This paper is devoted to formulation and analysis of fundamental aspects of mechanics of nanocomposite materials and structural members. These aspects most likely do not exhaust all of the possible fundamental characteristics of mechanics of nanocomposite materials and structural members, but, nevertheless, they permit to form the skeleton of direction of mechanics in hand. The proposed nine aspects are described and commented briefly.

The specificity of mechanics as science consists in that it is one of the most important sciences of fundamental character and at the same time its urgency is defined by significance for engineering of many problems of mechanics. At all of the stages of human progress, starting with the ancient world, the importance of mechanics for engineering cannot be overemphasized: in many cases, mechanics, and engineering were considered as a single whole. This specificity of mechanics is shown up, when the mechanics of materials was formed as the scientific direction, in which uniting of mechanics and engineering is very significant.

On the whole, investigations on mechanics of materials are defined or characterized by the fact that the information on

Thus, the structural mechanics of materials is meant to be the part of investigations on mechanics of materials, in which the internal structure of materials is taken into account in quantitative and qualitative sense,

When structural mechanics of materials is defined in such a way, then the object of its study is the large class of modern materials, including

In this paper, “

The corresponding notions and definitions to the four component parts mentioned above are comparatively established and widely used. The one only and necessary common requirement for all four scientific directions is to take into account the internal structure of material in mechanical models and in solving the corresponding problems.

Below, the proposed fundamental aspects of mechanics of nanocomposite materials and structural members permit to form the skeleton of this direction of mechanics. Introducing the term

An analysis of internal structure in materials and usage of the notion of structural levels give the straight track to differing the nanomechanics from macro-, meso-, and micromechanics. This notion arose in micromechanics, but it became very productive and maybe the most important for description of nanomechanics, too.

To characterize quantitatively the internal structure of materials as objects of study in structural mechanics of materials, it is expedient to introduce

In the case of reinforced concrete, the parameter

In the case of metals, alloys, and ceramics, the parameter

In the case of composite materials with polymeric and metallic matrices, the parameter

In the case of nanomaterials (nanocomposites), the parameter

For the convenience of readers, the relationships between used length units are shown as follows:

Based on analysis of proposals of different authors, within the above mentioned extended interpretation the four levels for parameter

Structural levels.

Thus, within the framework of this aspect, the tool of identification of the material as the nanomaterial is generated.

Constructing the mechanical models can be thought as the main goal of mechanics. Let us remember the well-known sentence of Truesdell’s [

The models of materials are by their sense some idealizations of the real materials, and applicability of every model should be tested. Thus, the experimental mechanics presents the special part of mechanics and forms the fundamental knowledge, which arises owing to direct contact with real nature (in solid mechanics, with real materials). For fundamental sciences, the necessity of attention to experiments and practice had been formulated far back by Leibniz in his statement “

So, when the process of deformation of materials is being described (modeled), then different models are applied taking into account the discrete structure of material at the atom level and not taking into account this structure within the framework of continuum representation.

Note that the continuum representation of material consists in that real piece of material (material body) is replaced by continuum of the same geometrical shape. In each point of continuum, the values of physical-mechanical parameters of material (physical-mechanical properties) and physical-mechanical fields (stresses, strains, temperature, and so on) are considered.

The following three types of media are studied:

The main advantage of continuum description consists in that it permits to apply the methods of continuous mathematics and, in particular, the differential and integral calculi. At present, owing to active development of the finite element method and discrete mathematics, the significance of continuum representation will be possibly refined.

Among the above mentioned models, the following principally distinguished models should be marked out as such, which are the most widespread ones.

In

In particular, the model exists for discretely arranged rigid particles (balls), placed at nodes of crystal lattice and jointed by springs. In this case, the interaction among neighbouring balls is realized by the link of their springs. This model is used in mechanics, too. As an example, the monograph [

In

Undoubtedly, the essential part of investigations in mechanics of structural members is referring to the case when through the thickness the member consists of several homogeneous anisotropic layers. In these investigations, the two-dimensional (for shells and plates) and one-dimensional (for rods) applied theories are mainly considered, which are constructed by introduction of hypotheses on distribution of stresses and displacements through the thickness.

Above, three models are considered comparatively briefly. These models along with other models are everywhere applied in structural mechanics of materials. Each of the models has its possibilities, advantages, disadvantages, when in mechanics of materials the concrete phenomena are being described, and specific difficulties in the realization.

