Załącznik nr 3b

Summary of professional accomplishments

dr inż. Hubert Jopek Poznan University of technology

Faculty of Mechanical Engineering and Management, Institute of Applied Mechanics

Poznań 2019

2

1. Personal data

Name and Surname: Hubert JOPEK

2. Diplomas and academic degrees

2011 PhD in technical sciences

Faculty of Mechanical Engineering and Management,

Poznan University of Technology

Dissertation: „Application of genetic algorithms to determine the optimal location of

sources when solving selected problems of applied mechanics”

Supervisor: dr hab. inż. Tomasz Stręk, prof. nadzw.

Reviewer: prof. dr hab. inż. Jan A Kołodziej

Reviewer: prof. dr hab. inż. Andrzej Radowicz

2008 Program Executive MBA Poznań-Atlanta,

Poznan University of Economics & Business

2006 Master of Arts in philosophy

Faculty of Social Sciences, Adam Mickiewicz University in Poznań

2004 Master of Science in Computational Mechanics of Construction

Faculty of Mechanical Engineering and Management,

Poznan University of Technology

3. Employments in scientific institutions

Place of employment

Poznan University of technology

Faculty of Mechanical Engineering and Management,

Institute of Applied Mechanics

Employment period: 01.10.2013 – present

3

4. Indication of scientific achievements described in Article 16 (2)of the Act of 14

March 2003 Law on Academic Degrees and Title and Degrees and Title in the

Arts (Journal of Laws of 2017 item 1789):

4. a. On the basis of Art.16 paragraph 2 section 1 of the Act of March 14, 2003 on academic degrees

and academic titles and degrees and title in art as a scientifc achievement I present a series of

related publications entitled:

„Modelling of mechanical properties

of auxetic composites and metamaterials”

4.b Publications included in the scientific achievements being the basis in the application in

habilitation procedure:

The articles listed below have been ordered according to the date of publication starting from the latest.

All publications were published in journals from the Journal Citation Reports database. For each work,

an Impact Factor is given in accordance with the year of issue, or the previous year in the case of latest

publications.

A1. Strȩk, T., Michalski, J., Jopek, H. (33%), Computational Analysis of the Mechanical

Impedance of the Sandwich Beam with Auxetic Metal Foam Core. Physica Status Solidi B

2019, 256, 1800423, doi:10.3390/ma11020294. IF: 1.729.

A2. Jopek, H. (50%), Strȩk, T., Thermoauxetic behavior of composite structures. Materials. 2018,

11, doi:10.3390/ma11020294. IF: 2.467.

A3. Jopek H (100%) Finite element analysis of tunable composite tubes reinforced with auxetic

structures, Materials, 2017, 10(12), 1386. IF: 2.467.

A4. Strek, T.; Matuszewska, A.; Jopek (33%), H. Finite Element Analysis of the Influence of the

Covering Auxetic Layer of Plate on the Contact Pressure. Physica Status Solidi B 2017,

1700103, doi:10.1002/pssb.201700103. IF: 1.729.

A5. Jopek, H. (50%); Strek T., Torsion of a Two-Phased Composite Bar With Helical Distribution

of Constituents. Physica Status Solidi B, 2017, 1700050, 1700050,

doi:10.1002/pssb.201700050. IF: 1.729.

A6. Strek T, Jopek H (40%), Idczak E., Wojciechowski K. W., Computational modelling of

structures with non-intuitive behavior, Materials, 2017, 10(12), 1359. IF: 2.467.

A7. Jopek, H. (100%) Computer simulation of bending a fibrous composite reinforced with

auxetic phase. Physica Status Solidi B 2016, 253, 1369–1377, doi:10.1002/pssb.201600117.

IF: 1.674.

A8. Strek, T.; Jopek, H. (35%); Fraska, A. Torsion of elliptical composite beams with auxetic

phase. Physica Status Solidi B 2016, 1359–1368, doi:10.1002/pssb.201600053. IF: 1.674.

A9. Strek, T.; Jopek, H. (45%); Wojciechowski, K. W. The influence of large deformations on

mechanical properties of sinusoidal ligament structures. Smart Materials and Structures 2016,

25, 54002, doi:10.1088/0964-1726/25/5/054002. IF: 2.909.

4

A10. Strek, T.; Jopek, H. (45%); Idczak, E. Computational design of two-phase auxetic structures.

Physica Status Solidi 2016, 253, 1387–1394, doi:10.1002/pssb.201600120. IF:1.674.

A11. Strek, T.; Jopek, H. (45%); Nienartowicz, M. Dynamic response of sandwich panels with

auxetic cores. Physica Status Solidi B, 2015, 252, 1540–1550, doi:10.1002/pssb.201552024.

IF: 1.522.

A12. Jopek, H. (50%); Strek, T., Thermal and structural dependence of auxetic properties of

composite materials. Physica Status Solidi B, 2015, 252, 1551–1558,

doi:10.1002/pssb.201552192. IF: 1.522.

A13. Strek, T.; Jopek, H. (40%); Maruszewski, B. T.; Nienartowicz, M. Computational analysis

of sandwich-structured composites with an auxetic phase. Physica Status Solidi B, 2014, 251,

354–366, doi:10.1002/pssb.201384250. IF: 1.489.

A14. Strek, T.; Jopek, H. (50%) Effective mechanical properties of concentric cylindrical

composites with auxetic phase. Phys. Physica Status Solidi B 2012, 249, 1359–1365,

doi:10.1002/pssb.201084218. IF: 1.489.

4. c. discussion of the scientific purpose of the work mentioned in point 4b and the results achieved

Scientific research that I have conducted after obtaining the doctoral degree concerns the mechanical

properties of materials and composites, including the so-called metamaterials i.e. materials with a

designed microstructure with given, often unique, properties. Special emphasis in the research was

placed on auxetics which are materials characterized by a negative Poisson ratio.

