A multiscale analysis of the mechanical behavior of a thermo-oxidized c/epoxy lamina

The mechanical behavior of carbon-fiber-reinforced polymer matrix composites having undergone a thermo-oxidation process is studied. The purpose is to perform a multiscale analysis of the consequences of oxidation on the intrinsic mechanical properties of the external composite ply and on the internal mechanical states experienced by the structure under mechanical loads. The effective mechanical properties of oxidized composite plies are determined according to the Eshelby–Kr?ner self-consistent homogenization procedure, depending on evolution of the oxidation process. The results obtained are compared with estimates found by the finite-element method. The macroscopic mechanical states are calculated for a unidirectional composite and laminates. The macroscopic stresses in each ply of the structure are determined by the classical lamination theory and the finite-element method, whereas the local stresses in the carbon fiber and epoxy matrix are calculated by using an analytical stress concentration relation.     

An analysis of contact deformation of auxetic composites

The adaptive mode of frictional interaction has been studied as a self-locking effect upon contact deformation of isotropic and anisotropic auxetic materials with a negative Poisson ratio. This effect manifests itself in the fact that the bearing capacity of the joint rises with increasing shear load. In particular, the parameters of stress state (contact load, tangential stresses, slippage, etc.) were determined for a double-lap joint under conditions of compression with or with out shear. The contact interaction was analyzed by the finite-element method for three profiles of symmetrically located contact elements (plane, cylindrical, and wedge-shaped). The Poisson ratio was varied within the range theoretically admissible for isotropic elastic media. Analogous calculations were also performed for a joint with a deformed element made of an anisotropic auxetic composite, whose reinforcement angle was varied. The maximum loads, tangential stresses, and slippage are obtained as nonlinear functions of Poisson ratio (in the isotropic case) and reinforcement angle of the composite material. The stress concentration and the increased ultimate shear forces are also estimated. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 681–692, September–October, 2006.     

Interaction between two neighboring circular holes in a prestretched simply supported orthotropic strip under bending

In this work, the influence of initial stretching of a simply supported plate-strip containing two circular holes on the stress concentration around the holes caused by bending of the strip is examined using the finite-element method. The mathematical formulation of the corresponding boundary-value problem is presented within the frame work of the three-dimensional linearized theory of elasticity (TDLTE) under a plane strain state. The material of the plate-strip is linearly elastic, homogeneous, and orthotropic. The numerical results obtained in investigating the influence of the initial stretching and the location of holes on the stress concentration are presented. In particular, it is established that the initial stretching significantly decreases the stress concentration at some characteristic points on the contour of the holes. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 827–838, November–December, 2008.     

A refined stress-strain analysis in the load transfer zone of flat specimens of high-strength unidirectional composites in uniaxial tension 3. Effect of grip misalignment

The influence of a preliminary bending induced by misalignment of the grips of a testing machine on the stress-strain state of a flat specimen made of a high-strength unidirectional carbon fiber composite under uniaxial tension is estimated. An analysis of the analytical solution obtained is carried out, and the results of finite-element calculations and modeling experiments are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 745–760, November–December, 2007.     

A nanocomposite based on a styrene-acrylate copolymer and native montmorillonite clay 1. Preparation, testing, and properties

The preparation of a polymer nanocomposite by compounding an aqueous polymer emulsion with an aqueous dispersion of montmorillonite clay is described. A styrene-acrylate copolymer emulsion and a purified native montmorillonite clay from Latvian deposits are used. An X-ray diffraction analysis and differential scanning calorimetric thermograms are shown. Data on the influence of montmorillonite concentration on the tensile stress-strain diagram, elasticity, yield stress, breaking stress, and ultimate elongation of the processed nanocomposite material are obtained. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 61–74, January–February, 2006.     

Predicting the elastoplastic response of fiber-reinforced metal matrix composites

This paper aims to investigate the effect of microstructure parameters (such as the cross-sectional shape of fibers and fiber volume fraction) on the stress–strain behavior of unidirectional composites subjected to off-axis loadings. A micromechanical model with a periodic microstructure is used to analyze a representative volume element. The fiber is linearly elastic, but the matrix is nonlinear. The Bodner–Partom model is used to characterize the nonlinear response of the fiber-reinforced composites. The analytical results obtained show that the flow stress of composites with square fibers is higher than with circular or elliptic ones. The difference in the elastoplastic response, which is affected by the fiber shape, can be disregarded if the fiber volume fraction is smaller than 0.15. Furthermore, the effect of fiber shape on the stress–strain behavior of the composite can be ignored if the off-axis loading angle is smaller than 30°.     

