Showing papers on "Representative elementary volume published in 2017"

The sequential addition and migration method to generate representative volume elements for the homogenization of short fiber reinforced plastics

Abstract: We present an algorithm for generating volume elements of short fiber reinforced plastic microstructures for prescribed fourth order fiber orientation tensor, fiber aspect ratio and solid volume fraction. The algorithm inserts fibers randomly into an existing microstructure, and removes the resulting overlap systematically based on a gradient descent method. In contrast to existing methods, large fiber aspect ratios (up to 150) and large volume fractions (60 vol% for isotropic orientation and aspect ratio of 33) can be reached. We study the effective linear elastic properties of the resulting microstructures, depending on fiber orientation, volume fraction as well as aspect ratio, and examine the size of a corresponding representative volume element.

Identifying Structure–Property Relationships Through DREAM.3D Representative Volume Elements and DAMASK Crystal Plasticity Simulations: An Integrated Computational Materials Engineering Approach

Abstract: Predicting, understanding, and controlling the mechanical behavior is the most important task when designing structural materials. Modern alloy systems—in which multiple deformation mechanisms, phases, and defects are introduced to overcome the inverse strength–ductility relationship—give raise to multiple possibilities for modifying the deformation behavior, rendering traditional, exclusively experimentally-based alloy development workflows inappropriate. For fast and efficient alloy design, it is therefore desirable to predict the mechanical performance of candidate alloys by simulation studies to replace time- and resource-consuming mechanical tests. Simulation tools suitable for this task need to correctly predict the mechanical behavior in dependence of alloy composition, microstructure, texture, phase fractions, and processing history. Here, an integrated computational materials engineering approach based on the open source software packages DREAM.3D and DAMASK (Dusseldorf Advanced Materials Simulation Kit) that enables such virtual material development is presented. More specific, our approach consists of the following three steps: (1) acquire statistical quantities that describe a microstructure, (2) build a representative volume element based on these quantities employing DREAM.3D, and (3) evaluate the representative volume using a predictive crystal plasticity material model provided by DAMASK. Exemplarily, these steps are here conducted for a high-manganese steel.

Micromechanical modeling of thermal expansion coefficients for unidirectional glass fiber-reinforced polyimide composites containing silica nanoparticles

Abstract: The coefficients of thermal expansion (CTEs) of unidirectional glass fiber-reinforced polyimide composites containing silica nanoparticles are investigated. To this end, a three-dimensional unit cell-based micromechanical model together with an individual representative volume element (RVE) with c × r × h sub-cells is proposed. The interphase region between silica nanoparticle and polyimide matrix is considered as an equivalent solid continuum. Comparisons are made between the results of present model with those of available cylinder model and experiment. The results reveal that with adding silica nanoparticles to glass fiber-reinforced polyimide composites, the transverse CTE of composite decreases, while its longitudinal CTE increases. The effects of fiber volume fraction and aspect ratio, interphase thickness and material properties, silica nanoparticle volume fraction and diameter on the thermal expansion behavior of silica nanoparticle-glass fiber-reinforced polyimide composites are studied. The obtained results could be useful to guide the design of composites with optimal CTEs.

A micromorphic computational homogenization framework for heterogeneous materials

Abstract: The conventional first-order computational homogenization framework is restricted to problems where the macro characteristic length scale is much larger than the underlying Representative Volume Element (RVE). In the absence of a clear separation of length scales, higher-order enrichment is required to capture the influence of the underlying rapid fluctuations, otherwise neglected in the first-order framework. In this contribution, focusing on matrix-inclusion composites, a novel computational homogenization framework is proposed such that standard continuum models at the micro-scale translate onto the macro-scale to recover a micromorphic continuum. Departing from the conventional FE 2 framework where a macroscopic strain tensor characterizes the average deformation within the RVE, our formulation introduces an additional macro kinematic field to characterize the average strain in the inclusions. The two macro kinematic fields, each characterizing a particular aspect of deformation within the RVE, thus provide critical information on the underlying rapid fluctuations. The net effect of these fluctuations, as well as the interactions between RVEs, are next incorporated naturally into the macroscopic virtual power statement through the Hill-Mandel condition. The excellent predictive capability of the proposed homogenization framework is illustrated through three benchmark examples. It is shown that the homogenized micromorphic model adequately captures the material responses, even in the absence of a clear separation of length scales between macro and micro.

