Physical constants of a nonlinear microstructural theory of two-phase elastic mixtures for several granular structural composites

Maslov, B. P.; Rushchitskii, Ya. Ya.; Коваленко, А. П.

doi:10.1007/bf02086483

Cited by 3 publications

(4 citation statements)

References 3 publications

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“…Discussion. It should be noted that one of the authors already participated in work on compiling tables of complete sets of physical constants for one class of particulate composites, both linear elastic and quadratically nonlinear [5,13]. The present study extends the idea of tabulating the physical properties of composites for different models to specific types of fibrous composites.…”

Section: Evolution Of Plane and Cylindrical Waves In Fibrous Micro-anmentioning

confidence: 92%

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Physical constants for one type of nonlinearly elastic fibrous micro-and nanocomposites with hard and soft nonlinearities

2005

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Sets of physical constants are tabulated for three structural models of fibrous composites with fibers of four types: Thornel-300 carbon microfibers, graphite whiskers, carbon zigzag nanotubes, and carbon chiral nanotubes. The matrix for all the types of composites is always ÉPON-828 epoxy rosin (in some cases with polystyrene or pyrex additive). The values of the physical constants are commented on and used to study the distinctions in the evolution of three types of waves (plane longitudinal, plane transverse, and cylindrical) propagating in materials with soft and hard nonlinearities Keywords: hyperelastic materials, Murnaghan potential, complete sets of elastic constants, plane and cylindrical waves, hard and soft nonlinearitiesIntroduction. The present study is based on the publication [8] devoted to the relationship of the approaches and methods in all the historically established divisions of the mechanics of materials: macro-, meso-, micro-, and nanomechanics. As indicated in [8], the main common feature of these four divisions is that they account for the microstructure of materials and their main difference is the range of typical length scales for inhomogeneities in the microstructure of a material.Note that the first results illustrating the fundamental conclusions of the study [8] were presented in the paper [9], which was the first to propose to consider four types of fibrous composite materials: two with microlevel fibers (Thornel 300 carbon microfibers and graphite whiskers) and two with nanolevel fibers (zigzag and chiral graphite nanotubes). What these types of materials have in common is the materials of the fibers (carbon) and the matrix (ÉPON 828 epoxy resin). The mechanical constants of the matrix and fibers (density, Young's modulus, shear modulus, and Poisson's ratio) and the determinate microstructure of composites needed henceforth were described in [9]. Of the variety of structural models of composites, we have chosen the following two: the model based on effective elastic moduli (model 1), which pertains to macromechanics and accounts for the microstructure of a material by means of effective moduli, and the model of two-phase elastic mixture (model 2ñ), which pertains to micromechanics and nanomechanics and accounts for the microstructure in a more complex way, using the concepts of two interpenetrating and interacting continua. The choice fell on these models because they account for the microstructure of composites in so different ways that the complete sets of mechanical constants used by the models do not overlap and the mechanical phenomena described by the models are equally different and are characteristic of different levels: macro, micro, and nano. The fibrous materials under consideration are supposed to possess standard symmetry-transverse isotropy. The analytic expressions for the set of constants are derived from the theory of effective moduli [1, 2] for the former model and from the theory of elastic mixture [5,7,8] for the latter model. These expressions are presented i...

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Section: Evolution Of Plane and Cylindrical Waves In Fibrous Micro-anmentioning

confidence: 92%

“…However, only the first model was studied using a nonlinear theory with the Murnaghan potential [13][14][15][16][17] (model 1n). Therefore, only the effective moduli of the second and third orders were calculated on the assumption that the fiber volume fraction is small (from 1 to 10%).…”

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Physical constants for one type of nonlinearly elastic fibrous micro-and nanocomposites with hard and soft nonlinearities

2005

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“…For the composite reinforced with unidirectional ellipsoidal inclusions, the correlation function is defined by the expression given in [5,7] …”

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“…The behavior of the composite material with an elastic matrix was studied thoroughly [3][4][5][6]. Numerous works investigated the concentration of mean stresses in viscoelastic composites composed of two constituents [7]. The solution of the problem of determining the concentration of mean stresses in the constituents (matrix and inclusions) of the multiconstituent viscoelastic composite material is given below.…”

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Stress Concentration in Microstructural Elements of Viscoelastic Composite Materials

Lyashenko

2005

Strength Mater

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539.4We present solution of the problem of estimating the stress concentration in the constituents (matrix and inclusions) of a multiconstituent viscoelastic composite material, depending on the shape of inclusions, properties of the matrix and the whole composite. The matrix material is isotropic and viscoelastic. A wide range of properties of inclusions (e.g., pores, solid and viscous particles) is considered. To solve this problem, we use the method of integral transformations.Progress in technology requires developing novel engineering structures, mechanisms and multi-purpose machines, which, in its turn, requires the use of materials with the properties that are absent for conventional materials and alloys. It is necessary to develop the composite materials in which the required properties are synthesized by selecting the appropriate constituents and controlling their mutual arrangement. The rheonomic properties are typical of many of those materials to one extent or the other. A negligible number of publications are devoted to the problem of stress concentration in viscoelastic bodies [1,2]. The behavior of the composite material with an elastic matrix was studied thoroughly [3][4][5][6]. Numerous works investigated the concentration of mean stresses in viscoelastic composites composed of two constituents [7]. The solution of the problem of determining the concentration of mean stresses in the constituents (matrix and inclusions) of the multiconstituent viscoelastic composite material is given below.The service conditions of the composite materials are characterized by high levels of external loads, temperatures, electric and magnetic fields. The linearity of relationships between the dynamic and kinetic parameters that describe the material behavior under such conditions can be violated and the use of the linear deformation theory results in considerable errors. These features are peculiar to the composites with both viscoelastic metallic and polymeric matrices which are increasingly used in elements of state-of-the-art structures.

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Wavelets in the propagation of waves in materials with microstructure

Cattani¹

2003 IEEE International Workshop on Workload Characterization (IEEE Cat. No.03EX775)

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Physical constants of a nonlinear microstructural theory of two-phase elastic mixtures for several granular structural composites

Cited by 3 publications

References 3 publications

Physical constants for one type of nonlinearly elastic fibrous micro-and nanocomposites with hard and soft nonlinearities

Physical constants for one type of nonlinearly elastic fibrous micro-and nanocomposites with hard and soft nonlinearities

Stress Concentration in Microstructural Elements of Viscoelastic Composite Materials

Wavelets in the propagation of waves in materials with microstructure

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