does not affect the resulting seal. Thus, the stress in the packaging material in the sealing zone can be significantly reduced, whereby a proper upper transverse seal can be achieved. On the contrary, if a deformation is not deliberately created in an area outside the sealing zone, an uncontrolled deformation may instead occur in the sealing zone, which may result in a seal with double-folded corners.

According to one embodiment the upper and lower transverse seals are essentially parallel to each other and essentially perpendicular to the first direction. Such an embodiment could be used in connection with the production of cushion shaped packages like the ones initially described which packages can be manufactured relatively simple and inexpensive.

According to one embodiment, the device comprises two opposing volume elements. They are separated by a volume distance and moveable in relation to each other so as to have a releasing state, in which the tube is moveable in relation to the volume elements, and a securing state, in. which the first part of the portion of the tube is arranged to be held between the volume elements . Further, the volume elements are arranged to be in contact .with an outer surface of the first part of the portion of the tube with a predetermined volume distance in the securing state to control the cross section of the first part of the portion.

The volume elements are moveable in relation to each other, and therefore also the tube. The volume elements can move in relation to each other in any suitable way, such as for example by a rotational or translational motion. Depending on the type of motion, the volume dis- tance may be variable. By volume distance is meant the distance between two fixed corresponding points on the respective volume elements.

The inventive device can be constructed so as to further comprise, besides for the volume elements, two opposing deformation elements. They are separated by a deformation distance and moveable in relation to the tube so as to have a releasing state, in which the tube is moveable in relation to the deformation elements, and a securing state, in which the second part of the portion of the tube is arranged to be held between the deformation elements. Further, the deformation elements are arranged to be in contact with an outer surface of the second part of portion of the tube with a predetermined deformation distance in the securing state to control the cross section of the second part of the portion.

The deformation element are moveable in relation to the tube, and in some embodiments also each other. Similar to the volume elements, the deformation elements can move in relation to the tube in any suitable way, such as for example by a rotational or translational motion. Further, just like above, the deformation distance may be variable. By deformation distance is meant the distance between two fixed corresponding points on the respective deformation elements . One advantage with a variable deformation distance and/or volume distance is that it might be easier to arrange the device in contact with the tube in the securing state since the deformation distance and/or volume distance could be smaller in the securing state than in the releasing state.

The volume and deformation elements can be relatively arranged in any suitable way. However, according to one embodiment, each of the deformation elements is arranged at a respective one of the volume elements . Such an embodiment covers all types of appropriate arrangements, such as for example that the deformation elements are integrally formed with, fixedly attached to, pivotal- Iy attached to, or just in contact with, the volume elements. For example, in a case where the deformation elements are integrally formed with the volume elements, the volume and deformation distances changes in accordance with one another.

The deformation elements can be constructed in a large number of ways. In accordance with one possible embodiment, each of the deformation elements is arranged as a projection from a tube contact surface of a respective one of the volume elements. As the name implies, the tube contact surface is that surface of the respective volume element that is arranged to be in contact with the tube in the securing state. Such an embodiment means that the deformation distance at all times will be less than the volume distance at a certain location by the deformation elements .

The inventive device can be constructed in such a way that a deformation extension of the deformation elements in a direction perpendicular to the first direction is smaller than a half periphery of the tube. In other words, the extension of the deformation elements in a direction parallel to the transverse seals is less than the extension of the tube, in a direction parallel to the transverse seals, in a flat-laid condition. In such an embodiment, it is possible for the deformation elements to act on limited parts of the tube to achieve the desired objective efficiently.

According to one embodiment, the deformation elements are formed so that the predetermined deformation distance in the securing state varies along a direction perpendicular to the first direction. This means that the cross section of the deformation elements is varying along a direction parallel to the upper and lower transverse seals.

The features described in the two above paragraphs, i.e. the limited deformation extension and the varying deformation distance, may both contribute to the cross section of the second part of the portion having a second tube extension varying along a direction parallel to the upper and lower transverse seals . This is advantageous for the deliberate creation of tube deformation in an area outside the sealing zone.