Probably, the most complex model from the point of view of obtaining the concrete results is the second one—the model of piecewise homogeneous body. Let us show in support two reasons.

In mechanics of composite materials, three models discussed above as well as many other models are applied to composite materials in the form of the sequence (chain) of models, which provide at the final stage the study within the structural members made of these composite materials. This reflects the specificity of mechanics as science.

Obviously, the sequences (chains) of used models for different composite materials, and studied within them, phenomena are different too, because the level scales (

When mechanics of composite materials are being constructed in the sense noted above, then different approaches and methods are utilized, which correspond to different scientific directions and scientific positions of single scientists. Nevertheless, despite such diversity of scientific directions, in construction of mechanics of composite materials,

The principle of continualization consists in

“

This principle is used widely, for example, within the framework of model 1 in transition to the continuum theory of dislocations in crystal lattices.

The principle of homogenization consists in “

The principle of homogenization is widely used within the framework of model 2 in micromechanics of composite materials, when different problems of statics, dynamics, stability, and fracture are being studied.

Usually, the area which a continuously inhomogeneous body (e.g., a composite material with the continuous changing in some direction number of micro- or nanospheres) or piece-wise homogeneous body (e.g., a composite material with uniformly distributed micro- or nanospheres by all of the directions) occupies is chosen, dimensions of which are essentially of less body sizes. This area should contain the sufficiently large number of inhomogeneities (e.g., granules) to provide the averaging correctness. Such an area is called

The averaged properties of the volume are usually attributed to the point at the volume center. As a result, the averaged properties are evaluated at every point of the body, and these properties should be constant—the body becomes the homogeneous one.

Very often, authors of different publications on materials are showing the color pictures of representative volumes in the form of cubes filled of discrete particles, which are looking very nice but do not image as a rule the real discrete structure.

The representative volume side length is compared with the characteristic length of body internal structure or with the characteristic length of inhomogeneities in the body (e.g., with micro- or nanosphere diameter). Exceeding the first length over the second one one order or more gives grounds to apply the averaging procedure.

Let us note that, from the abovestated continualization and homogenization principles, their principled distinction and methodological commonality follow (especially, in relation to the initial systems, to which they are applied).

Let us note finally that the procedures of continualization and homogenization are realized by means of different methods of averaging. At that, as a rule, the notion of representative volume is used.

Furthermore, three basic moments in realization of modeling with using the notion of representative volume and methods of averaging will be pointed.

Usually, the majority of authors are assuming that exceeding the first value over the second value on one or more orders gives grounds for the next modeling and averaging.

Parallel to selection of the representative volume

It is expedient to stress that only in the analysis situations, corresponding to conditions (

Consider as an example the procedure of determination of potential energy of deformation of elastic body in volumes

For volume

In the case of linearly elastic body, the following expression for volume

From (

It is necessary to note that, along with expression (

If the stated, in description of moment 1, reasons on determination of the linear sizes of the representative volume

“

Note that, in the practical realization of averaging procedure, the majority of authors are assuming additionally that in the material structural components (within the framework of the representative volume

Thus, the shown description of aspect 2 can be related to arguments about similarity of all four parts of structural mechanics of materials, because all of the continuum mechanics models of these parts are identical.

The feature of composite materials is their forming from the binder (matrix) and fillers (reinforcing elements). When composites as materials with the clearly shown internal structure are modeled, a row characterizing this structure geometrical parameters should be known.

Of course, when the approaches and methods of mechanics of composite materials of any level of internal structure are developed, one cannot orient the geometrical parameter

In this regard, the geometrical parameter

The introduced parameters

If at least one of conditions (

When the 3D relationships of continuum solid mechanics are used, this approach is the most exact and rigorous within the framework of continuum solid mechanics. Using this model, the investigations of problems of statics, dynamics, stability, and fracture in mechanics of composite materials are carried out. If at least one of conditions (

In this case, a composite material is modeled by the homogeneous anisotropic body with averaged properties. Some intermediate criteria between (

At present, the theoretical and experimental methods of determination of averaged constants are elaborated for composite materials in the framework of this model. Especially, the progress in development of theoretical methods should be emphasized.