The topic is related to the very rapid development of material technologies. The use of composites has

become more and more common for many years, which is why it is so important to be able to precisely

determine the mechanical properties of such materials if they are to be used in the creation of new

structures. Additionally, in recent years we have witnessed a kind of revolution in manufacturing, which

results from the development of rapid prototyping techniques, 3D printing, and the so-called 4D printing

and the use of such materials in various areas of life, from aeronautics through construction and

mechanical engineering, and biomedical engineering and medicine.

Devices allowing the production of almost any spatial structures are getting more and more common,

more accurate and faster. Their resolution is also getting higher, which already allows one to easily

achieve accuracy at the level of micrometres and even nanometers. It is a scale that corresponds to the

structure of materials, e.g. the size of steel grains, the pore size of PUR foam or expanded polystyrene

and many others. Since it is now possible to fabricate structures with such a level of detail, it is probably

a matter of time when technology develops so much that it will be possible to use it on an industrial

scale to produce materials with a specific microstructure. These materials, including composites, whose

structure has been precisely designed and manufactured by man are called metamaterials.

Others aspects of the development in this field are the possibility of optimization of such structures and

the production of so-called smart materials. The use of optimization algorithms at the stage of designing

the material's microstructure allows for obtaining such spatial distribution of the material (or materials)

that allows for obtaning the structure with the best properties (in the sense of the assumed criteria).

Furthermore, intelligent materials and structures are those whose properties can be modified in an

intended manner, e.g. by the influence of external factors such as temperature, magnetic field, electric

5

field, specific load, etc. The extremely important role of the microstructure and its impact on the

properties of materials is revealed, among others, in the case of auxetics. In almost all natural materials

and structures, the Poisson's ratio is positive, which means that in the simplest case, during the axial

stretching of the sample, the dimensions of its cross-section is getting smaller. This behavior seems

intuitive because most of the known materials behave in this way, but it turns out that it does not have

to be that way. There are materials that behave differently, i.e. during the axial stretching of the sample,

the cross-sectional dimension (at least in one direction) increases, and when pressed, the cross-sectional

dimension decreases - these materials are called auxetics; the Poisson's ratio for these materials is less

than zero, and because of their unintuitive behavior began to use the name "auxetos" proposed by Evans

[1], which in Greek means "that may be increased". Examples of such materials and structures have also

been found in nature, and include some minerals, e.g. cristobalite [2], as well as some tissues, for

example fragments of the skin and bones of some animals [3] and the Achilles tendons [4]. However,

most auxetics are produced artificially because the deformation mechanism results from the specific

geometry of the microstructure of these materials.

The first mention of the possibility of the existence of materials characterized by a negative Poisson

ratio can be found in Voigt's work [4] from the beginning of the XX century. Lempriere [5] then

presented theoretical considerations regarding three-dimensional isotropic materials characterized by a

negative Poisson coefficient. In the general case, on the basis of the classic theory of elasticity and

assuming the thermodynamic stability of materials, it is assumed that Poisson's ratio for isotropic

materials can varies in the range (-1.1) in the case of two-dimensional theory of elasticity and varies in

the range (-1, 0.5) for three-dimensional materials [6]. In the case of anisotropic materials, there are no

such limits. In the eighties of the twentieth century, Gibson [7] published a work on cellular materials

containing the results of theoretical and experimental research on materials characterized by a negative

Poisson's ratio, and Lakes [8] presented the method of producing a synthetic foam sample with auxetic

properties.

In recent years, studies of auxetic structures carried out by other researchers have concerned such issues

as:

• analysis of the behavior of new structures [12] and composites [13] characterized by negative

Poisson’s ratio;

• problems of determining the effective properties of auxetic metamaterials [14,15], topological

optimization of materials - including auxetics [16],

• research on smart materials and in particular materials whose Poisson’s ratio can be controlled

and changed by external factors in the range from positive to negative values [17,18,19];

• the dynamics of auxetic materials [19,20];

• the use of auxetic structures in functional design [21], or

• graphene analysis with respect to auxetic properties [22],

The following areas can be distinguished within the scope of my research: investigating composites

with the auxetic phase [A14, A13, A7, A4 A8 A5 A11, A1], smart materials modelling [A12, A2, A3,

A9] and topological optimization of the materials structure [ A13, A10, A6].

6

Investigating composites with the auxetic phase [A14, A13, A7, A4, A8, A5, A11, A1]

Composites are materials composed of at least two phases (constituent materials) characterized by

different properties. The combination of constituent materials allows obtaining composites whose

resulting properties are significantly different from the properties of individual components. The

properties of composites resulting from the combination of individual constituent materials are often

referred to as effective properties, e.g. Effective Young's modulus, effective Poisson's ratio, etc. The

effective values of the properties of the composite depend both on the properties of the individual

constituent materials as well as on their spatial distribution, i.e. the structure they form. For this reason,

also simple metamaterials made of only one basic material can significantly differ in effective properties

due to their microstructure.

For typical structures of composites, i.e. laminates and fiber reinforced composites, effective properties

(in particular, the Young's modulus) are usually within the range specified by Reuss and Voigt

estimates[9] ("rule of mixtures" and "inverse rule of mixtures'). In particular, to determine the upper and

lower estimation of the Young's modulus for a typical fiber-reinforced composite in a direction parallel

to the alignment of the fibers, the formula for the effective Young modulus may be used in the form of:

𝐸𝑒𝑓𝑓(𝑉𝑜𝑖𝑔ℎ𝑡) = ∑ 𝑓𝑖𝐸𝑖 .

The above formula shows that the effective value is the weighted average of the Young's modulus of

individual materials 𝐸𝑖 depending on the percentage of individual components 𝑓𝑖.