According to one possible embodiment of the device, the deformation elements are constructed so that a predetermined center deformation distance is smaller than predetermined end deformation distances . As the name implies, center deformation distance means the deformation distance between two fixed corresponding center points on the respective deformation elements. Correspondingly, end deformation distances mean the deformation distances between two fixed corresponding end points on the respective deformation elements, the deformation elements each having two ends resulting in two, possibly equal, end deformation distances . One example of a deformation element configuration having the above described features is the half pillow shape, which is highly advantageous in connection with the present invention.

For the sake of clarity it should be pointed out that the volume and deformation elements, and therefore the complete device, are in the securing state during transverse sealing and in the releasing state before and after sealing.

A method for holding a portion of a tube of packaging material during sealing for obtaining an upper transverse seal of the tube, the portion being arranged between the upper transverse seal and a lower transverse seal of the tube, according to the present invention, comprises controlling a cross section of a first part of the portion, by being in direct contact with it, so as to have a first tube extension in a first direction essentially perpendicular to a longitudinal direction of the tube. The method is characterized by further comprising controlling a cross section of a second part of the portion, by being in direct contact with, it, so as to have a second tube extension in the first direction. The first part is arranged between the lower transverse seal of the tube and the second part of the portion, the second part is arranged between the upper transverse seal of the tube and the first part of the portion, and the first tube extension is larger than the second tube extension.

The characteristics discussed in connection with the device are, of course, transferable to the method according to the present invention. Further, it should be stressed that the above-discussed characteristics may be combined in the same embodiment. Brief Description of the Drawings

The invention will be described in more detail with reference to the appended schematic drawings, which show an example of a presently preferred embodiment of the present invention.

Fig. Ia is a perspective view of a part of the device according to the present invention.

Fig. Ib is a perspective view of another part of the device according to the present invention.

Fig. 2a is a front view of a package produced by means of the device according to the present invention.

Fig. 2b is a side view of the package of fig. 2b.

Fig. 2c is a schematic cross section of the package, taken along line I-I in fig. 2a, when held by the device in the securing state.

Fig. 2d is a schematic cross section of the package, taken along line II-II in fig. 2b, when held by the device in the securing state.

Fig. 3a is a side view of the device according to the present invention, arranged with a package as shown in fig. 2a and 2b, in the securing state.

Fig. 3b is a side view of the device according to the present invention, arranged with no package, in the intermediate state.

Fig. 3c is a top view showing the deformation elements in their securing state. Fig. 4 is a schematic side view of an apparatus for transverse sealing.

.Fig. 5 is a perspective view of a part of the apparatus of fig. 4, schematically illustrated with a package for the purpose of clarity.

Fig. 6 is a flow chart illustrating a method for transverse sealing. Detailed Description of Preferred Embodiments

Fig. Ia shows a heating jaw 10, and fig. Ib shows a counter jaw 12, together forming the device 14 according to the present invention. The device 14 is to be used in producing packages 16 like the one illustrated in fig. 2a and 2b. The device 14 has different states, a releasing state as illustrated in fig. Ia + Ib, a securing state which is illustrated in fig. 3a, and an intermediate state of which an example is illustrated in fig. 3b. Releasing state corresponds to a device condition where a tube of packaging material is movable in relation to the device, as will be discussed in more detail below. In a similar way, securing state corresponds to a device condition where a portion of the tube is held between the jaws 10 and 12. Intermediate state is a generic term for all device conditions between releasing and securing state.

The jaws 10 and 12 each comprise a volume element 18 and 20, respectively, in the form of larger rectangular plates provided with smaller rectangular plates. The smaller rectangular plates are provided for the special purpose of fine adjustment of the package volume and will not be described further herein. Further, the jaws each comprise a deformation element, 22 and 24, respectively, fixedly attached to, and arranged as a projection from, a tube contact surface 26, 28 of the respective volume element 18, 20. As apparent from the figures, each of the deformation elements have the shape of half a pillow with the plane surface abutting against the corresponding tube contact surface of the volume elements and the curved surface arranged to be in contact with the tube of packaging material . The deformation elements are rigid components and will not be deformed in ordinary operation of the device.

