Determination Of Representative Volume Element Size Research Articles

Representative volume element size determination for viscoplastic properties in polycrystalline materials

The size of representative volume element (RVE) for 3D polycrystalline material is investigated. A statistical RVE size determination method is applied to a Voronoi tessellation-based pure copper microstructure. The definition of RVE has remained problematic in the literature for properties related to nonlinear viscoplastic behavior, e.g. apparent viscoplastic parameter, intrinsic plastic dissipation. Computational homogenization for elastic and plastic properties is performed within a crystal plasticity finite element framework, over many realizations of the stochastic microstructural model, using periodic boundary conditions. The generated data undergoes statistical treatment, from which RVE sizes are obtained. The method used for determining RVE sizes was found to be operational, even for viscoplasticity. The microscale analysis of the full-field simulation results reveals microstructure-relate heterogeneities which shed new light on the problem of RVE size determination for nonlinear properties.

Studying the representative volume of concrete using the entropy weight–grey correlation model

The representative volume element (RVE) plays an important role in the study of concrete properties. Meanwhile, RVE size determination itself is an issue that needs further study. For the first time, the problem of determining RVE size based on several factors is regarded as a multi-objective decision-making problem. A new method, the entropy weight–grey correlation model, is proposed, by comprehensively considering the influence of coarse aggregate content, aggregate average particle size and the aggregate fineness modulus. A two-dimensional concrete aggregate specimen, randomly generated by numerical simulation with an aggregate size of 5–20 mm, is taken as a case study, and the RVE size is determined as 6–7 times the maximum aggregate size. Then the finite-element method is used to verify its mechanical properties. This new method has the advantage of depending less on variable data compared to the traditional method, indicating a wider range of applicability. Additionally, the model is applied to determine the RVE size of three-dimensional concrete, which is similar to two-dimensional concrete. It provides a new comprehensive insight for the study of concrete RVE size, which could also be extended to apply to determining the RVE of other composite materials.

Determination of RVE size based on the 3D fracture persistence

This paper presents an application of a 3D fracture network model and 3D persistence to confirm the representative volume element (RVE) in a fractured rock mass. Based on field fracture data collected from the Songta dam site, a large 3D fracture network is generated to analyse the RVE. The 3D persistence, which is governed by the comprehensive characteristics of fracture location, orientation, size and density, strongly affects the shear strength of fractured rock masses. Hence, it is valuable to confirm the RVE size considering the persistence, which combines the geometric and mechanical properties of a rock mass. The persistence values of the entire model and of cubes of different sizes, which are located in the centre of the model, are determined. A relative error of 10% is selected as the benchmark to evaluate the similarity between the cubes and the model. Finally, 15 m is confirmed as the size of the RVE in the study area.

Determination of the size of the Representative Volume Element (RVE) for the simulation of heterogeneous polymers at finite strains

The definition of the size of the Representative Volume Element (RVE) is extremely important for the mechanics and physics of heterogeneous materials since it should statistically represent the micro-structure of the material. In the present contribution, a methodology based on statistical analysis and numerical experiments is proposed to determine the size of the RVE for heterogeneous amorphous polymers subjected to finite deformations. The approach is applied to Rubber Toughened Polystyrene (RT-PS) composed by a two phase random micro-structure. Different micro-structural samples with two different percentages of rubbery particles, namely 10% and 15%, inside the micro-structure are studied. Periodic boundary conditions (PBC) are enforced to the RVE due to their fast convergence to the theoretical/effective solution when the RVE size increases. The Finite Element Method (FEM) is used in combination with mathematical homogenization to obtain the macro-stress. Two criteria are proposed for the RVE size determination. The proposed statistical-numerical approach is general and easy to use, when compared to the previously proposed approaches, and covers other criteria available in the literature.

Towards gigantic RVE sizes for 3D stochastic fibrous networks

The size of representative volume element (RVE) for 3D stochastic fibrous media is investigated. A statistical RVE size determination method is applied to a specific model of random microstructure: Poisson fibers. The definition of RVE size is related to the concept of integral range. What happens in microstructures exhibiting an infinite integral range? Computational homogenization for thermal and elastic properties is performed through finite elements, over hundreds of realizations of the stochastic microstructural model, using uniform and mixed boundary conditions. The generated data undergoes statistical treatment, from which gigantic RVE sizes emerge. The method used for determining RVE sizes was found to be operational, even for pathological media, i.e., with infinite integral range, interconnected percolating porous phase and infinite contrast of properties.

A statistics based numerical investigation on the prediction of elasto-plastic behavior of WC–Co hard metal

This paper focuses on the evaluation of the nonlinear elasto-plastic behavior of a WC–Co composite by a computational micromechanics approach. Due to the non-periodic nature of the material, the difficulty underlies primarily in determining a representative volume element (RVE) which is efficient in embodying the microstructure of the material and the global material feature predicted from it would not been strongly distorted. For this purpose a statistics based methodology is proposed as well as a model generation technique which is capable to convert real images taken from scanning electron microscopy (SEM) automatically into a finite element model. Based on this technique, a series of SEM images were studied with the emphasis to investigate the impact of the RVE size on the prediction of the composite behavior in a statistical manner. Furthermore, the paper discusses the impact coming from additional factors, such as boundary conditions and element type. Simulation results based on various case studies are compared with experimental observations and a statistical perspective in RVE size determination is introduced.

Determination of the size of the representative volume element for random quasi-brittle composites

A representative volume element (RVE) is related to the domain size of a microstructure providing a “good” statistical representation of typical material properties. The size of an RVE for the class of quasi-brittle random heterogeneous materials under dynamic loading is one of the major questions to be answered in this paper. A new statistical strategy is thus proposed for the RVE size determination. The microstructure illustrating the methodology of the RVE size determination is a metal matrix composite with randomly distributed aligned brittle inclusions: the hydrided Zircaloy constituting nuclear claddings. For a given volume fraction of inclusions, the periodic RVE size is found in the case of overall elastic properties and of overall fracture energy. In the latter case, the term “representative” is discussed since the fracture tends to localize. A correlation factor between the “elastic” RVE and the “fracture” RVE is discussed.