The lower estimation of the effective Young's modulus of such composites can be obtained by

determining the value in the direction perpendicular to the arrangement of the fibers using the eq2

(inverse rule of mixtures) formula:):

𝐸𝑒𝑓𝑓(𝑅𝑒𝑢𝑠𝑠) =1

∑𝑓𝑖𝐸𝑖

.

However, these classic estimates constituting the widest range for the effective Young's modulus for

two-phase composites were further elaborated in later years and it was shown that in many cases this

range is much smaller as related to the estimation proposed by Hashin-Strikman [10] and by Milton[11].

In general, however, the estimation of the effective properties of composite materials is impossible in

an analytical way due to the complex geometry and its significant impact. Therefore, in my research I

used the Finite Element Method (FEA) implemented in the Comsol Multiphysics software, to model the

geometry of the considered materials and determine their effective properties. Using the basic definition

of the Young's modulus and the Poisson's coefficient resulting from generalized Hooke's law and

assuming the continuity and isotropy of the material at each point of the test sample and the continuity

of strains at the interface, the effective Poisson ratio can be determined using the following relationship:

𝜈𝑒𝑓𝑓 = −𝜀𝑡

𝜀𝑙,

where 𝜀𝑙 is the average strain in the axial direction, and 𝜀𝑡 is the average strain in the direction transverse

to the direction of the load.

7

In turn, the effective Young's modulus can be determined based on the formula:

𝐸𝑒𝑓𝑓 = −𝜎

𝜀,

where 𝜎 is stress and 𝜀 is strain in the direction of the load.

The first work concerned the study of the impact of the auxetic phase on the behavior of a cylindrical

composite made up of three concentric layers [A14]. The effect of auxetic material on the behavior of

such a composite subjected to axial stretching was analyzed (Figure 1A). Two configurations of the

layer system were considered: ANA and NAN where A is the auxetic material, and N a typical material

characterized by a positive Poisson value (non-auxetic material). Due to axial symmetry, the problem

was considered as two-dimensional. The basic parameter being the subject of my analysis is the

thickness of the middle layer, while maintaining the volume fraction of individual materials, which

means that the value of the internal and external radius of this layer simultaneously changed, so as to

maintain the assumed volume of both phases. As a result of the calculations, the Young's modulus was

determined depending on the thickness of individual layers and the method of their configuration (NAN

/ ANA). The results confirmed that the effective properties of such a composite are very strongly

dependent on the distribution of the individual layers. This dependence is strongly non-linear and the

values may differ far from those obtained from basic estimates (Voigt-Reuss). In addition, the study

examined the effect of Young's modulus of each constituents of the composite on the value of the

effective Poisson ratio of the composite, and the results obtained by me also indicated a strong non-

linear relationship between these values.

The analysis of the properties of the composite sample with the auxetic phase subjected to the

compressive load was also presented in the article on the study of sandwich panels [A13]. In this case,

it was assumed that the sample was a five-layer plate built in such a way that the outer skin was made

of a conventional material with high stiffness - in this case steel (Fig. 1B). The same material is used for

a wavy-shaped central layer (sinusoidal shape), while the two intermediate layers are characterized by

the Young's modulus which value is a few orders of magnitude lower, similar to the case of typical

sandwich panels.

A)

B)

Figure 1. A) A sample of a concentric composite subjected to axial stretching. B) A five-layer sandwich

panel with a wavy core

As part of the analysis, I examined the impact of the following parameters:

• amplitude and period of the function describing the sinusoidal wavy of the core layer,

• share of the volume of the middle layer,

• Poisson's ratio of the soft core layer.

8

The value of Poisson's ratio of soft core layers was taken in the range <-0.99, 0.49>. To estimate the

effect of the above parameters, the value of the elastic energy of the compressed compression of the

sample was determined. Considering that the stiffness of the analyzed element gets higher as the value

of the total elastic energy of deformation decreases. The obtained results indicate that the use of material

with Poisson's ratio of ν = 0 results in the highest values of this energy. A composite with higher stiffness

can be obtained both by using a conventional material with a positive Poisson's ratio positive, and by

using an auxetic, but the range of positive values in the case of isotropic materials is limited to

ν = 0.5 while the range of negative values is higher which gives greater possibilities for designing

sandwich panel with the expected stiffness. As a result of these surveys, four patent applications were

filed in 2016, and they are currently being considered.

The results of my research on the influence of the auxetic phase on the behavior of the auxetic composite

I also presented in the article [A7] dedicated to the analysis of the behavior of a composite reinforced

with parallel fibers subjected to a bending load. The work was considered a composite, in which the

matrix is made of a conventional material (Figure 2A), Poisson's ratio of the fiber material was one of

the parameters of the simulation tests. Another the parameters were the fiber distribution in the analyzed

composite and the continuous load distribution on the upper surface of the considered sample. The

fragment of the composite in which there was a reinforcement corresponding to the volume of one fiber

was considered, however, four geometrical configurations of fiber placement were considered in the

analyzed fragment of the composite, i.e.:

• whole fiber in the middle,

• fiber separated in half - each of the halves at the side edges of the composite piece

• fiber separated in half - each of the halves at the upper and lower edges of the composite,

respectively

• fiber separated into quarters - each quarter in one of the four corners of the analyzed geometry.

The above configurations of the fiber arrangement were significant due to the influence of the load,

whose distribution on the upper surface was not constant but parabolic and did not cover the entire length

of the upper edge of the sample. The adopted load model was associated with the simulation of the load

of a composite fragment with the force resulting from the interaction of an element such as an indenter

or similar object striking a spot in the sample. Also in this case the elastic energy value was calculated

in order to compare the results obtained for equal parameter values. Similarly as in the case of a sandwich

panel, also in this case, the change of the Poisson's value of one of the phases of the composite

significantly affects the behavior of the whole sample. Depending on the value of the other parameters,

and hence on the distribution of fibers in the sample, the characteristics obtained were slightly different.

