Representative Volume Element Geometry Research Articles

Numerical Mesoscale Analysis of Textile Reinforced Concrete.

This contribution presents a framework for Numerical Material Testing (NMT) of textile reinforced concrete based on the mesomechanical analysis of a Representative Volume Element (RVE). Hence, the focus of this work is on the construction of a proper RVE representing the dominant mechanical characteristics of Textile Reinforced Concrete (TRC). For this purpose, the RVE geometry is derived from the periodic mesostructure. Furthermore, sufficient constitutive models for the individual composite constituents as well as their interfacial interactions are considered, accounting for the particular mechanical properties. The textile yarns are modeled as elastic transversal isotropic unidirectional layers. For the concrete matrix, an advanced gradient enhanced microplane model is utilized considering the complex plasticity and damage behavior at multiaxial loading conditions. The mechanical interactions of the constituents are modeled by an interface formulation considering debonding and friction as well as contact. These individual constitutive models are calibrated by corresponding experimental results. Finally, the damage mechanisms as well as the load bearing behavior of the constructed TRC-RVE are analyzed within an NMT procedure based on a first-order homogenization approach. Moreover, the effective constitutive characteristics of the composite at macroscale are derived. The numerical results are discussed and compared to experimental results.

Multiscale computational modelling of closed cell metallic foams with detailed microstructural morphological control

This contribution addresses the multiscale computational modelling of closed cell metallic foams by means of an integrated Representative Volume Element (RVE) generation and computation strategy. The microstructural geometry is computationally generated by controlling relevant fine scale features such as the distribution of cell sizes, the spatial organization of cell sizes and that of cell wall thicknesses and curvatures. The number of faces per cell and of edges per face are also set to comply with the experimentally observed values. The computational generation of the RVE is built on three ingredients: (i) a random close inclusions packing algorithm based on random sequential addition assisted by neighbour distance control, (ii) a distance field-based shape tessellation (morphing) that allows reproducing cell wall curvatures and varying cell wall thicknesses from the inclusions packing, (iii) a close control of the shape of the cells. The RVE geometry is thus described using implicit functions, thereby allowing a seamless transition towards a recently developed mesh generation technique for heterogeneous microstructures represented by such implicit functions, enabling simulations in standard softwares. This controlled generation methodology is illustrated based on experimental data available in literature for morphological indicators relevant to the foam mechanical behaviour. A qualitative and quantitative agreement between FE results and experimental data is obtained for the mechanical response of a commercially available ALPORAS foam. The individual contribution of each microstructural feature (size distributions, wall thickness and curvatures) to the average behaviour of closed cell foams is assessed through FE computations on increasingly complex geometries.

A non-local transient-gradient enhanced damage modelling method incorporating variable Poisson’s ratio for brittle bi-material composites

Widely reported damage modelling methods inherently use elastic brittle rapidly decaying responses for materials under both uniaxial tension and compression, in spite of the existence of ample experimental evidences that the damaging process under compression is significantly different to that under tension. This paper reports a damage evolution law suitable for representing the gradual damaging under compression. Sensitivity of the parameters of the law has been systematically presented. Internal damaging process of brittle materials has been represented through increase in Poisson’s ratio, thus treating this property as a variable affected by the damage levels. These damage evolution laws have been incorporated into a diffused form of non-local transient-enhanced model and applied to the analysis of masonry through two geometrically different representative volume elements (RVE) with periodic boundary conditions. It has been shown that the geometry of the RVE is insignificant to the prediction of the stress-strain responses of masonry assemblages, thereby supporting adoption of a simple geometry of RVE for predicting the behaviour of bi-material brittle composites.

Modeling of constitutive behavior of anisotropic composite material using multi-scale approach

The paper is focused on determining the elastic-plastic behavior of anisotropic composite materials. One of the main goals of this study is to compute effective material properties by analyzing material behavior at microstructure level. The effective material properties were investigated with the use of homogenization procedure connected with volume averaging of stress and strain values in RVE (Representative Volume Element). Three dimensional RVE geometry that represents material microstructure is taken into consideration. The spatial distribution of the particles is determined with experimental data. A boundary value problem is solved by using the finite element method and enforcing periodic boundary conditions. In addition, another approaches based on two step homogenization method and orientation averaging procedure are proposed. Results obtained numerically by using different approaches are presented, compared and related to the experimental results.DOI: http://dx.doi.org/10.5755/j01.mech.21.2.10276

Geometrical characterization and micro-structural modeling of short steel fiber composites

Short steel fiber reinforced polymer composites are a newly introduced class of materials which combines outstanding properties of stiffness and ductility. The first step in modeling composite mechanical properties is the generation of a representative volume element (RVE) which accurately describes the distinctive microstructure of the material. Injection molded short steel fiber composites exhibit a complex microstructure due to the three-dimensional orientation, waviness and entanglements of the fibers. The present work proposes a data structure for description of the RVE geometry and algorithms for RVE random generation. The micro-structure of short steel fiber reinforced polycarbonate samples was determined using X-ray micro-computed tomography (micro-CT) and the model input parameters were identified using a specialized image processing methodology, based on the Mimics software package. Model generated RVEs were satisfactory compared qualitatively as well as quantitatively against the real micro-CT reconstructed volumes.