Effective response of classical, auxetic and chiral magnetoelastic materials by use of a new variational principle

Abstract: This work provides a rigorous analysis of the effective response, i.e., average magnetization and magnetostriction, of magnetoelastic composites that are subjected to overall magnetic and mechanical loads. It clarifies the differences between a coupled magnetomechanical analysis in which one applies a Eulerian (current) magnetic field and an electroactive one where the Lagrangian (reference) electric field is usually applied. For this, we propose an augmented vector potential variational formulation to carry out numerical periodic homogenization studies of magnetoelastic solids at finite strains and magnetic fields. We show that the developed variational principle can be used for bottom-up design of microstructures with desired magnetomechanical coupling by properly canceling out the macro-geometry and specimen shape effects. To achieve that, we properly treat the average Maxwell stresses arising from the medium surrounding the magnetoelastic representative volume element (RVE), while at the same time we impose a uniform average Eulerian and not Lagrangian magnetic field. The developed variational principle is then used to study a large number of ideal as well as more realistic two-dimensional microstructures. We study the effect of particle volume fraction, particle distribution and particle shape and orientation upon the effective magnetoelastic response at finite strains. We consider also unstructured isotropic microstructures based on random adsorption algorithms and we carry out a convergence study of the representativity of the proposed unit cells. Finally, three-phase two-dimensional auxetic microstructures are analyzed. The first consists of a periodic distribution of voids and particle chains in a polymer matrix, while the second takes advantage of particle shape and chirality to produce negative and positive swelling by proper change of the chirality and the applied magnetic field.

Multiscale modeling of regularly staggered carbon fibers embedded in nano-reinforced composites

Abstract: This article deals with the multiscale modeling of stress transfer characteristics of nano-reinforced polymer composite reinforced with regularly staggered carbon fibers. The distinctive feature of construction of nano-reinforced composite is such that the microscale carbon fibers are packed in hexagonal array in the carbon nanotube reinforced polymer matrix (CNRP). We considered three different cases of CNRP, in which carbon nanotubes (CNTs) are: (i) aligned along the direction of carbon fiber, (ii) aligned radially to the axis of carbon fiber, and (iii) randomly dispersed. Accordingly, multiscale models were developed. First, molecular dynamics (MD) simulations and then Mori-Tanaka technique were used to estimate the effective elastic properties of CNRP. Second, a micromechanical three-phase shear lag model was developed considering the staggering effect of microscale fibers and the application of radial loads on the cylindrical representative volume element (RVE) of nano-reinforced composite. Our results reveal that the stress transfer characteristics of the nano-reinforced composite are significantly improved by controlling the CNT morphology, particularly, when they are randomly dispersed around the microscale fiber. The results from the developed shear lag model were also validated with the finite element shear lag simulations and found to be in good agreement.

A cutting force predicting model in orthogonal machining of unidirectional CFRP for entire range of fiber orientation

Abstract: Cutting force prediction of orthogonal cutting unidirectional carbon fiber-reinforced plastic (UD-CFRP) is crucial in the reduction of machining defects. This paper aims to construct a force prediction model for orthogonal cutting of UD-CFRP using beams on elastic foundation theory and the minimum potential energy principle (MPEP) when fiber orientation (θ) varies from 0° to 180°. Models for different fiber orientation ranges were established separately, i.e., (1) 0°< θ < 90°, (2) 90°≤ θ < 180°, and (3) 0°. The deformation of the fibers was considered as a bending problem of a beam on elastic foundation. Total cutting force was composed of cutting forces from rake face, tool edge, and relief face of the cutting tool. As 0°< θ < 90°, Vlazov’s elastic foundation was introduced to calculate pressing forces between cutting tool edge and the representative volume element (RVE). The force applied on rake face was the integral value of resistant forces from those micro-elements of the curved chip based on well-established shear angle-cutting force relationships in Piispanen’s card model. When 90°≤ θ < 180°, non-uniform Winkler foundation was applied to calculate force between rake face and the RVE. When θ = 0°, the energy equation of the splitting process was constructed by using virtual crack close technique, and plugging force between rake face and the chip was derived from the equation. This mechanical model reveals mapping relationships between cutting forces and key variables such as the fiber orientation, rake angle, depth of cut, and so on. Corresponding experiments were conducted, and predictions were in acceptable agreement with the experimental measurements.

Calibration and validation of a continuum damage mechanics model in aid of axial crush simulation of braided composite tubes

Abstract: We present the details of a combined experimental and numerical study used to calibrate the parameters of a macro-mechanical damage model that is incorporated as a user material model in the explicit finite element program, LS-DYNA, to represent the progressive damage behaviour of composites at the level of the representative volume element. Specifically, the model parameters defining the transverse tensile and axial compressive response of a triaxially-braided carbon fibre/epoxy composite are determined based on results from notched tensile, 4-point bend and eccentric compression tests. To demonstrate the validity of the material model and its calibrated input parameters, the response of notched tensile coupon and eccentric compression tests are simulated and shown to correlate well with experimental measurements. Further validation of the model is provided here and in Ref. [1] through successful simulation of the axial crushing of square tubes made of the same material.

