Effect of anisometry of a platelike nanofiller on the elastic constants of a transversely isotropic composite

Analysis results for the elastic properties of a composite with a small amount of coplanarly arranged platelike filler particles are presented. The geometrical form of the particles is described by an oblate ellipsoid of revolution. The calculations are performed by formulas obtained by using the Eshelby approach for media with a low concentration of inclusions. The effect of anisometry of the ellipsoidal particles and of the ratio between the elastic moduli of the filler and matrix on the effective elastic constants of the composite is discussed. Calculation results are compared with experimental data for the elastic moduli of a nanocomposite containing completely exfoliated particles of an unmodified montmorillonite. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 493–504, July–August, 2008.     

Dynamic properties of composite laminates and panels with highly contrasting directions of anisotropy

An asymptotic analysis of the dynamic stress-strain state of a thin laminar packet of anisotropic layers is presented. The statement is nonclassical, since in layer materials the ratio of elastic moduli in the longitudinal and transverse directions can generate small parameters comparable to the relative half-thickness of the packet, as, for example, in high-strength unidirectional composites. Alternation of strong load-carrying layers and a relatively soft filler with a similar difference in the elastic moduli between the layers is also allowed. The averaged two-dimensional equations and the total stress tensor in the layers are determined. The results are classified with respect to the types of anisotropy and the indices of differences in the elastic moduli. It is shown that first-approximation models lead to kinematic relations similar to those of the theories of high-order shear strains. Institute of Problems of Mechanics, Russian Academy of Sciences, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 5, pp. 605–614, September–October, 1999.     

Numerical calculation of effective elastic moduli for incompressible porous material

Incompressible elastic material with a periodic system of pores is considered. Processes are studied with a typical length which is much more than the typical diameter of pores and the typical distance between pores. Porous material behaves as a certain “effective” material without pores in such processes. The method of calculation of effective moduli based on mathematical homogenization theory is described. The estimates for the effective moduli are proved. The results of numerical calculations of effective moduli for materials with spherical and cubic pores are presented. The dependence of the effective moduli on the volume fracture of pores is investigated. The explicit formulae for effective coefficients are deduced. Comparison with the effective moduli for compressible materials is performed. Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995. Lomonosov Moscow State University, Department of Mathematics and Mechanics, Moscow. Published in Mekhanika Kompozitnykh Materialov, No. 5, pp. 579–587, September–October, 1996.     

Elasticity of composites with irregularly oriented shape-anisotropic filler particles

A variant of determining the elastic characteristics of composites containing irregularly oriented shape-anisotropic filler particles of two types (short fibers and thin platelets) is considered. The effective elastic constants of the composites are calculated by using the method of orientational averaging of elastic characteristics of isolated transversely isotropic structural elements reinforced with unidirectionally oriented short fibers or coplanarly arranged thin platelets. The superposition of elastic properties of the irregularly oriented structural elements, with account of their orientational distribution in the composite material, is accepted. The calculation results are compared with experimental data for the effective elastic moduli of polymeric composites reinforced with short glass fibers and of polymeric nanocomposites containing the platelet-type particles of organically modified montmorillonite. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 285–300, May–June, 2006.     

Plane problems of stability of composite materials with a finite-size filler

The plane problem of three-dimensional stability is solved for a transversely compressed composite material reinforced with ribbons taking into account the inhomogeneous initial state. An approximate solution of the problems is based on the net method. The effect of the ribbon form factor, the ratio between the elastic moduli of the matrix and filler, and Poisson ratio of the filler on the critical deformation of the material is investigated. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 1, pp. 77–86, January–February, 2000.     