However, in all the cases analyzed, one can indicate such a composite whose elastic strain energy value

was the same as for the composite with a material characterized with a positive Poisson ratio. However,

the inverse relationship is not true, i.e. it was possible to obtain structures with higher stiffness for the

auxetic material. For some of the geometrical configurations, the differences in the determined

maximum displacement of the test sample for the composite reinforced with conventional material were

many times greater than the displacements obtained for the composite reinforced with auxetic fibers.

The development of these studies was the article [A4], in which the results of research on the effect of

the auxetic layer covering the bending sample were published (figure 2B). In this case, the scope of

related research was also extended with the load characteristic, i.e. instead of modeling the impact of an

object on the test sample by means of a load with a given pressure distribution, a contact issue analysis

was performed in which the plate under test is pressed by an indenter of the roller section and the contact

9

pressure value is determined on this basis. As the numerical method of complementing MES in the

analysis of the contact problem, the augmented Lagrangian method was used so that the boundary

condition in the contact zone was replaced by an expression containing the Lagrange multiplier, which

in this case corresponded to the contact pressure value.

A)

B)

Figure 2. A) Scheme of the composite reinforced with fibers of the subjected bending load. B) Diagram

of the plate covered with the auxetic layer subjected to bending as a result of the operation of the identer.

The example was analyzed in two variants, i.e.: with a covering layer with a thickness d, and without

this layer, in order to be able to compare the results and determine the significance of this layer and in

particular the effect of its Poisson ratio of this layer. The obtained results confirm that the use of a layer

with different properties can significantly affect the contact issue, whereas in the case of a layer made

of auxetic material (especially in the case of values close to -1), this effect was very large.

As part of research on auxetic composites, simulations of twisting two-phase composite beam were also

carried out in which one of the phases was a material characterized by negative Poisson's ratio. The first

of the [A8] works concerned the twisting of a prismatic beam with an elliptical cross-section (and in a

particular circular case) whose cross-section was divided into an even number of sectors constructed

alternately from two different materials; At the same time, the conditions of continuity at the interface

were assumed. In addition, in all analyzed cases the percentage share of individual phases was equal to

50%. The parameters of the numerical simulation were as follows: the number of sectors n, the half-axis

ratio of the considered elliptical cross-section sp, and the angle φ, which is responsible for ordering

sectors in the cross-section - this is the angle between the x-axis and the edge of the first sector with the

auxetic phase. The effect of the Poisson ratio was also analyzed. Among many obtained results, one of

the most interesting was that such distribution of material in the elliptical composite rod reinforced with

strongly auxetic material (Poisson's value close to -1), which exhibited higher torsional stiffness than an

analogue rod with a circular cross-section (made of the same materials with a similar division into

sectors). It was a result obtained only for some narrow ranges of considered parameters, but interesting

because it indicates a different behavior than in the case of homogeneous beams in which the highest

stiffness is characterized by a beam with a circular cross-section.

The second work [A5] devoted to the torsional problem related to a two-phase prismatic bar with a

circular cross-section in which two materials were arranged in helical shape. This time, in order to better

reflect the actual conditions of joining two different phases, the existence of a narrow transition phase

between two materials was assumed, in which the material properties gradually change from the values

characterizing the first material to the values characterizing the second material. As part of the

10

simulation study, several parameters were also considered, including: values of material constants of

individual phases, in particular the effect of the negative Poisson's ratio and geometrical parameters

describing the helix, i.e. the helix pitch and the number of coils. In order to compare individual cases,

the value of total strain energy was determined. The obtained results clearly indicate that the use of

auxetics as one of the phases of the helical composite, with unchanged values of the other parameters,

significantly influences the value of the total energy of elastic deformation and increases the stiffness of

the composite. Particularly high impact can be observed for auxetics with extreme Poisson values - close

to -1.

A)

B)

Figure 3. The structure of the composite based on the A) re-entrant honeycomb and B) rotating squares

geometries

The paper [A11] presents an analysis of composite panels subjected to harmonic load. The core of the

analyzed sandwich panel designed using two popular auxetic structures (Figures 3A-3B), i.e. the

structure of re-entrant honeycomb and a structure based on rotating squares. It was assumed that the

structures analyzed were made of a conventional material whose mechanical properties (Young's

modulus and Poisson's ratio) correspond to the properties of steel.

In most works on auxetic structures, it is assumed that there are voids with no material at all. In this

article, however, I proposed a different approach, one that is often used in practice - filling empty spaces

with other material, more susceptible to deformation. Thanks to this, it was possible to examine the

behavior of the composite constructed from the auxetic structure taking into account the properties of

the second material, which were treated as parameters during the simulation. The concept of the so-

called hierarchical auxetics was used here among ohers. Metamaterials, including hierarchical auxetics

are so, whose structure is at least two-level, i.e. in the microstructure of the selected material, one can

distinguish specific characteristic geometry (e.g. rotating squares in the case of auxetics), at the same

time these elements also have some own microstructure that can be duplicated this parent. In the example

given, this would mean that each of the rotating squares would also be made of smaller, rotating squares.

By doing this, you can analyze materials with a fractal structure, but usually the tests are limited to two

or three levels of such a hierarchy. It is also possible that the individual levels of the hierarchical

microstructure are different from each other. In the analyzed case, the structure is made of material the

high stiffness was typical auxetic geometry, however the empty spaces were filled with other material,

the properties of which in some cases were also characterized by the negative values of the Poisson ratio.

