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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, an extended rigid block spring method (RBSM) is proposed to model the deformation and failure of anisotropic cohesive brittle materials, which is applied to a typical clayey rock which exhibits a transversely isotropic behavior.

42 citations

01 Jan 2010
TL;DR: In this article, the weakest-link model is used to model the statistical size effect on the nominal strength of structure according to the weakest link model, and the boundary layer approach is extended to the deterministic analysis of the mean response of structures with distributed softening damage.
Abstract: Applications of the nonlocal models are hampered by unresolved problems in the treatment of boundary conditions. There are many competing variants such as deleting the outside protruding part of nonlocal integral, with rescaling on the interior part, or moving the outside protruding part into a Dirac delta function at the boundary or at the center points of nonlocal domain. The proper boundary conditions are also unclear for the gradient models, including the strongly nonlocal implicit gradient model of Peerlings and de Borst leading to the Helmholtz equation for nonlocal strain. All these models are phenomenological, give very different results, and there are no fundamental criteria for choosing the correct variant. Modeling of the statistical size effect on the nominal strength of structure according to the weakest-link model inspires a new, more physical approach. The weakest-link model (for a structure of positive geometry) requires subdividing the structure volume into elements roughly equal to the representative volume element of material (RVE), whose size corresponds to the diameter of the nonlocal averaging domain (and also to the autocorrelation length). The layer of RVEs along the surface is logically treated as a boundary layer whose deformation depends only on the average continuum strain or stress over the thickness, approximated by values at the centerline (or center surface) of the layer. In the interior excluding the boundary layer, the nonlocal averaging of the contributions to failure probability may be applied without problems since the nonlocal integral domain does not protrude outside the boundary of the body. The results of the nonlocal boundary layer (NBL) model agree closely with direct calculations of failure probability according to the weakest-link model. Subsequently, the boundary layer approach is extended to the deterministic analysis of the mean response of structures with distributed softening damage. The notorious problems with the formulation of boundary conditions for the nonlocal approach are eliminated because no nonlocal integral domain can protrude beyond the boundary. Demonstration is given for the gradient models, while for integral-type models it is still in progress at the time of writing

42 citations

Journal ArticleDOI
TL;DR: In this article, the influence of weak interface between particles and matrix on mechanical properties of metal matrix -ceramic reinforced composites is studied, and the experimental results have been confirmed qualitatively by the computer simulations.

42 citations

Journal ArticleDOI
TL;DR: In this paper, a quantitative description of the diffusion coefficient in a porous medium is provided by fitting parameters, geometric, or shape factors to capture the porous medium's structure in more detail.
Abstract: An accurate quantitative description of the diffusion coefficient in a porous medium is essential for predictive transport modeling. Well-established relations, such as proposed by Buckingham, Penman, and Millington–Quirk, relate the scalar diffusion coefficient to the porous medium’s porosity. To capture the porous medium’s structure in more detail, further models include fitting parameters, geometric, or shape factors. Some models additionally account for the tortuosity, e.g., via Archie’s law. A validation of such models has been carried out mainly via experiments relating the proposed description to a specific class of porous media (by means of parameter fitting). Contrary to these approaches, upscaling methods directly enable calculating the full, potentially anisotropic, effective diffusion tensor without any fitting parameters. As input only the geometric information in terms of a representative elementary volume is needed. To compute the diffusion–porosity relations, supplementary cell problems must be solved numerically and their (flux) solutions must be integrated. We apply this approach to provide easy-to-use quantitative diffusion–porosity relations that are based on representative single grain, platy, blocky, prismatic soil structures, porous networks, or random porous media. As a discretization method, we use the discontinuous Galerkin method on structured grids. To make the relations explicit, interpolation of the obtained data is used. We furthermore compare the obtained diffusion–porosity relations with the well-established relations mentioned above and also with the well-known Voigt–Reiss or Hashin–Shtrikman bounds. We discuss the ranges of validity and further provide the explicit relations between the diffusion and surface area and comment on the role of a tortuosity–porosity relation.

42 citations

Journal ArticleDOI
TL;DR: In this paper, a simple and efficient generator of random fiber distribution with diverse fiber volume fractions (V f ) for unidirectional composites by a random fiber removal technique was proposed.
Abstract: In this paper, we propose a simple and efficient generator of random fiber distribution with diverse fiber volume fractions ( V f ) for unidirectional composites by a random fiber removal technique. From the representative volume element (RVE) consisting of 100 fibers that have a maximum V f of about 65% in this work, also termed the master model, we randomly eliminate fibers to match the predefined V f ranging from 60%, 55%, 45%, 35%, 25%, 15%, and 5%, which are lower than that of the master model. Accordingly, 100 RVE samples for each V f can be constructed in a straightforward manner. To demonstrate the performance of the proposed algorithm, its fiber locations are verified in terms of statistical spatial metrics, such as the nearest neighbor orientation, Ripley's K function, and pair distribution function. Furthermore, the elastic properties and the anisotropic ratios of the generated RVEs are investigated and compared to those of other random fiber generation algorithms.

42 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023134
2022241
2021243
2020293
2019287
2018253