The volume elements are separated by a volume distance, equal to the shortest distance between two corresponding points on the volume elements . As will be described in further detail below, the volume distance is variable and differs between the. states of the device 14. In the securing state, the volume elements are arranged with- their tube contact surfaces parallel and facing each other. This means that the volume distance in the securing state will be the same between at any two corresponding points on the tube contact surfaces. Similarly, the deformation elements are separated by a deformation distance, equal to the shortest distance between two corresponding points on the curved surface of the deformation elements. Further, the deformation distance is variable and differs between the states of the device 14. In the securing state, as illustrated in figure 3c_# the deformation elements are arranged with their curved surfaces facing each other, and their plane surfaces being parallel. This means that the deformation distance in the securing state will be varying along the deformation extension 27 of the deformation elements 22, 24 in a direction parallel to the tube contact surfaces and perpendicular to a longitudinal direction of the tube. In this particular embodiment, where the deformation elements are formed as half pillows, this means, in the securing state, that the deformation distance in the middle of the deformation elements, i.e. the center deformation distance 29, will be smaller than the deformation distances at the edges of the deformation elements, i.e. the end deformation distances 31.

Fig. 4 schematically illustrates an apparatus 38 for transverse sealing of a tube 40 of packaging material comprising nine devices 14 like the ones described above. For the sake of clarity, only one device 14 is illustrated in the figure. The packaging material is of the initially described type, i.e. a paper core layer coated with a thermoplastic material. The apparatus 38 includes two transport chains 42 and 44 moving at a constant speed along paths defined by drive means 46, 48 and 50, 52, respectively. The heating jaws 10 are arranged in succession evenly along the chain 42, whereas the counter jaws 12 are correspondingly arranged along the chain 44. This successive arrangement is illustrated for two of the heating jaws in fig. 5. The tube 40, schematically illustrated by dashed lines, is arranged to be received in the area between the chains 42 and 44 and is fed at the speed of the chains. In this area, each of the heating jaws 10 is arranged to engage with a corresponding one of the counter jaws 12 to make a transverse seal of the tube and cut the tube in the area of this seal. The engagement is effected by means of engagement means 54 and 56 comprised in the heating jaw 10 and the counter jaw 12, respectively. The heating jaw further includes a heating bar 58 arranged to interact with a sealing dolly 60 included in the counter jaw to effect the transverse sealing. Additionally, the heating jaw comprises a cutting means (not shown) arranged to move in a slot 59 in the heating bar 58 to cut the tube after sealing.

Fig. 6 illustrates a method of transverse sealing according to which the apparatus 38 operates. To explain this operation, one of the devices 14 will be followed through a complete cycle. The cycle begins at point α (see fig. 4) and the method starts with moving the jaws of the device in question from this point to point β (step A) . During this movement, the jaws, and therefore the device, are in the releasing state. The jaws have no contact neither with the tube nor each other during this phase of the cycle. When passing point β, the jaws 10, 12 will engage with each other (step B) by the engagement means 54, 56, as illustrated in fig. 3b. Hereby, the de- vice changes from the releasing state to the intermediate state. The jaws are in contact with each other and the tube, and moves with the tube.

At the moment of jaw engagement, the volume elements are inclined away from each other, as illustrated in fig. 3b. The inclination will decrease with the continuous motion, and when the device enters the securing state by the volume elements obtaining the securing state (step C) and the deformation elements obtaining the securing state (step D) , it will be essentially zero, as described above and illustrated in fig. 3a. With the volume and deformation elements arranged like this, a portion of the tube is held (step E) for subsequent transverse sealing (step F) and cutting (step G) , as will be further discussed below.