Γ-convergence for incompressible elastic plates

We derive a two-dimensional model for elastic plates as a Γ-limit of three-dimensional nonlinear elasticity with the constraint of incompressibility. The resulting model describes plate bending, and is determined from the isochoric elastic moduli of the three-dimensional problem. Without the constraint of incompressibility, a plate theory was first derived by Friesecke et al. (Comm Pure Appl Math 55:1461–1506, 2002). We extend their result to the case of p growth at infinity with p ϵ [1, 2), and to the case of incompressible materials. The main difficulty is the construction of a recovery sequence which satisfies the nonlinear constraint pointwise. One main ingredient is the density of smooth isometries in W ^2,2 isometries, which was obtained by Pakzad (J Differ Geom 66:47–69, 2004) for convex domains and by Hornung (Comptes Rendus Mathematique 346:189–192, 2008) for piecewise C ¹ domains.     

Application of the method of conditional moments to investigating the deformation properties of orthotropic composites with fiber microdamages

A model of deformation of stochastic composites subjected to microdamage is developed for the case of orthotropic materials with microdamages accumulating in the fibers. The composite is treated as a matrix strengthened with elliptic fibers with orthotropic elastic properties. The fractured microvolumes are modeled by a system of randomly distributed quasi-spherical pores. The porosity balance equation and relations for determining the effective elastic moduli for the case of a fibrous composite with orthotropic components are used as the fundamental relations. The fracture criterion is given as a limit value of the intensity of average shear stresses occurring in the undamaged part of the material, which is assumed to be a random function of coordinates and is described by the Weibull distribution. Based on an analytical and numerical approach, the algorithm for determining the nonlinear deformation properties of such a material is constructed. The nonlinearity of composite deformations is caused by the accumulation of microdamages in the fibers. By using a numerical solution, the nonlinear stress–strain diagrams for an orthotropic composite in uniaxial tension are obtained. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 17–30, January–February, 2009.     

Influence of nanofillers on the thermal and mechanical behavior of DGEBA-based adhesives for bonded-in timber connections

Results of an experimental investigation into the thermal behavior and mechanical properties of a room-temperature-cured epoxy adhesive (diglycidyl ether of bisphenol A, DGEBA) cross-linked with polyetheramines and filled with different fillers, namely nanosilica, liquid rubber (CTBN), and clay, are reported. The nanosilica and liquid rubber increased the flexural strength and elastic modulus of the adhesive systems; the addition of clay particles raised the elastic modulus significantly, but embrittled the adhesive. Establishing a correct cure time is very important for bonded-in timber structures, as it will affect the bond strength. A study on the effect of cure time on the flexural strength was carried out, from which it follows that the adhesives should be cured for at least 20 days at room temperature. The damping characteristics and the glass-transition temperature of the adhesives were determined by using a dynamic mechanical thermal analysis. The results showed that the filled adhesives had a higher storage modulus, which was in agreement with the elastic moduli determined from static bending tests. The introduction of the fillers increased its glass-transition temperature considerably. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 599–614, September–October, 2006.     

Effect of interphase layers on the elastic properties of a carbon-nanotube-reinforced composite

A variant of a stepwise analysis of the elastic properties of a carbon-nanotube-reinforced composite with account of the effect of interphase layers between the nanotubes and the polymer matrix is reported. The preliminary calculation of the elastic constants of a structural element incorporating a nanotube and an interphase layer and the subsequent calculation of independent elastic constants of a composite with such transversely isotropic structural elements oriented in one direction are both performed by using the Mori–Tanaka theory of an equivalent medium. The calculations are carried out for a wide range of ratios between the elastic moduli of the interphase layer and matrix. The elastic constants of a composite with randomly oriented nanotubes are obtained by using the method of orientational averaging.     

Scattering of plane harmonic waves on a cylindrical cavity with an elliptical cross section in an orthotropic medium

The diffraction of a plane longitudinal harmonic wave on a cavity with a smooth curvilinear cross section in a rectilinearly orthotropic medium is solved by using small perturbations in the elastic moduli and introducing generalized wave potentials. Results are presented from a numerical analysis of the dynamic stresses in the near diffraction field and at the boundary of an elliptical cavity including variations in the relative incident wavelength, eccentricity of the cavity, and degree of anisotropy of the medium. Donetsk State University. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 29, pp. 102–110, 1999.     