The Method of Three-Point Bending in Testing Thin High-Strength Reinforced Plastics at Large Deflections

A method is presented for determining the flexural strength of unidirectional composites from three-point bending tests at large deflections. An analytical model is proposed for calculating the flexural stress in testing thin bars in the case of large deflections. The model takes into account the changes in the support reactions at bar ends and in the span of the bar caused by its deflection. In the model offered, the influence of transverse shear and the friction at supports are neglected. The problem is solved in elliptic integrals of the first and second kind. The results obtained are compared with experimental tension data. The method elaborated for calculating flexural stresses has an obvious advantage over the conventional engineering procedure, because the calculation accuracy of the stresses increases considerably in the case of large deflections. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 5, pp. 691–704, September–October, 2005.     

Emission of screw dislocations from the surface of a thin defect into an isotropic medium

By using the method of jump functions, we investigate the quasistatic stress field and stress concentration near a thin strip at the interface between materials during emission of screw dislocations from it into the medium. We construct analytic solutions in the cases of finite and semiinfinite cracks and perfectly rigid films. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp. 67–75, April–June, 1998.     

Equal-stressed reinforcement of metal-composite plates with fibers of constant cross section in steady-state creep

The problem on equal-stressed reinforcement of metal-composite plates with fibers of constant cross section, loaded in their plane and operating under the conditions of steady-state creep, is formulated. A qualitative analysis of the corresponding system of resolving equations and boundary conditions is performed. An important case of the problem is considered, where both the reinforcing fibers and the matrix are equally stressed. A method for numerically solving this problem is developed. Particular analytical and approximate solutions are discussed, with the example of which changes in the reinforcement structure in relation to the stress level in the reinforcing fibers are clarified. It is shown that nonunique solutions to such problems can exist. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 1, pp. 11–34, January–February, 2008.     

An exact analysis for mode III cracks between two dissimilar magnetoelectroelastic layers

This paper develops a closed-form solution for an interface crack in a layered magnetoelectroelastic strip of finite width. The strip is subjected to anti-plane mechanical and in-plane electric and magnetic fields. Explicit expressions for the stress, electric, and magnetic fields, together with their intensity factors, are obtained for two extreme cases of an impermeable and a permeable cracks. The stress intensity factor does not depend on the electromagnetic boundary conditions assumed for the crack. However, the electrically and magnetically permeable boundary conditions on the crack profile have a significant influence on the crack-tip electromagnetic field intensity factors. Solutions for some special cases, such as a central crack, an edge crack, two symmetric collinear cracks, and a row of collinear interface cracks, are also obtained in closed forms. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 763–784, November–December, 2008.     

A refined stress-strain analysis in the load transfer zone of flat specimens of high-strength unidirectional composites in uniaxial tension 2. Finite-element parametric analysis

A detailed finite-element analysis of the stress-strain state in the load transfer zone of uneasily tensioned flat test specimens made of a high-strength unidirectional carbon fiber-epoxy composite is carried out with account of the elastoplastic behavior of a structural polyurethane adhesive. Various schemes of introduction of external loads into the specimens are considered. A numerical finite-element analysis of different configurations of specimen tabs allowed us to put forward a technique for significantly reducing the dangerous concentration of operating stresses. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 43–58, January–February, 2007.     

A comparative study of fiber-matrix interactions by using micromechanical models

The purpose of this study is to describe the interfacial interactions in terms of stress distributions on short fibers in fiber-matrix unit-cell models. The fiber and matrix are subjected to tensile loading. The study consists of three main parts. First, fiber-matrix cell segments are modeled using a 3D finite-element analysis (FEA) with ANSYS. Three different finite-element geometrical unit-cell models are generated in order to simulate the Cox analytical model: a fiber-matrix combination, a single fiber, and a single matrix element. The second part contains the results of 3D FE analyses, which are applied to the Cox formulations by using a computer program developed. In the last part, the analytical solutions for distributions of normal and shear stresses are investigated. Cox 2D linear elasticity solutions, together with finite-element ones, are presented in detail in graphs. The interfacial interactions between the fibers and matrix are also discussed considering the relative changes in the distributions of normal and shear stresses. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 505–520, July–August, 2008.     