I carried out an analysis aimed at determining the effective properties of such a composite. A very

11

interesting and important result obtained in this work was to show that it is possible to obtain a composite

made of two conventional materials (in Poisson ratios greater than zero), which is not a porous material,

yet showing an effective Poisson ratio of values less than zero.

The continuation of research on the dynamics of auxetic structures was the article [A1] dedicated to the

analysis of a composite bar one side fixed, made of external skins built of aluminum and a core made of

aluminum foam. As part of the conducted simulations, the effect of density, damping ratio and Poisson's

ratio of core material of the composite was analyzed, which changed from -0.9 to 0.45 to the mechanical

impedance value of the analyzed system. The mechanical impedance is a dynamic parameter, expressed

by the value of the harmonic force acting on the system in relation to the vibration velocity. As a result

of the tests, it was found that the auxetic material has a significant impact on the dynamics of the system

- the use of material with negative Poisson's values allowed for shifting the resonant frequencies of the

system to higher frequencies. This effect was particularly noticeable for the core material characterized

by Poisson's ratio with values close to minus 1.

Smart materials modelling [A12, A2, A3 , A9]

Intelligent materials, i.e. materials whose properties can be modified by external factors, are modern

materials, and research on them is becoming more and more popular. My research included, among

others, designing structures whose effective Poisson ratio could be changed by the appropriate

interaction of external fields. In the paper [A12], the analysis of the structure of the material, whose

Poisson ratio could take both positive and negative values depending on the temperature, was presented.

The analyzed material is a two-phase composite made of parallel elliptical fibers. The fibers are arranged

in such a way that the adjacent fibers are rotated by 90 ° so that the axis of the large ellipse is oriented

alternately vertically or horizontally. Such a distribution of elliptical fibers allows to obtain a structure

that is very similar to the typical auxetic geometry of rotating squares and forms the matrix of the

composite. The materials of the individual phases of the composite have been selected in a special way.

The matrix forming the auxetic structure is made of a material characterized by high stiffness, and its

Young's modulus does not significantly change its value in the selected temperature range - such

conditions are met by many metals, e.g. typical carbon steel. In turn, the fiber material was selected so

that its Young's modulus was lower than the matrix material and its value changes significantly (even

by an order of magnitude or more) in the selected temperature range - this type of behavior is exhibited

by many polymers. As a result, a composite was obtained that at low temperatures behaves like a

conventional material with a positive effective Poisson ratio, while at higher temperatures the values of

the effective Poisson ratio are negative. Depending on the desired temperature, we obtain a material that

is an auxetic or not. Additionally, the work involved a parametric analysis of the impact of the elliptical

fiber geometry.

Continuation of work on the influence of temperature on the auxetic properties was an article titled

"Thermoauxetic behavior of composite structures" [A2] in which I proposed two new geometries of a

two-phase composite microstructure that are modifications to existing typical auxetic geometries

(Figures 4A-4D).

12

A)

B)

C)

D)

Figure 4. Modified auxetic structures: A) re-entrant honeycomb with linking elements, B) re-entrant

honeycomb with filling, C) anti-tetrachiral with connectors and D) anti-tetrachiral with filling

Two auxetic geometries were chosen: re-entrant honeycomb and anti-tetrachiral, and the modifications

were based on introducing additional linking elements made of another material. In a special case, the

linking material was used to fill all the free spaces of the auxetic geometry. As in the previous work, the

material used to create the auxetic structure was characterized by a high value of the Young's modulus

and its low sensitivity to temperature changes in the selected range - the analyzed materials are steel or

aluminum. In turn, the linking material was characterized by greater susceptibility to deformation, and

the value of the Young's modulus was strongly dependent on the temperature - the selected matrices

were PMMA or polyamide. The properties of the composite were tested in the range of 200-400K and

the obtained results confirmed that the proper selection of conventional materials allows to create a

composite whose effective Poisson ratio can vary in a large range from positive to negative values

depending on the set temperature.

A)

B)

Figure 5. Change of the effective Poisson ratio of the composite depending on the temperature for A)

re-entrant honeycob structures with linking elements and B) re-entrant honeycomb with filling

The effective values of Poisson's ratio for the analyzed structures presented in the graph (Figure 5A)

depend on the geometrical dimensions of the connector (parameter F). For example, for the value of

F = 0.1, the value of the effective Poisson’s ratio decreases from the value 0.2 at a temperature of 200K

to almost -0.15 at 400K. The variability range of the Poisson's ratio for the composite with the fill was

even larger (Fig. 5B), it should be noted that such large changes of the effective Poisson's ratio were

obtained for the simulated material, for which it was assumed that in the selected temperature range its

Young's modulus decreases in the range from 50 to 5 GPa.

13

For PMMA and polyamide materials, the change in the Young's modulus as a function of the

temperature in this range is smaller and as a result also the variability of the effective Poisson ratio is

not so great. Another possibility of influencing the mechanical properties of composites is to use as one

of the phases of a ferromagnetic material. In this case, the factor that allows you to change and the

control of selected effective mechanical properties of the composite is the magnetic field.

As part of the research published in the article [A3], I analyzed the behavior of a stent built from a

structure based on auxetic geometry with filling with ferromagnetic material (Fig. 6A). The proposed

structure, thanks to the use of the auxetic structure, may behave in a typical manner for the auxetic,

which in the case of a stent means that during stretching it will increase its volume. On the other hand,

the use of ferromagnetic material, whose Young's modulus depends on the intensity of the magnetic

field to fill the stent, allows to control the behavior of this structure and therefore may under certain

conditions it may behave as if it were made of a conventional material, so during stretching, reduce the

diameter of the cross-section section.

