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 paper, the influence of membrane stresses applied during the molding process on the mechanical properties of the finished composite was investigated, and it was shown that a uniaxial tensile stress applied to the preform results in an increase in tensile modulus and a corresponding reduction in transverse modulus, as a result of reduced crimp in the loading direction with a corresponding increase in the transverse direction.
61 citations
TL;DR: In this article, an algorithm was developed to generate random representative volume elements (RVE) with varying volume fractions and minimum distances between fibers, and the results compared to those for periodic microstructured RVEs in terms of the range of stress values, maximum stress, and homogenized stiffness values.
Abstract: Random and periodic representations of composite microstructures are inherently different both in terms of the resultant range of stresses that each phase carries as well as the total load over the entire volume comprising both matrix and fiber phases. In this study, an algorithm was developed to generate random representative volume elements (RVE) with varying volume fractions and minimum distances between fibers. The random microstructures were analyzed using finite element models (FEM) and the results compared to those for periodic microstructured RVEs in terms of the range of stress values, maximum stress, and homogenized stiffness values. Using a large number of random RVE analyses, a meaningful estimation for range and average maximum stress in the matrix phase was achieved. Results show that random microstructures exhibit a much larger range of stress values than periodic microstructures, resulting in an uneven distribution of load and distinct areas of high and low stress concentration in the matrix. It is shown that the maximum stress in the matrix phase, often responsible for failure initiation, is largely dependent on the random morphology, minimum distances between fibers, and volume fraction. Moreover, it is shown that the predicted overall load-carrying capacity of the matrix changes depending on the use of random or periodic microstructures.
61 citations
TL;DR: In this paper, a recently developed micromechanical theory for the thermo-elastic response of functionally graded composites is further extended to include the inelastic and temperature-dependent response of the constituent phases.
61 citations
TL;DR: In this paper, the homogenization method based on the finite element method (FEM) is used as it has advantages, such as it is appropriate for estimating the effective properties of composites with a given periodic fiber distribution and complicated geometries.
61 citations
TL;DR: In this paper, the Dirichlet-Eshelby tensor is used to characterize the elastic fields due to inclusions embedded in a finite elastic medium, which is the first paper in a series concerned with the precise characterization of elastic fields.
Abstract: This is the first paper in a series concerned with the precise characterization of the elastic fields due to inclusions embedded in a finite elastic medium. A novel solution procedure has been developed to systematically solve a type of Fredholm integral equations based on symmetry, self-similarity, and invariant group arguments. In this paper, we consider a two-dimensional (2D) circular inclusion within a finite, circular representative volume element (RVE). The RVE is considered isotropic, linear elastic and is subjected to a displacement (Dirichlet) boundary condition. Starting from the 2D plane strain Navier equation and by using our new solution technique, we obtain the exact disturbance displacement and strain fields due to a prescribed constant eigenstrain field within the inclusion. The solution is characterized by the so-called Dirichlet-Eshelby tensor, which is provided in closed form for both the exterior and interior region of the inclusion. Some immediate applications of the Dirichlet-Eshelby tensor are discussed briefly.
60 citations