Effect of carbon nanotube orientation on the mechanical properties of nanocomposites

Carbon nanotubes (CNTs) have been regarded as ideal reinforcements of high-performance composites with enormous applications. In this paper, nano-structure is modeled as a linearly elastic composite medium, which consists of a homogeneous matrix having hexagonal representative volume elements (RVEs) and homogeneous cylindrical nanotubes with various inclination angles. Effects of inclined carbon nanotubes on mechanical properties are investigated for nano-composites using 3-D hexagonal representative volume element (RVE) with short and straight CNTs. The CNT is modeled as a continuum hollow cylindrical shape elastic material with different angles. The effect of the inclination of the CNT and its parameters is studied. Numerical equations are used to extract the effective material properties for the hexagonal RVE under axial as well as lateral loading conditions. The computational results indicated that elastic modulus of nano-composite is remarkably dependent on the orientation of the dispersed SWNTs. It is observed that the inclination significantly reduces the effective Young’s modulus of elasticity under an axial stretch. When compared with lateral loading case, effective reinforcement is found better in axial loading case. The effective moduli are very sensitive to the inclination and this sensitivity decreases with the increase of the waviness. In the case of short CNTs, increasing trend is observed up to a specific value of waviness index. It is also found from the simulation results that geometry of RVE does not have much significance on stiffness of nano-structures. The results obtained for straight CNTs are consistent with ERM results for hexagonal RVEs, which validate the proposed model results.

Effect of Pinhole Defects on the Elasticity of Carbon Nanotube Based Nanocomposites

Carbon nanotubes (CNTs) have been regarded as an ideal reinforcements of high-performance composites with enormous applications. In this paper, the effects of pinhole defect are investigated for carbon nanotube based nanocomposites using a 3D representative volume element (RVE) with long CNTs. The CNT is modeled as a continuum hollow cylindrical shape elastic material with pinholes in it. These defects are considered on the single wall (CNTs). The mechanical properties such as Young’s modulus of elasticity are evaluated for various pinhole locations and number of defects. The influence of the pinhole defects on the nanocomposite is studied under an axial load condition. Numerical equations are used to extract the effective material properties for the different geometries of RVEs with nondefective CNTs. The field-emission microscopy (FEM) results obtained for nondefective CNTs are consistent with the analytical results for cylindrical RVEs, which validate the proposed model. It is observed that the presence of pinhole defects significantly reduces the effective reinforcement when compared with nondefective nanotubes, and this reinforcement decreases with the increase in the number of pinhole defects. It is also found from the simulation results that the geometry of RVE does not have much significance on the stiffness of nanocomposites.

Influence of uniaxial and biaxial tension on meso-scale geometry and strain fields in a woven composite

Representative volume element (RVE) of a woven composite is often idealised to have identical geometry in the warp and weft directions. While this may be true in the case of consolidating a completely relaxed preform with equal warp and weft densities, majority of woven composites have non-ideal RVE geometry. The present paper investigates the influence of membrane stresses – applied during the moulding process – on the mechanical properties of the finished composite. Crimp interchange due to uniaxial stress and tow flattening due to biaxial stress have been computed by a fabric compliance model developed by the authors. Compliance model is based on the principle of stationary potential energy by taking into consideration tow bending, compression and extensional energies, and the external work done by the tensile forces. It has been shown that a uniaxial tensile stress applied to the preform results in an increase in tensile modulus and a corresponding reduction in the transverse modulus, as a result of reduced crimp in the loading direction with a corresponding increase in the transverse direction. Tensile strength and stiffness increase in the loading direction, and the mode of failure initiation changes from ‘knee phenomena’ to tow failure. A biaxial stress applied during the forming stage results in crimp reduction in both axial and transverse directions; this leads to an improved tensile modulus and strength of a composite laminate. RVE of the deformed geometry has been modelled using ABAQUS CAE pre-processor. The elastic moduli were computed using the concept of equivalent strain energy proposed by Zhang and Harding. The resulting strain fields were compared for various cases of uniaxial and biaxial extension.

Prediction of elastic properties of carbon nanotube reinforced composites

In this paper, the macroscopic elastic properties of carbon nanotube reinforced composites are evaluated through analysing the elastic deformation of a representative volume element (RVE) under various loading conditions. This RVE contains three components, i.e. a carbon nanotube, a transition layer between the nanotube and polymer matrix and an outer polymer matrix body. First, based on the force field theory of molecular mechanics and computational structural mechanics, an equivalent beam model is constructed to model the carbon nanotube effectively. The explicit relationships between the material properties of the equivalent beam element and the force constants have been set-up. Second, to describe the interaction between the nanotube and the outer polymer matrix at the level of atoms, the molecular mechanics and molecular dynamics computations have been performed to obtain the thickness and material properties of the transition layer. Moreover, an efficient three-dimensional eight-noded brick finite element is employed to model the transition layer and the outer polymer matrix. The macroscopic behaviours of the RVE can then be evaluated through the traditional finite element method. In the numerical simulations, the influences of various important factors, such as the stiffness of transition layer and geometry of RVE, on the final macroscopic material properties of composites have been investigated in detail.