Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3

effective properties Related Abstracts

3 Estimation of Effective Mechanical Properties of Linear Elastic Materials with Voids Due to Volume and Surface Defects

Authors: Sergey A. Lurie, Yury O. Solyaev, Dmitry B. Volkov-Bogorodsky, Alexander V. Volkov


The media with voids is considered and the method of the analytical estimation of the effective mechanical properties in the theory of elastic materials with voids is proposed. The variational model of the porous media is discussed, which is based on the model of the media with fields of conserved dislocations. It is shown that this model is fully consistent with the known model of the linear elastic materials with voids. In the present work, the generalized model of the porous media is proposed in which the specific surface properties are associated with the field of defects-pores in the volume of the deformed body. Unlike typical surface elasticity model, the strain energy density of the considered model includes the special part of the surface energy with the quadratic form of the free distortion tensor. In the result, the non-classical boundary conditions take modified form of the balance equations of volume and surface stresses. The analytical approach is proposed in the present work which allows to receive the simple enough engineering estimations for effective characteristics of the media with free dilatation. In particular, the effective flexural modulus and Poisson's ratio are determined for the problem of a beam pure bending. Here, the known voids elasticity solution was expanded on the generalized model with the surface effects. Received results allow us to compare the deformed state of the porous beam with the equivalent classic beam to introduce effective bending rigidity. Obtained analytical expressions for the effective properties depend on the thickness of the beam as a parameter. It is shown that the flexural modulus of the porous beam is decreased with an increasing of its thickness and the effective Poisson's ratio of the porous beams can take negative values for the certain values of the model parameters. On the other hand, the effective shear modulus is constant under variation of all values of the non-classical model parameters. Solutions received for a beam pure bending and the hydrostatic loading of the porous media are compared. It is shown that an analytical estimation for the bulk modulus of the porous material under hydrostatic compression gives an asymptotic value for the effective bulk modulus of the porous beam in the case of beam thickness increasing. Additionally, it is shown that the scale effects appear due to the surface properties of the porous media. Obtained results allow us to offer the procedure of an experimental identification of the non-classical parameters in the theory of the linear elastic materials with voids based on the bending tests for samples with different thickness. Finally, the problem of implementation of the Saint-Venant hypothesis for the transverse stresses in the porous beam are discussed. These stresses are different from zero in the solution of the voids elasticity theory, but satisfy the integral equilibrium equations. In this work, the exact value of the introduced surface parameter was found, which provides the vanishing of the transverse stresses on the free surfaces of a beam.

Keywords: effective properties, scale effects, surface defects, voids elasticity

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2 Analysis of Overall Thermo-Elastic Properties of Random Particulate Nanocomposites with Various Interphase Models

Authors: Lidiia Nazarenko, Henryk Stolarski, Holm Altenbach


In the paper, a (hierarchical) approach to analysis of thermo-elastic properties of random composites with interphases is outlined and illustrated. It is based on the statistical homogenization method – the method of conditional moments – combined with recently introduced notion of the energy-equivalent inhomogeneity which, in this paper, is extended to include thermal effects. After exposition of the general principles, the approach is applied in the investigation of the effective thermo-elastic properties of a material with randomly distributed nanoparticles. The basic idea of equivalent inhomogeneity is to replace the inhomogeneity and the surrounding it interphase by a single equivalent inhomogeneity of constant stiffness tensor and coefficient of thermal expansion, combining thermal and elastic properties of both. The equivalent inhomogeneity is then perfectly bonded to the matrix which allows to analyze composites with interphases using techniques devised for problems without interphases. From the mechanical viewpoint, definition of the equivalent inhomogeneity is based on Hill’s energy equivalence principle, applied to the problem consisting only of the original inhomogeneity and its interphase. It is more general than the definitions proposed in the past in that, conceptually and practically, it allows to consider inhomogeneities of various shapes and various models of interphases. This is illustrated considering spherical particles with two models of interphases, Gurtin-Murdoch material surface model and spring layer model. The resulting equivalent inhomogeneities are subsequently used to determine effective thermo-elastic properties of randomly distributed particulate composites. The effective stiffness tensor and coefficient of thermal extension of the material with so defined equivalent inhomogeneities are determined by the method of conditional moments. Closed-form expressions for the effective thermo-elastic parameters of a composite consisting of a matrix and randomly distributed spherical inhomogeneities are derived for the bulk and the shear moduli as well as for the coefficient of thermal expansion. Dependence of the effective parameters on the interphase properties is included in the resulting expressions, exhibiting analytically the nature of the size-effects in nanomaterials. As a numerical example, the epoxy matrix with randomly distributed spherical glass particles is investigated. The dependence of the effective bulk and shear moduli, as well as of the effective thermal expansion coefficient on the particle volume fraction (for different radii of nanoparticles) and on the radius of nanoparticle (for fixed volume fraction of nanoparticles) for different interphase models are compared to and discussed in the context of other theoretical predictions. Possible applications of the proposed approach to short-fiber composites with various types of interphases are discussed.

Keywords: effective properties, energy equivalence, Gurtin-Murdoch surface model, interphase, random composites, spherical equivalent inhomogeneity, spring layer model

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1 A Numerical Study on Micromechanical Aspects in Short Fiber Composites

Authors: I. Ioannou, I. M. Gitman


This study focused on the contribution of micro-mechanical parameters on the macro-mechanical response of short fiber composites, namely polypropylene matrix reinforced by glass fibers. In the framework of this paper, an attention has been given to the glass fibers length, as micromechanical parameter influences the overall macroscopic material’s behavior. Three dimensional numerical models were developed and analyzed through the concept of a Representative Volume Element (RVE). Results of the RVE-based approach were compared with analytical Halpin-Tsai’s model.

Keywords: Homogenization, representative volume element, effective properties, short fiber reinforced composites

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