The portion 62 (62a + 62b) held by the device forms a piece of a package 16, as illustrated in fig. 2a, 2b and 5. The package 16 has an upper and a lower transverse seal 64 and 66, respectively, which seals are parallel to each other and perpendicular to a length axis 67 of the tube 40. As illustrated in fig. 3a, the volume elements are arranged to act on a first part 62a of the portion 62 to control its cross section and give it a first tube extension 72 in a first direction x. This is illustrated in fig. 2c showing a schematic cross section of the package, taken along line I-I in fig. 2a, when held by the device in the securing state. Further, the deformation elements are arranged to act on a second part 62b of the portion 62 to control its cross section and give it a second tube extension 74 in the first direction x. This is illustrated in fig. 2d showing a schematic cross section of the package, taken along line II-II in fig. 2a, when held by the device in the securing state. As apparent from the figures, the volume and deformation elements act on the tube portion 62 which is filled with an intended product. In turn, the product acts on the tube wall resulting in two cross sections differing from each other. The cross section of fig. 2c has the shape of a "flattened" ellipse, whereas the cross section of fig. 2d has the shape of a dog bone. By this action, the tube wall is deliberately deformed by indentations (not illustrated) in the encircled areas 76, 78 in fig. 2a. This deformation stabilizes the package during transverse sealing so that the package is essentially stress free in a zone where the transverse sealing is to be effected. Consequently, a plain seal can be obtained.

To effect the transverse sealing, the tube is squeezed and flat laid between the heating bar and the sealing dolly to heat the thermoplastic material in the area of the sealing zone. The heating bar in combination with the sealing dolly accomplishes two transverse seals, an upper seal of one package and a lower seal of another package. The cutting element cuts the tube between these two seals after the sealing operation has been completed to separate and release the packages.

After the cutting, the state of the device 14 is again changed from securing state to intermediate state by the deformation elements obtaining an intermediate state (step H) and the volume elements obtaining an intermediate state (step I) as a consequence of continued jaw movement. Thereafter, the jaws are disengaged from each other (step J) to again obtain the releasing state of the device. Then, the cycle is complete and the jaws are back at point α.

Thus, from point α to point β, the device 14 is in its releasing state, and from point β to point α the device is first in its intermediate state, then in its securing state and then in its intermediate state again.

The description set forth above has been directed towards one of the nine devices of the apparatus 38. However, this is for clarifying purposes only, and it should be seen that all nine devices operate in a similar way.

In the above-described embodiment, the transverse sealing has been effected by means of a heating bar. However, any suitable technique for transverse sealing could be used, such as ultrasonic sealing and induction heat sealing.

As briefly mentioned above, the tube is naturally filled with the intended product prior to transverse sealing. For example, the sealed tube can be filled with a liquid product, such as a beverage.

Some of the steps of the method, like steps C and D, and steps H and I, are performed simultaneously, although not apparent from fig. 6.

Moreover, it should be pointed out that the figures are not drawn according to scale.

The above-described embodiment shall only be seen as an example. A person skilled in the art realizes that the embodiment discussed can be combined and varied in a number of ways without deviating from the inventive conception.

As an example, the volume elements need not be plates but can have any suitable form, such as a rib form. Similarly, the deformation elements need not be formed as half pillows but can have any suitable form, such as the form of part of an ellipsoid.

The jaws do not have to be provided on transport chains like the ones described above, but could instead be provided on e.g. rotating wheels.

The invention can be applied in connection with several different types of packages, the cushion shaped package just being exemplary.

Finally, the deformation elements 22, 24 need not be attached to the volume elements 18, 20, but could instead be separate. In such an embodiment, the volume and deformation elements could apply a pressure independently onto the portion, in the first and seconds parts of it, respectively.

Claims

• CLAIMS

1. A device (14) for holding a portion (62) of a tube (40) of packaging material during sealing for obtaining an upper transverse seal (64) of the tube, the por- tion being arranged between the upper transverse seal and a lower transverse seal (66) of the tube, wherein the device is arranged to control a cross section of a first part (62a) of the portion, by being in direct contact with it, so as to have a first tube extension (72) in a first direction (x) essentially perpendicular to a longitudinal direction (67) of the tube, c h a r a c t e r i z e d in that the device further is arranged to control a cross section of a second part (62b) of the portion, by being in direct contact with it, so as to have a second tube extension (74) in the first direction, the first part being arranged between the lower transverse seal of the tube and the second part of the portion, the second part being arranged between the upper transverse seal of the tube and the first part of the portion, and the first tube extension being larger than the second tube extension.

