Topic
Representative elementary volume
About: Representative elementary volume is a research topic. Over the lifetime, 4105 publications have been published within this topic receiving 86863 citations.
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TL;DR: In this article, the apparent stiffness tensors of two-dimensional elastic composite samples smaller than the representative volume element (RVE) are studied as a function of system size, and the results show that the difference between the Dirichlet, Neumann and the effective stiffensors depends strongly on the phase stiffness contrast ratio.
Abstract: The apparent stiffness tensors of two-dimensional elastic composite samples smaller thanthe representative volume element (RVE) are studied as a function of system size. Numericalexperiments are used to investigate how the apparent properties of the composite converge withincreasing scale factor n, defined to be the ratio between the linear size of the composite and thelinear size of the unit cell. Under affine (Dirichlet-type) or homogeneous stress (Neumann-type) boundary conditions, the apparent elastic moduli overestimate orunderestimate, respectively, the effective elastic moduli of the infinitely periodic system. Theresults show that the difference between the Dirichlet, Neumann and the effective stiffnesstensors depends strongly on the phase stiffness contrast ratio. Dirichlet boundary conditionsprovide a more accurate estimate of the effective elastic properties of stiff matrix composites,whereas Neumann boundary conditions provide a more accurate estimate for compliant matrixstructures. It is shown that the apparent bulk and shear moduli may lie outside of theHashin–Shtrikman bounds. However, these bounds provide good upper and lower estimates forthe apparent bulk and shear moduli of structures with a scale factor n ⩾ 2. A similar approach isused to study hierarchical composites containing two distinct structural levels with a finiteseparation of length scales. It is shown, numerically, that the error associated with replacing thesmallest-scale regions by an equivalent homogeneous medium is very small, even when the ratiobetween the length scales is as low as three.
115 citations
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TL;DR: In this paper, a micromechanical theory for the thermoelastic response of functionally graded composites with non-uniform fiber spacing in the through-thickness direction is further extended to enable analysis of material architectures characterized by arbitrarily nonuniform fibre spacing in two directions.
114 citations
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TL;DR: In this paper, a wide strip bias extension test has been used to measure the constitutive shear properties of textile preforms, which has been found to give significantly better results in comparison to conventional narrow strip bias test.
Abstract: Textile preforms undergo complex in-plane and out-of-plane deformations during forming processes. In-plane shear is the most significant mode of deformation during draping or forming around double-curvature surfaces. This paper reports an improved method for measuring the constitutive shear properties of textile preforms—a wide strip bias extension test has been found to give significantly better results in comparison to conventional narrow strip bias test. Shear angles, computed directly from global strains, were in close agreement to those measured using an optical method. Constitutive shear stress–strain relation, computed from the bias extension test data, was in good agreement with KES (Kawabata Evaluation System) test results. Meso-scale tow deformations have been measured using two techniques: an inexpensive flatbed scanner-based full-field strain measurement technique for measuring in-plane tow deformations and a strain-freezing technique for measuring through-thickness tow deformations. With this data, a 3D Representative Volume Element (RVE) can be constructed for each stage of shear deformation. Beyond the geometric shear limit, tow deformations during bias extension appear to be somewhat different from those normally expected from pure shear—a reduction in tow thickness and tow cross-sectional area and a corresponding increase in packing factor.
114 citations
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TL;DR: The proposed theory will increase the safety of concrete structures, composite parts of aircraft or ships, microelectronic components,microelectromechanical systems, prosthetic devices, etc, and improve protection against hazards such as landslides, avalanches, ice breaks, and rock or soil failures.
Abstract: In mechanical design as well as protection from various natural hazards, one must ensure an extremely low failure probability such as 10−6. How to achieve that goal is adequately understood only for the limiting cases of brittle or ductile structures. Here we present a theory to do that for the transitional class of quasibrittle structures, having brittle constituents and characterized by nonnegligible size of material inhomogeneities. We show that the probability distribution of strength of the representative volume element of material is governed by the Maxwell–Boltzmann distribution of atomic energies and the stress dependence of activation energy barriers; that it is statistically modeled by a hierarchy of series and parallel couplings; and that it consists of a broad Gaussian core having a grafted far-left power-law tail with zero threshold and amplitude depending on temperature and load duration. With increasing structure size, the Gaussian core shrinks and Weibull tail expands according to the weakest-link model for a finite chain of representative volume elements. The model captures experimentally observed deviations of the strength distribution from Weibull distribution and of the mean strength scaling law from a power law. These deviations can be exploited for verification and calibration. The proposed theory will increase the safety of concrete structures, composite parts of aircraft or ships, microelectronic components, microelectromechanical systems, prosthetic devices, etc. It also will improve protection against hazards such as landslides, avalanches, ice breaks, and rock or soil failures.
114 citations
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TL;DR: In this paper, a micromechanics model is presented to predict thermoelastic properties of composites reinforced with plain weave fabrics, where a representative volume element is chosen for analysis and the fiber architecture is described by a few simple functions.
Abstract: A micromechanics model is presented to predict thermoelastic properties of composites reinforced with plain weave fabrics. A representative volume element is chosen for analysis and the fiber architecture is described by a few simple functions. Equations are developed to calculate various phase fractions from geometric parameters that can be measured on a cross section. Effective elastic moduli and effective thermal expansion coefficients are determined under the assumption of uniform strain inside the representative volume element. The resulting model is similar to the classical laminated theory, and hence is easier to use than other models available in the literature. An experimental correlation is provided for a number of Nicalon SiC/CVI SiC and Graphite/CVI SiC composite laminates.
113 citations