Finally, it seems to be expedient to note that

Let us stop on some perspectives of developing based on model 2 approach. First of all, discreteness of structure of nanoformations as mechanical systems is of common knowledge. Also, when physical-mechanical properties of nanoformations are being determined, the concept of

Taking into account the insufficient level of studying the properties of nanoformations and the existence of, at present, quite good base of mechanical characteristics of microcomposite materials, let us adduce first the necessary facts from micromechanics of materials for the following comparative discussion. Among many important achievements of micromechanics of composite materials, let us show only two.

Below, as an example, the list for such set for aramid fibers (kevlars) is shown [

At present, the information on mechanical characteristics of nanoformations is still insufficient, and the listed above example with fourteen characteristics of certain fiber can be understood as the very distant goal in nanomechanics.

Thus, aspect 3 can be, like aspect 2, related to arguments about similarity of all four parts of structural mechanics of materials, because two basic models of the continuum mechanics of these parts are identical.

The problem of allowance for the edge and near-the-surface effects is important for all of the parts of mechanics of materials. As a rule, analysis of this problem permits to estimate the validity of continuum models.

Remember that, in structural mechanics of composites (in the broad sense) and in mechanics of composite materials (in the more narrow sense), the principles of continualization and homogenization are utilized. According to the first one, the discrete structure is changed (modeling) by the continuous structure. According to the second one, the piecewise homogeneous structure is changed (modeling) by the homogeneous structure.

It is necessary to take into account that principles of continualization and homogenization are referring to modeling the properties of material as the infinite continuum.

When different problems of structural mechanics of materials (problems of statics, dynamics, stability, and fracture) are being studied, analysis is necessary to be carried out as a rule for the material occupying the finite volume, which is also characterized by the boundary surface. On the boundary surface, for all of the basic mechanical processes, some boundary conditions are formulated for the material. In this regard, the question on applicability of principles of continualization and homogenization near the boundary surface and on this surface arises. The answer to this question can be formulated as follows:

“

The proof of this statement seems to be quite evident, because near the boundary surface (under loading of arbitrary type) the representative volume of material is inherent in this material basic property-property of

Note also that, in composite materials, when the material is being modeled by the piecewise homogeneous medium, the inhomogeneous fields of stresses and strains near the boundary surface in each component (each homogeneous medium) arise as a rule. The statement above is true for all of the four scales mechanics (macro-, meso-, micro-, and nano-).

Below, inapplicability of principles of continualization and homogenization near the boundary surface is illustrated by an example of layered materials within the framework of micromechanics of composite materials. More specifically, let us consider the layered composite material formed of two alternating layers of constant thickness, which are made of materials with distinguishing properties.

In Figures

The layered material with boundary surface parallel to interfaces.

The layered material with boundary surface placed perpendicularly to interfaces.

It seems obvious that, owing to presence of boundary surface with arbitrary sizes of the representative area in Figures

When applied to statical problems, this phenomenon corresponds to the Saint-Venant edge effect.

When applied to problems of wave dynamics, this phenomenon corresponds to onset of surface waves with amplitude damping with moving off from the boundary surface.

The notion of surface instability for homogeneous anisotropic body (which corresponds to

Thus, in problems of statics, dynamics, and stability of mechanics of homogeneous materials (including

It is obvious that similar type effects take place both for materials with discrete structure (

Taking into account the considerations above, it seems expedient to form the following conclusions.

At present, a row of results is obtained in studying the edge and near-the-surface effects of the shown type in Figures

Note that the strong method of solving the problems on near-the-surface effects in the case when the boundary surface is parallel to interfaces is proposed in the monograph [

When applied to edge effects in the case when the boundary surface is perpendicular to interfaces in layered or fibrous materials, the results of studying the static problems of materials are stated in [

For the near-the-surface effects, when the boundary surface is parallel to interfaces, the results on constructing the surface instability of layered materials are stated in [

For the near-the-surface effects in fibrous unilateral composites, when the boundary surface is parallel to fibers, the results on constructing the surface instability are stated in [

Let us show finally the exceptional example of composite material, in which the type of loading and the structure of composite are such that the edge and near-the-surface effects shown in Figures

Layered composite material composed of orthotropic layers of constant thickness.