Lattice Boltzmann simulations of convection heat transfer in porous media

Abstract: A non-orthogonal multiple-relaxation-time (MRT) lattice Boltzmann (LB) method is developed to study convection heat transfer in porous media at the representative elementary volume scale based on the generalized non-Darcy model. In the method, two different LB models are constructed: one is constructed in the framework of the double-distribution-function approach, and the other is constructed in the framework of the hybrid approach. In particular, the transformation matrices used in the MRT-LB models are non-orthogonal matrices. The present method is applied to study mixed convection flow in a porous channel and natural convection flow in a porous cavity. It is found that the numerical results are in good agreement with the analytical solutions and/or other results reported in previous studies. Furthermore, the non-orthogonal MRT-LB method shows better numerical stability in comparison with the BGK-LB method.

Mechanisms of Dispersion in a Porous Medium

Abstract: This paper studies the mechanisms of dispersion in the laminar flow through the pore space of a $3$-dimensional porous medium. We focus on pre-asymptotic transport prior to the asymptotic hydrodynamic dispersion regime, in which solute motion may be described by the average flow velocity and a hydrodynamic dispersion coefficient. High performance numerical flow and transport simulations of solute breakthrough at the outlet of a sand-like porous medium evidence marked deviations from the hydrodynamic dispersion paradigm and identifies two distinct regimes. The first regime is characterized by a broad distribution of advective residence times in single pores. The second regime is characterized by diffusive mass transfer into low-velocity region in the wake of solute grains. These mechanisms are quantified systematically in the framework of a time-domain random walk for the motion of marked elements (particles) of the transported material quantity. The model is parameterized with the characteristics of the porous medium under consideration and captures both pre-asymptotic regimes. Macroscale transport is described by an integro-differential equation for solute concentration, whose memory kernels are given in terms of the distribution of mean pore velocities and trapping times. This approach quantifies the physical non-equilibrium caused by a broad distribution of mass transfer time scales, both advective and diffusive, on the representative elementary volume (REV). Thus, while the REV indicates the scale at which medium properties like porosity can be uniquely defined, this does not imply that transport can be characterized by hydrodynamic dispersion.

Predictive Model of Graphene Based Polymer Nanocomposites: Electrical Performance

Abstract: In this computational work, a new simulation tool on the graphene/polymer nanocomposites electrical response is developed based on the finite element method (FEM). This approach is built on the multi-scale multi-physics format, consisting of a unit cell and a representative volume element (RVE). The FE methodology is proven to be a reliable and flexible tool on the simulation of the electrical response without inducing the complexity of raw programming codes, while it is able to model any geometry, thus the response of any component. This characteristic is supported by its ability in preliminary stage to predict accurately the percolation threshold of experimental material structures and its sensitivity on the effect of different manufacturing methodologies. Especially, the percolation threshold of two material structures of the same constituents (PVDF/Graphene) prepared with different methods was predicted highlighting the effect of the material preparation on the filler distribution, percolation probability and percolation threshold. The assumption of the random filler distribution was proven to be efficient on modelling material structures obtained by solution methods, while the through-the –thickness normal particle distribution was more appropriate for nanocomposites constructed by film hot-pressing. Moreover, the parametrical analysis examine the effect of each parameter on the variables of the percolation law. These graphs could be used as a preliminary design tool for more effective material system manufacturing.

Numerical predictions of the anisotropic viscoelastic response of uni-directional fibre composites

Abstract: Finite Element (FE) simulations are conducted to predict the viscoelastic properties of uni-directional (UD) fibre composites. The response of both periodic unit cells and random stochastic volume elements (SVEs) is analysed; the fibres are assumed to behave as linear elastic isotropic solids while the matrix is taken as a linear viscoelastic solid. Monte Carlo analyses are conducted to determine the probability distributions of all viscoelastic properties. Simulations are conducted on SVEs of increasing size in order to determine the suitable size of a representative volume element (RVE). The predictions of the FE simulations are compared to those of existing theories and it is found that the Mori-Tanaka (1973) and Lielens (1999) models are the most effective in predicting the anisotropic viscoelastic response of the RVE.

Estimation of REV Size for Fractured Rock Mass Based on Damage Coefficient

Abstract: Estimation of representative elementary volume (REV) is significant to analyze fractured rock mass in the framework of continuum mechanics. Engineers can therefore simplify the analysis by using an equivalent rock block with an average property, and the influence of fractures can be neglected in finite element modelling. The indicators to determine the REV size based on the joint geometrical parameters include the volumetric fracture intensity (P 32) and the fracture tensor, but this type of calculation generally provides a lower bound evaluation. A novel conceptual framework of damage coefficient is introduced in this paper to consider the mechanical properties of fractures, such as joint aperture and roughness. A parametric study has been performed to establish the correlation between the proposed dimensionless damage coefficient and the traditional derived P 32 value. The effectiveness of the developed method is demonstrated by a case study, where a larger mechanical REV size is indeed calculated based on the damage coefficient.