A)

B)

Figure 6. A) Composite stent geometry B) Change in stent behavior depending on the change in the ratio

of Young's modulus of individual components, eg through the influence of the magnetic field

The basis for the simulation tests were the results of previous works, which showed that the change of

the effective Poisson's composite may be made by changing the Young's modulus of one of the

composite materials. In connection with the above, no specific values of Young's modulus of

constituent materials were analyzed in this paper, parametric analysis concerned only the mutual ratio

of Young's modulus of both materials. The results showing the change in the internal diameter of the

stretched stent, depending on the change in the ratio of Young's modulus, are presented in Figure 6B.

In [A9] I investigated the properties of metamaterial with a structure made of sinusoidal elements. The

work analyzed various combinations of mutual arrangement of these elements and their impact on the

effective mechanical properties of the resulting material with a given structure. The simulations

performed included the analysis of the behavior of the material subjected to small and large strains,

while taking into account the material model with non-linear elasticity (hyperelastic Neo-Hookean). Due

to large deformations, an alternative formula was also used to determine the value of the effective

Poisson ratio in the following form:

𝜈𝑒𝑓𝑓 = −log (1+𝜀𝑡)

log (1+𝜀𝑙).,

14

and the results are compared to those obtained for the standard formula. It has been shown that

depending on the arrangement of sinusoidal elements in the microstructure, it is possible to obtain a

material with an effective Poisson's ratio that varies in a wide range from negative to positive values.

The influence of large deformations on the values of the effective Poisson ratio was also analyzed, which

allowed to confirm a strong relationship between the negative Poisson's ratio and the geometry of the

material's microstructure. When the geometry of the microstructure was strongly distorted due to larger

strains, an effective Poisson ratio was obtained with negative values is much more difficult.

Topological optimization of the material structure [A13, A10, A6]

One of the issues concerning research on the mechanical properties of materials is the analysis of their

micro and macroscopic structure. In particular, one of the dynamically developing directions of research

is topological optimization, the use of which allows to optimize the structure of the material so as to

obtain certain desirable values of selected mechanical properties. Materials and composites so obtained

are often referred to as metamaterials. As part of my research, I also dealt with this issue. The problem

of topological optimization consists in the distribution of one or more materials in a given volume in

such a way that the resulting structure meets the set criteria. One of the common methods of interpolating

the properties of materials used in this type of optimization is the SIMP method (solid isotropic material

with penalization). In the simplest terms, this method boils down to the fact that the stiffness matrix in

a given area is expressed by the following formula:

𝐷(𝑟, 𝒙) = 𝑟(𝑥)𝑝𝐷0,

where D0 is the rigidity of the selected isotropic material, p is the penalty parameter, and r is a control

variable that can be interpreted as a generalized material density parameter and it should meet the

following condition:

0 ≤ ∫ 𝑟(𝒙)𝑑𝑉𝑉

≤ 𝑉𝑓 ,

where Vf is the specified amount of material that can be spread in the analyzed area. Using the SIMP

method for a two-phase composite, you can define approximation functions, which are responsible for

the distribution of selected material properties of individual constituent materials in a selected area. For

example, wanting to make topological optimization in the selected area in such a way as to use two

materials with Young's modules E1 and E2, respectively, the approximation function representing the

generalized value of the Young's modulus in the considered area will be defined using the variable r in

the following way:

𝐸(𝑟) = 𝐸1 + 𝑟(𝑥)𝑝(𝐸2 − 𝐸1).

The above algorithm was used, among others in the aforementioned work [A13] in which the distribution

of two materials in the core of the sandwich panel was optimized, one of the materials characterized by

a negative Poisson ratio. The criterion of the objective function was the minimum value of deformation

energy. The results obtained were compared with the results obtained for a sandwich panel with a wavy

core, and it resulted that the use of topological optimization allowed to obtain a sandwich panel with

higher stiffness.

15

The continuation of work on topological optimization in relation to sandwich panels was the article

[A10], in which the two-phase structure of the sandwich panel core was also optimized. In this case, the

SIMP method was also used to approximate the mechanical properties of individual materials.

As a function of the goal in the optimization problem, the minimum and maximum value of the effective

Poisson’ ratio of the core of the plate was assumed. Importantly, in numerical studies, positive Poisson

values were assumed for both materials. For the structure obtained as a result of topological optimization

in the problem of minimizing the value of the effective Poisson's core, the boards achieved negative

values (depending on the percentage of particular phases even below -3), while in the maximization

issue the obtained Poisson score exceeded in some cases the value of 5. Of course Poisson's values are

impossible to achieve for isotropic materials. However, the resulting structures were very strongly

anisotropic and the obtained results concerned one selected direction. However, it is worth noting that

the analyzed composite was made entirely from conventional materials, i.e. characterized by positive

Poisson values, and the entire analyzed volume was filled with material (no voids in the material

structure).

A)

B)

Figure 6. A) Honeycomb type geometry with a negative Poisson's effective ratio B) re-entrant

honeycomb geometry with a positive effective Poisson's ratio.

The development of studies on topological optimization of auxetic structures was the paper [A6], which

presents the analysis of two typical structures, i.e.: conventional honeycomb and auxetic re-entrant

honeycomb. In this case, only a single cell of the analyzed structures was examined. The aim of the

study was to analyze whether it is possible to obtain a structure characterized by a negative effective

Poisson ratio based on honeycomb geometry and the opposite - a structure characterized by positive

Poisson values in the case of re-entrant honeycvomb geometry. In both cases, this result was achieved

by creating cells in the form of composites built of two materials and positioning them appropriately in

the area of the analyzed geometries.

References:

[1] Evans K., Endeavour, 1991, 15 (4): 170–174,

[2] Williams J.L.; Lewis J.L. J Biomech Eng 1982, 104(1):50-56.

[3] Gatt R. et al., Acta biomaterialia 2015, 24, 201-208.