Landau–Ginzburg/Calabi–Yau correspondence for quintic three-folds via symplectic transformations

We compute the recently introduced Fan–Jarvis–Ruan–Witten theory of W-curves in genus zero for quintic polynomials in five variables and we show that it matches the Gromov–Witten genus-zero theory of the quintic three-fold via a symplectic transformation. More specifically, we show that the J-function encoding the Fan–Jarvis–Ruan–Witten theory on the A-side equals via a mirror map the I-function embodying the period integrals at the Gepner point on the B-side. This identification inscribes the physical Landau–Ginzburg/Calabi–Yau correspondence within the enumerative geometry of moduli of curves, matches the genus-zero invariants computed by the physicists Huang, Klemm, and Quackenbush at the Gepner point, and yields via Givental’s quantization a prediction on the relation between the full higher genus potential of the quintic three-fold and that of Fan–Jarvis–Ruan–Witten theory.     

Differaction of plane deformation waves on a cylindrical cavity in an anisotropic bulk composed of a monoclinic system

An analytic-numerical method based on perturbations in the elastic moduli is proposed for solving problems involving the diffraction of two-dimensional longitudinal-shear harmonic deformation waves on a cavity with a smooth curvilinear cross section in an elastic medium with an anisotropy corresponding to a monoclinic system in the dynamic deformation plane. Results from a numerical analysis of the distribution of the dynamic stresses in the near diffraction field are presented for the case of longitudinal waves scattered on a dome-shaped cavity as the direction of the incident wave and the degree of anisotropy of the medium are varied. Donetsk State University. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 137–147, 1999.     

Nanocomposites based on a styrene-acrylate copolymer and organically modified montmorillonite 1. Mechanical properties

The preparation of polymer nanocomposites by mixing a solution of a styrene-acrylate copolymer with a suspension of organically modified montmorillonite in dimethyl formamide is described. Seven different compositions with organomontmorillonite content from 0 to 7 wt.% were prepared and tested. Results of their X-ray diffraction analysis are presented. Data on the influence of organomontmorillonite content on the tensile stress-strain curves, elastic modulus, strength, and ultimate elongation of the nanocomposites are obtained. The concentration dependences of elastic properties of materials with differently oriented platelike nanoparticles is analyzed by using an algorithm elaborated for stepwise calculations of elastic constants with account of the features of structural hierarchy of intercalated and exfoliated nanocomposites. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 375–388, May–June, 2006.     

Genus-one stable maps, local equations, and Vakil–Zinger’s desingularization

We describe an algebro-geometric approach to Vakil–Zinger’s desingularization of the main component of the moduli of genus one stable maps to \mathbbPⁿ{\mathbb{P}^{n}} (Vakil and Zinger in Res Announc Am Math Soc 13:53–59, 2007; Geom Topol 12(1):1–95, 2008). Our approach is based on understanding the local structure of this moduli space; it also gives a partial desingularization of the entire moduli space. The results proved should extend to higher genera.     

Thermomechanical and adhesive properties of radiation-modified polymer composites for thermosetting products

Gamma-irradiated blends of polyethylene (PE) with ethylene-propylene-diene copolymer (EPDM) and a thermotropic liquid-crystalline polymer (LCP) are investigated at absorbed radiation doses not exceeding 150 kGy (10 kGy=1 Mrad). The temperature dependences of elastic moduli, tension diagrams at a temperature above the melting point of the crystalline phase of PE, and long-term strain recovery curves for oriented test specimens are presented. The kinetics of thermal relaxation and shrinkage stresses in previously oriented composite specimens upon their heating and cooling is investigated. Data on the influence of LCP additions on the adhesive interaction of the compositions with steel are obtained. The peculiarities of thermomechanical and adhesion properties of these composites are discussed taking into account the morphologic and calorimetric data obtained. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 379–394, May–June, 2000.     