2. A device (14) according to claim 1, wherein the upper (64) and lower (66) transverse seals are essentially parallel to each other and essentially perpendicular to the first direction (x) .

3. A device (14) according to any one of claims 1-2, comprising two opposing volume elements (18, 20) separated by a volume distance and moveable in relation to each other so as to have a releasing state, in which the tube (40) is moveable in relation to the volume elements, and a securing state, in which the first part (62a) of the portion -(62) of the tube is arranged to be held between the volume elements, and wherein the volume elements are arranged to be in contact with an outer surface of the first part of the portion of the tube with a predetermi- ned volume distance in the securing state to control the cross section of the first part of the portion.

4. A device (14) according to claim 3, further comprising two opposing deformation elements (22, 24) sepa- rated by a deformation distance and moveable in relation to the tube (40) so as to have a releasing state, in which the tube is moveable in relation to the deformation elements, and a securing state, in which the second part (62b) of the portion (62) of the tube is arranged to be held between the deformation elements, and wherein the deformation elements are arranged to be in contact with an outer surface of the second part of the portion of the tube with a predetermined deformation distance in the securing state to control the cross section of the second part of the portion.

5. A device (14) according to claim 4, wherein each of the deformation elements (22, 24) is arranged at a respective one of the volume elements (18, 20) .

6. A device (14) according to any one of claims 4-5, wherein each of the deformation elements (22, 24) is arranged as a projection from a tube contact surface (26, 28) of a respective one of the volume elements (18, 20) .

7. A device (14) according to any one of claims 4-6, wherein a deformation extension (27) of the deformation elements (22, 24) in a direction perpendicular to the first direction (x) is smaller than a half periphery of the tube (40) .

8. A device (14) according to any one of claims 4-7, wherein the predetermined deformation distance in the securing state varies along a direction perpendicular to the first direction (x) .

9. A device (14) according to any one of claims 4-8, wherein a predetermined center deformation distance (29) is smaller than predetermined end deformation distances (31).

10. A method for holding (step E) a portion of a tube of packaging material during sealing for obtaining an upper transverse seal of the tube, the portion being arranged between the upper transverse seal and a lower transverse seal of the tube, comprising controlling (step C) a cross section of a first part of the portion, by being in direct contact with it, so as to have a first tube extension in a first direction essentially perpendicular to a longitudinal direction of the tube, c h a r a c t e r i z e d by further comprising controlling (step D) a cross section of a second part of the portion, by being in direct contact with it, so as to have a second tube extension in the first direction, the first part being arranged between the lower transverse seal of the tube and the second part of the portion, the second part being arranged between the upper transverse seal of the tube and the first part of the portion, and the first tube extension being larger than the second tube extension.

11. A method according to claim 10, wherein the upper and lower transverse seals are essentially parallel to each other and essentially perpendicular to the first direction.

12. A method according to any one of claims 10-11, further comprising moving two opposing volume elements, which are separated.by a volume distance, in relation to each other to obtain a releasing state (step I + step J) , in which the tube is moveable in relation to the volume elements, and a securing state (step B + step C) , in which the first part of the portion of the tube is arranged to be held between the volume elements, and further comprising arranging the volume elements in contact with an outer surface of the first part of the portion of the tube with a predetermined volume distance in the securing state to control the cross section of the first part of the portion.

13. A method according to claim 12, further comprising moving two opposing deformation elements, which are separated by a deformation distance, in relation to each other to obtain a releasing state (step H + step J) , in which the tube is moveable in relation to the deformation elements, and a securing state (step B + step D), in which the second part of the portion of the tube is ar- ranged to be held between the deformation elements, and further comprising arranging the deformation elements in contact with an outer surface of the second part of the portion of the tube with a predetermined deformation distance in the securing state to control the cross section of the second part of the portion.

14. A method according to claim 13 , each of the deformation elements being arranged at a respective one of the volume elements, wherein moving one of the volume elements and the corresponding deformation element in- volves one common movement.