[4] W. Voigt, Lehrbuch der Kristallphysik. B. G. Teubner-Verlag, Leipzig, Berlin 1928

[5] B. M. Lempriere, AIAA J. 1968, 6, 2226.

16

[6] L. J. Gibson, The elastic and plastic behaviour of cellular materials, Ph.D. Thesis, Churchill

College, University of Cambridge, UK 1981.

[7] K. W. Wojciechowski, Mol. Phys. 1987, 61, 1247.

[8] R. S. Lakes, Science 1987, 235, 1038.

[9] Hill, R. J. Mech. Phys. Solids, 1963, 11, 357-372.

[10] Hashin, Z., Shtrikman, S. J., Mech. Phys. Solids, 1963, 11, 127-140.

[11] Milton, G. W., Phan-Thien, N. Proc. R. Soc. Lond. A, 1982, 380, 305-331.

[12] Alderson, A. et al., Compos. Sci. Technol., 2010, 70, 1034–1041.

[13] Pozniak, A.A.; et al.,Compos. Part B Eng. 2016, 94, 379–388.

[14] Gilat, R.; Aboudi, Materials 2013, 6, 726–737.

[15] Dirrenberger et al., Int. J. Mech. Mater. Des. 2013, 9, 21–33.

[16] Czarnecki, S.; Lewinski, T., Int. J., Solids Struct. 2017, 110–111, 315–331.

[17] Li, D.; Ma, J.; Dong, L.; Lakes, R.S., control. Mater. Lett. 2016, 181, 285–288.

[18] Grima J.N., et al. Smart Mater. Struct., 2013, 22 084016

[19] Scarpa F., Tomlinson G., J. Sound Vib. 2000, 230, 45.

[20] Bianchi M., Scarpa F., Smart Mater. Struct. 2013, 22, 084010.

[21] Smardzewski J., Jasińska D., Janus-Michalska M., Composite Structures, 2014 113: 354–361,

[22] Grima, J. N. et al. Adv. Mater.,2015, 27: 1455-1459. 22

5. Summary of scientific activity

5.a. List of publications not included in the scientific achievement being the basis in the application

in habilitation procedure

[1] Jopek H.; Strek T, Optimization of the Effective Thermal Conductivity of a Composite,

Convection and Conduction Heat Transfer, Dr. Amimul Ahsan (Ed.), ISBN: 978-953-307-

582-2, (2011).

[2] Jopek H.; Kołodziej J.A., Application of genetic algorithms for optimal positions of source

points in method of fundamental solutions, Computer Assisted Mechanics And Engineering,

vol. 15, pp 215-224;2008.

[3] Strek T.; Jopek H. Computer simulation of heat transfer through a ferrofluid;

Phys. Stat. Sol. (b) 244, No. 3, 1027–1037; 2007.

[4] H. Jopek, Simulation of Thermal Convection Depending on the Angle Between Gravity Force

and Temperature Gradient; Systems. Journal of Transdyscyplinary Systems Science, vol. 11,

pp. 29-34; 2006.

[5] Jopek H.; Kołodziej J.A.; Stręk T., Laminar flow in trapezoidal groove at finite Bond

numbers with shear stress at the liquid-vapour interface by the method of fundamental

solutions; Computer Assisted Mechanics And Engineering, vol. 13, pp 395-405; 2006

[6] Jopek H.; Strek T., Symplectic Integrators For Cascade Of Mass-Spring System;

Vibrations in Physical Systems, vol. 22, pp. 155-160; 2006.

[7] Jopek H.; Strek T., The Rayleigh-Bénard convection analysis by the lorenz dynamical system;

Vibrations in Physical Systems,vol 21, 2004.

17

5.b Participation in national and international scientific conferences

1. Jopek H., An analysis of auxetic composites under complex loading, 9th International

Conference Auxetics and other materials and models with ‘negative’ characteristics, 10-13

September 2018, Sheffield, United Kingdom

2. Jopek H., Modelling of magnetically tunable auxetic compoiste, 8th International Conference

Auxetics and other materials and models with ‘negative’ characteristics, 11-15 September

2017, Heraklion, Crete, Grece

3. Matuszewska A., Strek T., Jopek H., Contact problem in auxetics, 8th International

Conference Auxetics and other materials and models with ‘negative’ characteristics, 11-15

September 2017, Heraklion, Crete, Grece

4. Jopek H., Strek T., Computational modelling of thermoauxetic composite structures, 7th

International Conference Auxetics and other materials and models with ‘negative’

characteristics, 12-16 September 2016, Szymbark, Poland

5. Strek T., Jopek H., Fraska A., Torsion of auxetic bar, 6th International Conference Auxetics

and other materials and models with ‘negative’ characteristics, 11-18 September 2015, Malta,

6. Jopek H., Tabaszewski M., Stręk T., Acoustic properties of sandwich panels, VI International

Symposium on Trends in Continuum Physics, 2014, pp 23-25.

7. Strek T., Jopek H., Nienartowicz M., Idczak E., Computational modelling of modern

materials, IV Manufacturing Conference, Poznan, Poland, December 8th-10th, 2014

8. Jopek H., Strek T., Thermal and structural dependence of auxetic properties of composite

materials, 5th International Conference Auxetics and other materials and models with

"negative" characteristics, 15-19 September 2014, Poznan (Poland)

9. Strek T., Jopek H., Finite element analysis of effective properties of sandwich panel with

two-phase core, 15-19 September 2014, Poznan, Poland

10. Maruszewski B.T., Jopek H., Strek T., Optimization of the effective heat transfer coefficient

in composite materials, Pan American Congress of Applied Mechanics, (PACAM XII),

Trinidad, 2012

11. Stręk T., Jopek H, Effective mechanical properties of concentric cylindrical composite with

auxetic component, Auxetics 2011, Szczecin, 6-9.9.2011.