The case of plane strain in the plane

Note that at the end face of each layer the following boundary conditions

The similar phenomenon of absence of edge effects arises also in the fibrous unilateral composite materials under their compression through the rigid discs along the reinforcing fibers. This phenomenon of homogeneous stress-strain state in the matrix and the fibers arises, when additionally assuming the coefficient of transverse expansion of the matrix and the fibers to be identical.

The shown above discussion of the edge and near-the-surface effects forms a separate aspect of structural mechanics of materials, which provides the best understanding of results, which are obtained by means of principles of continualization and homogenization. This aspect testifies similarity of all four parts of structural mechanics of materials, including the nanomechanics of materials.

These phenomena arise in all of the kinds of composite materials and are studied very intensively. To analyze such phenomena, it seems convenient to introduce the notion of

“

When the nanoformations and matrix are united into a nanocomposite, the phenomena occur at interfaces with participation of more deep-laid mechanisms that take place, for example, in the case of microcomposites.

The point is that in the general case the nanoformations consist of a system of curvilinear layers; in turn, each layer consists of a system of atoms, interaction among which is determined by force of interatomic interaction.

Therefore, when the nanoformations and matrix are being composed into a nanocomposite, seemingly, the interaction of atoms of the “end” layer of atoms on nanoformation with the neighboring atoms of polymeric matrix must occur owing to forces of interatomic interaction.

Thus, some intermediate layer arises from materials of nanoformations and polymeric matrix, inside which the interaction of atoms of nanoformations and polymeric matrix is observed. For example, in Figure

The molecular structure of nanocomposite crystallic polyethylene—CNT.

Note that Figure

Let us note also that studying this phenomenon and finding the characterizing regularities seem to be the complex and urgent physical-chemical problem. The solution of this problem can be realized by representatives of corresponding scientific directions only.

To describe the phenomena in the intermediate layer within the framework of mechanics of nanocomposites in cases like those shown above, it is expedient to use the traditional approaches of mechanics developed early, when the related problems are being considered.

The tradition in mechanics in an analysis of phenomena occurring in the intermediate thin layers or on surfaces of thin bodies consists in

“

Consider the following few examples.

In the classical theory of wing flow, the boundary conditions on the wing surface are

In the classical theory of contact interaction of elastic bodies, in the case when the stamp bottom has some deviations from the plane form, the boundary conditions are

In the problem of dynamical interaction of fluid and elastic (including thin-wall) bodies, the boundary conditions on vibrating interface are

Taking into account these traditional, in mechanics approaches and practice of modeling of nanoformations and matrix by continuum systems, the following, corresponding to and adopted in mechanics, exactness approach can be proposed:

“

This approach has been proposed at the first time, seemingly, in [

Ascertainment of concrete structure of boundary conditions, reflecting the phenomena in intermediate layer, is still problematic, because physicists and chemists still have not built the sufficiently grounded theory of such phenomena.

Because establishing the concrete structure of boundary conditions at geometrical interface seems to be problematic, the development of bilateral estimates for these conditions becomes of special urgency. Such estimates permit to estimate also the values of corresponding quantities.

From the point of view of mechanics, the most

Thus,

It should be also stressed that numerous problems exist in mechanics of microcomposites that are associated with necessity to provide the corresponding adhesion strength at interface. These problems are arising because of the existence of various mechanisms at interface. But these mechanisms in microcomposites are not linked with the interatomic forces action, contrary to nanocomposites, in which this action can be essential.

Such an aspect exists in every physical theory. It forms the necessary element in the theory and, of course, should be discussed when applied to the structural mechanics of materials. Below, the reasons and information are expounded, arising in analysis of the validity ranges of continuum mechanics of materials.

Let us note that undoubtedly the strong and full solution of the problem of validity ranges is difficult to realize from mathematical point of view. In this regard,

Remember that, in mechanics of composite materials, the basic relationships of continuum mechanics of materials are used to describe the deformation of matrix and each reinforced element. Note also that validity of continuum mechanics of materials in cases of macro-, meso-, and micromechanics is analyzed quite well. Here, the case of nanomechanics is discussed.

Return now to relationships (

The typical example of the filler used to produce the nanocomposites is

At present, in overwhelming number of theoretical publications, to determine the properties of carbon nanotubes, the approaches of molecular structural physics are used. They are based on the Cauchy-Born method [

Note that attempt to describe the deformation of reinforcing elements, especially nanotubes, within the framework of continuum solid mechanics, seems to be perspective and probably

Taking into account the abovementioned, the problem of validity of basic relationships of continuum solid mechanics in the study of mechanical processes on the nanolevel (

At that, it should be noted that the mechanical fields (stress and strain fields) in a nanoformation (e.g., in the nanotube) change by spatial variables.

