Deformation and long-term damage of homogeneous and composite materials of stochastic structure (Review)

The studies of mathematical models for the coupled processes of deformation and long-time damage of stochastic composite materials are systematized. Damage is modeled by stochastically arranged micropores. The damage of a single microvolume is characterized by its stress-rupture strength determined by the dependence of the time to brittle fracture on the difference between the equivalent stress and its limit, which is the ultimate strength, according to the Huber–Mises or Schleicher–Nadai criteria, and assumed to be a random function of coordinates. The equation of damage balance at an arbitrary time and the equations relating macrostresses and macrostrains constitute a closed system. Algorithms of calculating the time dependence of microdamage and macrostresses are developed. The effect of temperature and nonlinearity on the curves is studied     

Theory of indentation on multiferroic composite materials

This article presents a general theory on indentation over a multiferroic composite half-space. The material is transversely isotropic and magneto-electro-elastic with its axis of symmetry normal to the surface of the half-space. Based on the corresponding half-space Green’s functions to point sources applied on the surface, explicit expressions for the generalized pressure vs. indentation depth are derived for the first time for the three common indenters (flat-ended, conical, and spherical punches). The important multiphase coupling issue is discussed in detail, with the weak and strong coupling being correctly revisited. The derived analytical solutions of indentation will not only serve as benchmarks for future numerical studies of multiphase composites, but also have important applications to experimental test and characterization of multiphase materials, in particular, of multiferroic properties.     

Forced vibrations of laminated materials with a stochastic structure

S. P. Timoshenko Institute of Mechanics of the Ukrainian Academy of Sciences, Kiev. "Energiya" Scientific-Industrial Association, Moscow. Translated from Prikladnaya Mekhanika, Vol. 30, No. 5, pp. 24–31, May, 1994.     

Theory of elastic-plastic deformation of randomly reinforced composite materials

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 120–124, September–October, 1991.     

Effect of structure of composite materials on their elastic properties

A statistical formulation is proposed for determining the bounds of elastic macrocharacteristics of a composite material by using classical variational theorems of the elasticity theory. The calculation scheme provided takes into account the correlation effects of the second and third order; it also provides estimates for elastic macrocharacteristics by taking into account the constant, the latter being that physical characteristic of the material which reflects its structure.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 153–159, March–April, 1973.     

基于纤维随机分布的单向复合材料拉伸破坏过程模拟

单向复合材料的极限拉伸强度受纤维强度变化和纤维随机分布的影响。本文提出了一种合理的纤维随机分布假设,并以此建立了剪滞数值模型。利用蒙特卡罗模拟方法结合现有模型分析了单向复合材料的拉伸失效过程,得到极限拉伸强度。与文献模型相比较的结果表明,本文的模型结果更理想。     

Theory of perfect plasticity of composite materials,taking account of volume compressibility

The practical importance and timeliness of the study of the mechanical macroscopic behavior of composite microinhomogeneous media are determined by its ability to give criteria for estimating the limiting load of various structural elements, the flow of multiphase dispersed systems, the deformation of materials made by powder metallurgy methods, etc. The theoretical prediction of the properties of composites is generally most effectively realized when their structural representations are based on the theory of random fields. Application of the strong isotropy hypothesis [1] for the statistical averaging of certain relations of a perfectly plastic body with microstructure permits the determination of its macroscopic yield surface.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 164–167, May–June, 1981.     

Strength of composite materials

Here we consider the class of composites in which the strength of the contact between the materials is less than the strength of the components. It is found that the strength of such a material is independent of the size of the initial defect within certain limits but is determined by the shape and size of the most hazardous [weakest] inclusion. A theoretical relationship is deduced for the strength in relation to the size of the largest inclusion, which agrees well with experiment [1], This mechanism probably plays a part in the failure of steel and may be one reason for the scale effect in steel.     

Theory of dynamic processes in mechanical systems and materials of regular structure

The theory of vibrations and waves in natural and synthesized materials of regular structure is analyzed. Models based on different averaging and continualization methods are outlined. Emphasis is on periodically inhomogeneous structures. The exact solutions are obtained and analyzed using the closed-form solution of infinite algebraic systems, representing equations in Hamiltonian operator form and solving them based on the theory of differential equations with periodic coefficients, mode selection rule, and methods of drawing wave shapes at limit and arbitrary frequencies     

Effective electrostrictive properties of stochastic two-component materials

The paper addresses electrostriction as a nonlinear electromechanical effect in inhomogeneous two-component materials. The method of conditional moments is developed to determine the effective electrostrictive properties of such materials. Exact expressions for the effective characteristics of isotropic composites with oriented inclusions are given. The effect of the shape and volume fraction of inclusions on the effective properties of composite materials is examined. Relevant graphs are plotted Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 3–11, September 2008.     

Deterministic and stochastic optimization of composite cylindrical laminates

The paper is focused on optimization of prestress and placement of fibers in laminated cylindrical composites. It also involves a stochastic study of prestress deviation in particular layers. Optimization (design) parameters considered in control of internal stresses are the eigenstrains. The behavior of a certain functional serving for optimization of the eigenstrains with stochastically perturbed and correlated values in a laminated cylindrical structure is examined. In the first part, a deterministic optimization of composite laminated cylinders is performed by means of the eigenstrains produced in the layers during the fabrication process. Because fabrication of laminates is sensitive to deviation of eigenstrain magnitudes, as shown from stochastic study, an additional minimization of the eigenstrains is introduced.     

Mechanics of composite materials with distorted structure (review). continuum theory,fiber composites

Conclusions Investigations of the mechanics of composite materials with structural distortion within the framework of the continuum approach and within the framework of the model of a piecewise-homogeneous body for fibrous composite materials have been reviewed in the present work. On the basis of this review, these investigations must be regarded as in their early stages, In our view, the next stages in this work are to investigate the characteristic static and dynamic problems within the framework of continuum theory [10, 21, 23] and to investigate the stress-strain state in fibrous composite materials with structural distortion taking account of the mutual influence of the fibers.Institute of Mathematics and Mechanics, Academy of Sciences of the Azerbaidzhan SSR, Baku. Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No, 5, pp. 3–20, May, 1991.     

Transient waves in composite materials

A continuum theory for transient wave propagation in three-dimensional composite materials is given. The derived model provides a set of governing equations for the prediction of dynamic response of elastic composites to impulsive loadings. Pulse propagation normal to the direction of layering in periodically bilaminated media, and normal to the fiber direction in unidirectional long-fiber composites are obtained as special cases. The dynamic response of the composite is determined solely from the materials properties of the constituents (assumed in general to be orthotropic) and their geometrical dimensions. The predicted propagating transient waves are checked with exact solutions for impacted laminated composites, and with measured data for a fiber-reinforced material. Applications are given for pulse propagation in particulate composites and in tri-othogonally fiber-reinforced materials.