12. Jopek H., Stręk T., Projektowanie materiałów o zadanym efektywnym współczynniku

przewodzenia ciepła, XLIX Sympozjon "Modelowanie w mechanice", Wisła, 21-25 lutego

2010.

13. Jopek H., Kołodziej J.A.; Application of genetic algorithms for optimal positions of source

points in method of fundamental solutions; Leuven Symposium on Applied Mechanics in

Engineering (LSAME.08), 5th International Workshop on Trefftz Methods (TREFFTZ.08);

Leuven, Belgium 31 March- 2 April 2008.

14. Jopek H.; Optimization of heat sources position using genetic algorithm; IV International

Conference Trends In Continuum Physics (TRECOP’07) ; Lviv, Ukraine, 16-20 September

2007.

15. Jopek H.; Simulation of Thermal Convection Depending on the Angle Between Gravity Force

and Temperature Gradient; XVII Krajowa Konferencja Mechaniki Płynów, Bełchatów, 17-

21 września 2006.

16. Jopek H., T. Strek; Symplectic Integrators For Cascade Of Mass-Spring System; Vibrations

in Physical Systems, vol. 22, pp. 155-160; 2006.

18

17. Kolodziej J. A.; Strek T., Jopek. H., Laminar flow in trapezoidal grooves at finite Bond

numbers with shear stress at the liquid-vapor interface by method of fundamental solution,

The 10th International Conference on Numerical Methods in Continuum Mechanics

(NMCM2005) & 4th Workshop on Trefftz Methods; Zilina, Slovakia, August 23-26 2005.

18. T. Strek, H. Jopek; Computer simulation of heat transfer through a ferrofluid; 2nd Workshop

on "Auxetics and Related Systems"; Bedlewo, August 19-23, 2005.

19. H. Jopek, T. Strek; The Rayleigh-Bénard convection analysis by the Lorenz dynamical system;

XXI Symposium Vibrations In Physical Systems; Poznań-Kiekrz, 2004.

5. c Scientific internships

• I completed a research internship from 1 February to 28 February 2018. at the Institute of Rail

Vehicles Tabor, Poznań

• I was invited to take a three-month research internship at Sheffield-Hallam University to the

Institute of Materials and Engineering Research (MERI - Materials and Engineering Research

Institute). The internship begins in April 2019. As part of the internship I will conduct research

with prof. Andy Alderson, a recognized specialist in materials research and in particular

auxetics.

5.d Synthetic summary of scientific achievements as at March 28, 2019.

Scientific publications in journals from the Journal Citation Reports database 15

Monographs, scientific publications in magazines other than those in the JCR database 6

Total impact factor according to the Journal Citation Reports (JCR) list, according to

the year of publication:

27.612

Total impact factor according to the Journal Citation Reports (JCR) list, according to

with the year of publication converted in accordance with my percentage share

14.337

Number of publications citations

Web of Science database 288

Scopus database 318

Hirsch index (according to Web of Science and Scopus) 10

Papers at international conferences 19

Participation in organizational committees of scientific conferences 5

Membership in the editorial team of international journals 2

Reviewing publications in international journals 19

Participation in research and development projects 1

19

5.e Reviewing scientific articles in international journals

• Journal of Composite Science (https://www.mdpi.com/journal/jcs) – 3 reviews

• Materials (https://www.mdpi.com/journal/materials) – 3 reviews

• Carbon (https://www.journals.elsevier.com/carbon) – 1 reviews

• Composite Structures (https://www.journals.elsevier.com/composite-structures) – 1 review

• Physica Status Solidi (B) (https://onlinelibrary.wiley.com/journal/15213951) – 4 reviews

• Vibrations in Physical Systems (http://vibsys.put.poznan.pl/) – 5 reviews

• International Journal of Mechanical Sciences (https://www.journals.elsevier.com/international-

journal-of-mechanical-sciences) – 1 review

• Smart Materials and Structures (www.iopscience.org/sms) – 1 review

6. Organizational, promoting and didactic activities

As part of my didactic activity, I conducted classes at the first and second degree, conducting lectures,

exercises, projects and laboratories. In particular, these are the following classes and lectures: technical

mechanics, ergonomics and systems engineering

As part of my didactic activity, I taught first and second level studies, including lectures in English for

students within the Erasmus program. So far I have been a promoter of 24 B.Sc. theses and 8 M.Sc.

theses.

I am also an auxiliary promoter for PhD student M.Sc. Eligiusz Idczak, whose dissertation is entitled.

"Topological optimization of two-phase auxetic metamaterials"

Promoting activity

As part of the popularization of science, I organized and since 2016 I coordinate the cooperation between

the Faculty of Mechanical Engineering and Management and the 3rd High School in Poznań by

organizing and conducting lectures for the so-called academic classes.

Organizational activity

Since 2016, I have been the deputy director of the Institute of Applied Mechanics at the Faculty of

Mechanical Engineering and Management at the Poznan University of Technology

I am a member of:

• Dean's Education Commission

• Faculty Educational Quality Group

International cooperation, organization of conferences, participation in the editorial office of

magazines::

• Scientific cooperation within the COSSMAT Center (Center for COmplex Systems and

Smart MATerials), which includes several research centers in the world dealing with

physics / material mechanics. The Institute of Applied Mechanics is also a member of this

organization and I cooperate with other centers as part of the team of prof. Tomasz Stręk.

• member of the organizing committee of the international Vibsys 2016 conference

20

• member of the organizing committee of the international Vibsys 2018 conference

• one of guest editors of the special issue of "Materials"

(https://www.mdpi.com/journal/materials)

• member of the editorial board of the journal "Vibrations in Physical Systems" published

by Poznan University of Technology, indexed in the Scopus database.