Introduce, therefore,

Thus, the problem of validity ranges is equivalent to the problem of determination of ranges for parameter

To solve this problem, it seems necessary to use the introduced before and the characterized internal structure of material geometrical parameter

Taking into account the information above on atom sizes and distances between atoms, it can be assumed that parameters

The values in (

Qualitative and partially quantitative solutions of the problem under consideration can be carried out by introducing the model of anisotropic homogeneous body. It is necessary for applicability of this model that the parameter

So, it follows from (

If the condition “

Thus, when the mechanical fields, for which the parameter

The condition (

The condition (

Finally, note once more that the abovestated analysis is approximate and seemingly has substantially the qualitative character. Nevertheless, it is sufficiently expedient, because the problem of validity ranges of continuum mechanics in analysis of mechanical fields in the modern structurally inhomogeneous materials has a character of traditionally constantly discussed problem.

So, the above-considered aspect of mechanics of nanocomposite materials allows to elaborate the constructive tool for separation of objects of nanomechanics from the general set of objects, which includes the micro-, meso-, and macroobjects too. This aspect can, like aspect 1, be related to those ones which show the distinction between mechanics of nanocomposite materials and mechanics of composite materials of the higher structural levels.

The view on mechanics of nanocomposite materials in the light of approaches “bottom-up” and “top-down” seems very meaningful, since it highlights the specificity of nanolevel composite materials.

In technology, the two approaches “bottom-up” and “top-down” are generally known. Sometimes, “bottom-up” is commented as “nucleation and growth,” and “top-down” is commented as “comminution and dispersion” [

The approach “bottom-up” consists in the making of materials, starting with the smallest particles up to more massive formations. In this approach, the most essential is the basis: the aggregate of smallest particles and their character. The basis forms the foundation for constructing the more massive volumes of material. This basis is called the bottom.

The approach “top-down” consists in the making of materials, starting with the large volumes of material (bulk materials, source of raw materials) in direction towords the smaller formations (pieces) of material. The rough material is pressed, cut, found, or in some different way formed into pieces or products. In this approach, the most important are the tool resources, by which the lower limit in sizes of product or material piece is determined.

But mechanics as one of the oldest sciences has also the “canonical” terminology; thus, the situation needs some discussion. In mechanics as science, the basic approach can be apparently meant as constructing the models of phenomena, processes, and materials. With allowance for the historical experience, the models in mechanics of materials are developed in direction of studying the structure of material with more and more fine scale of internal structure.

When the terminology above is being considered, it seems expedient to refer to the review in [

This sentence testifies that the term “bottom-up” is used in technology and it was used in the making of the microcomposites (they correspond to microlevel and are studied in micromechanics).

Let us separate three moments.

Thus, in technology of making the nanocomposites, the “bottom-up” approach is realized by making the material starting with the aggregate of atoms. This terminology is found everywhere in publications on nanotechnology and nanomaterials. So, in the book [

Thus, it can be thought that the terms

In correspondence [

Thus, the aspect in hand is useful for mechanics of nanocomposite materials, because it allows to segregate this part of structural mechanics of material among other parts.

The challenging nanocomposites can be defined as the produced, at present and in the future, materials that can be applied in structural elements with allowance for features of loading and optimal correspondence of functioning of the elements under this loading.

Such optimality is realized by means of creating the anisotropy of deformation and strength properties of structural elements. The possibility of this creation is one of the most characteristic features of composites along with the high strength-to-weight ratio and high modularity.

These special properties can be formed in nanocomposites only by the straightening in directions of prevailing reinforcing the quite elongated and straightline nanoformations (CNT, nanoropes, nanofibers, and so on) as fillers, which should be coordinated with the force fluxes and be high-modulus ones.

Like the cases of macro- and microcomposites,

It is worthy to note that at present the overwhelming number of publications on nanocomposites is devoted to analysis of nanocomposites under dispersive distribution in matrix of the comparatively short nanoformations as fillers. At that, the clearly expressed directions of reinforcing are absent. These dispersive nanocomposites can be classified as the type of hardened matrix, which is frequently reflected in terminology of publications.