Effective elastic moduli and stress concentrator factors in random structure aligned fiber composites

We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing a statistically uniform random set of aligned fibers. Effective elastic moduli as well as the stress concentrator factors in the components are estimated. The micromechanical approach is based on the Green’s function technique as well as on the generalization of the “multiparticle effective field method” (MEFM, see for references, Buryachenko [1]). The refined version of the MEFM takes into account the variation of the effective fields acting on each pair of fibers. The dependence of effective elastic moduli and stress concentrator factors on the radial distribution function of the fiber locations is analyzed. Received: October 20, 2004     

Effective transverse elastic moduli of composites at non-dilute concentration of a random field of aligned fibers

We consider a transversal loading of a linearly elastic isotropic media containing the identical isotropic aligned circular fibers at non-dilute concentration c. By the use of solution obtained by the Kolosov–Muskhelishvili complex potential method for two interacting circles subjected to three different applied stresses at infinity, and exact integral representations for both the stress and strain distributions in a microinhomogeneous medium, one estimates the effective moduli of the composite accurately to order c². Received: March 4, 2003; revised: August 8, 2003     

Resonance methods for determining the complex shear moduli of orthotropic composites

A survey of various methods for determining the complex elasticity and shear moduli from the resonant frequencies of flexural and torsional vibrations of rectangular rods cut out from a plate of an orthotropic composite is presented. The errors in the computed values of dynamic shear moduli caused by inaccuracies in the experimental determination of resonance frequencies are examined. A new variant of the resonance method is developed, which permits one to find three complex shear moduli of a composite from the resonant frequencies and the damping of torsional vibrations of three rods oriented along three symmetry axes of the material. For computing the moduli in the case of an overdetermined system, an algorithm of nonlinear optimization based on the least-squares method is recommended. From the results obtained it follows that, for determining the interlaminar shear moduli with a necessary accuracy, the rods must be sufficiently thick. It is shown that a good agreement alone between calculated and experimental frequencies of flexural and torsional vibrations of rods does not ensure a reliable determination of the moduli of interlaminar shear if experiments are carried out on wide test specimens cut out from a thin plate. Recommendations are given for the choice of geometrical sizes of test specimens for resonance experiments. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 721–744, November–December, 2007.     

Compactified Jacobians of curves with spine decompositions

A curve, that is, a connected, reduced, projective scheme of dimension 1 over an algebraically closed field, admits two types of compactifications of its (generalized) Jacobian: the moduli schemes of P-quasistable torsion-free, rank-1 sheaves and Seshadri’s moduli schemes of S-equivalence classes of semistable torsion-free, rank-1 sheaves. Both are constructed with respect to a choice of polarization. The former are fine moduli spaces which were shown to be complete; here we show that they are actually projective. The latter are just coarse moduli spaces. Here we give a sufficient condition for when these two types of moduli spaces are equal. Eduardo Esteves is Supported by CNPq, Processos 301117/04-7 and 470761/06-7, by CNPq/FAPERJ, Processo E-26/171.174/2003, and by the Institut Mittag–Leffler (Djursholm, Sweden).     

A nanocomposite based on a styrene-acrylate copolymer and native montmorillonite clay 2. Modeling the elastic properties

A variant of stepwise determination of the elastic characteristics of quasi-isotropic polymer-silicate nanocomposites with randomly oriented platelike filler particles is considered. First, the elastic constants of transversely isotropic structural elements with coplanarly placed filler particles are obtained, and then they are averaged over all spatial directions by using the orientational averaging method. The characteristic features of the hierarchical structure of exfoliated and intercalated nanocomposites are also considered. The concentration dependences of elastic constants of a nanocomposite based on a styrene-acrylate copolymer and native montmorillonite clay are modeled, and the results obtained are compared with experimental data. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 235–246, March–April, 2006.