Fundamental solution of generalized thermo-viscoelasticity using the finite element method

The present paper is aimed at an investigation of the temperature, displacement, and stress in a viscoelastic half space of Kelven–Voigt type. The formulation is applied according to three theories of generalized thermoelasticity: Lord–Shulman with one relaxation time, Green–Lindsay with two relaxation times, as well as the coupled theory. The nondimensional governing equations are solved by the finite element method. Numerical results for the temperature distribution, displacement, and thermal stress are represented graphically. Comparisons are made with the results predicted by the CD, L-S, and G-L theories in the presence and absence of the viscoelastic relaxation time.     

The influence of anisotropy on the stress concentration near a hole in a conical shell

On the basis of the variational method we discuss an approach to the computation of the stress-strain state of a conical shell made of a composite material and weakened by a hole. For a glass-plastic shell with a round unreinforced hole we study the influence of the variation of an interlayer shear and orthotropy on the stress concentration. Two tables. Bibliography: 4 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 22, pp. 63–67, 1991.     

Analytical solution of the nonstationary boltzmann equation in the BGC model

Using the Case method, the analytical solution to the BGC nonstationary kinetic equation is constructed. As an application, the problem of a point-like source of heat or particles is considered. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 1, pp. 139–148, October, 1997.     

Applications of nonstandard analysis to ideal boundaries in potential theory

A solution is given of the generalized Dirichlet problem for an arbitrary compactification of a Brelot harmonic space. A method of obtaining the Martin-Choquet integral representation of positive harmonic functions is given, and the existence is established of an ideal boundary Δ supporting the maximal representing measures for positive bounded and quasibounded harmonic functions with almost all points of Δ being regular for the Dirichlet problem. This work was supported by a grant from the U. S. National Science Foundation. The results in Sections 1–5 were presented at the 1974 Oberwolfach Conferences on Potential Theory and Nonstandard Analysis; Sections 1–6 were discussed at the Abraham Robinson Memorial Conference, Yale, University, May 1975.     

A note on the prior parameter choice in finite mixture models of distributions from exponential families

This work presents a new scheme to obtain the prior distribution parameters in the framework of Rufo et al. (Comput Stat 21:621–637, 2006). Firstly, an analytical expression of the proposed Kullback–Leibler divergence is derived for each distribution in the considered family. Therefore, no previous simulation technique is needed to estimate integrals and thus, the error related to this procedure is avoided. Secondly, a global optimization algorithm based on interval arithmetic is applied to obtain the prior parameters from the derived expression. The main advantage by using this approach is that all solutions are found and rightly bounded. Finally, an application comparing this strategy with the previous one illustrates the proposal.     

Dependence of thermooxidative aging parameters on composite properties

An analytical relationship between the thermooxidation rate constants and mechanical properties of composite materials under isothermal and dynamic conditions is obtained. With the example of epoxy-based composites, it is shown that the kinetic parameters of thermooxidation can be used to predict the internal stresses and breakdown voltage of coatings. The calculated drop in the impact toughness exceeds its experimental value by 30%, while the calculated relative breaking elongation is 1.5–2 times greater than the experimental one. A considerable decrease in these indices is observed at a loss of 0.1–1 wt.% of volatile products of thermooxidation. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 237–248, January–February, 2000.     

Elastoplastic stress analysis of thick laminated metal-matrix composite plates by the finite-element method

The elastoplastic stress state of a laminated stainless-steel-fiber-reinforced aluminum-matrix plates, with or without a hole, subjected to a pressure on their top is examined by using the finite-element method. The analysis is carried out for three layouts: (0/90/0/90)_s, (45/-45/45/-45)_s, and (30/60/30/60)_s. The Newton-Raphson method is used to solve the nonlinear problem. The distributions of equivalent stresses and the plastic zones of the plates without a hole and with a hole of various diameters are determined. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 531–544, July–August, 2006.     

Variational conditions with smooth constraints: structure and analysis

 This is an expository paper about the analysis of variational conditions over sets defined in finite-dimensional spaces by fairly smooth functions satisfying a constraint qualification. The primary focus is on results that can provide quantitative and computable sensitivity information for particular instances of the problems under study, and our objective is to give a personal view of the state of current knowledge in this area and of gaps in that knowledge that require future work. The writing style is informal, in keeping with the objective of focusing the reader's attention on the basic concepts and the relationships between them, rather than on details of the particular results themselves. Received: December 1, 2002 / Accepted: April 25, 2003 Published online: May 28, 2003 Key words. variational condition – variational inequality – complementarity – sensitivity – stability – nondegeneracy Mathematics Subject Classification (2000): Primary: 90C31. Secondary: 47J20, 49J40, 49J53, 90C33