But this type of engineering cannot define the progress of perspective nanocomposites, in which reinforcing is coordinated with loading.

The considerations above testify that in constructing the foundations of mechanics of nanocomposites with polymeric matrix the quite substantiated is the basic approach, which can be meant as “

The formulated basic approach consists of the following four parts.

Part I. Modeling of the nanoformations by the linear elastic isotropic homogeneous body with averaged values of elastic constants, which are obtained with attracting the concept of

Part II. Modeling of the polymeric matrix (binder) by the linear isotropic homogeneous elastic or viscoelastic body. The similar modeling was used traditionally in constructing the foundations of mechanics of microcomposites. Under moderate temperatures or under comparatively short-time loading, a polymeric matrix in nanocomposites can be modeled by the linear isotropic elastic body.

Part III. Modeling of the interaction of nanoformations and polymeric matrix (in the thin intermediate layer with allowance for forces of interatomic interaction) by certain boundary conditions with transferring these conditions on the

Part IV. Determination of the averaged values of elastic constants for nanocomposites using various methods of

In this way, within the framework of the basic approach, the different problems of statics, dynamics, stability, and fracture of nanocomposite materials and structural elements made of these materials are carried out.

It was mentioned before, in analysis of problems of mechanics of nanocomposites, that the model of piece-wise homogeneous medium (after realization of the concept of

In analysis of problems in mechanics of structural elements made of nanocomposites, the application of the

Of course, in this part of mechanics, an analysis of multilayered constructions (e.g., constructing the models and theories of multilayered rods, plates, and shells) is actual. In this case, for each single element of construction (for each layer), the model of anisotropic homogeneous body with averaged elastic constants is used.

It is necessary to point out that actually a number of reviews on different problems of mechanics of nanocomposites are published [

Note also that the essential moment in the basic approach is

The abovestated considerations on mechanics of nanocomposites form the theoretical prerequisites for studying the basic problems arising in this part of mechanics: statical and dynamical problems, problems of stability, and fracture mechanics problems. In such studies, the statements of problems and methods of solving analogous to the approaches that are developed in mechanics of microcomposite can be used (see, e.g., multivolume editions [

In the studies within the framework of mechanics of structural members, it seems mostly promising and may be solely possible to apply the approach when the nanocomposite (piece-wise material) is changed on the homogeneous material with averaged properties.

Thus, in problems of mechanics of structural members made of nanocomposites, first

When applied to determination of averaged properties of nanocomposites, two approaches can be seemingly singled out as follows:

Approach 1: determination of averaged constants within the framework of the model of anisotropic homogeneous body (the structural model of the first order),

Approach 2: determination of averaged parameters within the framework of the structural models of the second order.

As applied to nanocomposites, when the averaged constants are being determined within the framework of the model of anisotropic elastic homogeneous body, the statements of problems and methods of studying that are developed for granular, fibrous, and layered microcomposites of determined and stochastic structure can be applied, as they. These statements and methods are expounded in numerous publications (e.g., in [

It is necessary to note that in this case the values of averaged constants are asymptotically exact and follow from the rigorous results obtained within the framework of three-dimensional theory under some conditions.

When applied to theory of wave propagation, these conditions correspond to the situation, when the ratios of geometrical parameter characterizing the internal structure of nanocomposite to the wavelength are tending to zero, that is, as if corresponding to the long-wave approximation.

Similar conditions are applied in other problems of mechanics of nanocomposite materials.

Thus, this aspect can be related to arguments about similarity of all four parts of structural mechanics of materials, because at present all known ways of transition from mechanics of materials to mechanics of structural members in these parts are identical.

Thus, the considered aspects of mechanics of nanocomposite materials and structural members permit to outline the similarities and distinctions of this part of structural mechanics when comparing with the other three parts—macro-, meso-, and micromechanics of materials and structural members.

The irony of fate for mechanics of nanocomposite materials and structural members consists in that similarities are essentially more studied, and they determine the tight link among all of the four parts, which is little known beyond the mechanics of materials and structural members.

Sometimes, the nature of human perception is that distinctions are fixed more often and with significantly less impediments.

Therefore, the nanomechanics in whole is represented up to this time through the prism of distinctions despite the presence of a big corpus of similarities.