Showing papers on "Representative elementary volume published in 2019"

Development of an ABAQUS plugin tool for periodic RVE homogenisation

Abstract: EasyPBC is an ABAQUS CAE plugin developed to estimate the homogenised effective elastic properties of user created periodic representative volume element (RVE), all within ABAQUS without the need to use third-party software. The plugin automatically applies the concepts of the periodic RVE homogenisation method in the software’s user interface by categorising, creating, and linking sets necessary for achieving deformable periodic boundary surfaces, which can distort and no longer remain plane. Additionally, it allows the user to benefit from finite element analysis data within ABAQUS CAE interface after calculating homogenised properties. In this article, the algorithm of the plugin based on periodic RVE homogenisation method is explained, which could be developed for other commercial FE software packages. Furthermore, examples of its implementation and verification are illustrated.

Exploring the 3D architectures of deep material network in data-driven multiscale mechanics

Abstract: This paper extends the deep material network (DMN) proposed by Liu et al. (2019) to tackle general 3-dimensional (3D) problems with arbitrary material and geometric nonlinearities. It discovers a new way of describing multiscale heterogeneous materials by a multi-layer network structure and mechanistic building blocks. The data-driven framework of DMN is discussed in detail about the offline training and online extrapolation stages. Analytical solutions of the 3D building block with a two-layer structure in both small- and finite-strain formulations are derived based on interfacial equilibrium conditions and kinematic constraints. With linear elastic data generated by direct numerical simulations on a representative volume element (RVE), the network can be effectively trained in the offline stage using stochastic gradient descent and advanced model compression algorithms. Efficiency and accuracy of DMN on addressing the long-standing 3D RVE challenges with complex morphologies and material laws are validated through numerical experiments, including 1) hyperelastic particle-reinforced rubber composite with Mullins effect; 2) polycrystalline materials with rate-dependent crystal plasticity; 3) carbon fiber reinforced polymer (CFRP) composites with fiber anisotropic elasticity and matrix plasticity. In particular, we demonstrate a three-scale homogenization procedure of CFRP system by concatenating the microscale and mesoscale material networks. The complete learning and extrapolation procedures of DMN establish a reliable data-driven framework for multiscale material modeling and design.

Consistent application of periodic boundary conditions in implicit and explicit finite element simulations of damage in composites

Abstract: This paper presents an implementation-dedicated analysis of Periodic Boundary Conditions (PBCs) for Finite Element (FE) models incorporating highly non-linear effects due to plasticity and damage. This research addresses fiber-reinforced composite materials modeled at micros-scale level using a Representative Volume Element (RVE), where its overall mechanical response is obtained via homogenization techniques. For the sake of clearness, a unidirectional ply with randomly distributed fibers RVE model is assumed. PBCs are implemented for implicit and explicit FE solvers, where conformal and non-conformal meshes can be used. The influence of applying PBCs in the reliability of the mechanical response under tension and shear loading is assessed. Furthermore, the Poisson effect and the consistency of damage and fiber debonding propagation through the periodic boundaries are reported as well as their impact on the homogenized results. Likewise, numerical aspects like computational performance and accuracy are evaluated comparing implicit- versus explicit-based solutions.

Beyond Kozeny–Carman: Predicting the Permeability in Porous Media

Abstract: Various processes such as heterogeneous reactions or biofilm growth alter a porous medium’s underlying geometric structure. This significantly affects its hydrodynamic parameters, in particular the medium’s effective permeability. An accurate, quantitative description of the permeability is, however, essential for predictive flow and transport modeling. Well-established relations such as the Kozeny–Carman equation or power law approaches including fitting parameters relate the porous medium’s porosity to a scalar permeability coefficient. Opposed to this, upscaling methods directly enable calculating the full, potentially anisotropic, permeability tensor. As input, only the geometric information in terms of a representative elementary volume is needed. To compute the porosity–permeability relations, supplementary cell problems must be solved numerically on this volume and their solutions must be integrated. We apply this approach to provide easy-to-use quantitative porosity–permeability relations that are based on representative single grain, platy, blocky, prismatic soil structures, porous networks, and real geometries obtained from CT-data. As a discretization method, we use discontinuous Galerkin method on structured grids. To make the relations explicit, interpolation of the obtained data is used. We compare the outcome with the well-established relations and investigate the ranges of the validity. From our investigations, we conclude whether Kozeny–Carman-type or power law-type porosity–permeability relations are more reasonable for various prototypic representative elementary volumes. Finally, we investigate the impact of a microporous solid matrix onto the permeability.

Derivation of heterogeneous material laws via data-driven principal component expansions

Abstract: A new data-driven method that generalizes experimentally measured and/or computational generated data sets under different loading paths to build three dimensional nonlinear elastic material law with objectivity under arbitrary loadings using neural networks is proposed. The proposed approach is first demonstrated by exploiting the concept of representative volume element (RVE) in the principal strain and stress spaces to numerically generate the data. A computational data-training algorithm on the generalization of these principal space data to three dimensional objective isotropic material laws subjected to arbitrary deformation is given. To validate these data-driven derived material laws, large deformation and buckling analysis of nonlinear elastic solids with reference material models and engineering structure with microstructure are performed. Numerical experiments show that only seven sets of data under different stress loading paths on RVEs are required to reach reasonable accuracy. The requirements for constitutive law such as objectivity are preserved approximately. The consistent tangent modulus is also derived. The proposed approach also shows a great potential to obtain the material law between different scales in the multiscale analysis by pure data.

Multiscale modeling of the elastic moduli of CNT-reinforced polymers and fitting of efficiency parameters for the use of the extended rule-of-mixtures

Abstract: In this work, a bottom-up multiscale modeling approach is developed to estimate the effective elastic moduli of Carbon NanoTube (CNT)-reinforced polymer composites. The homogenization process comprises two successive steps, including an atomistic-based computational model and a micromechanics approach at the nano- and micro-scales, respectively. Firstly, the atomistic-based finite element model defines a cylindrical Representative Volume Element (RVE) that accounts for a carbon nanotube, the immediately surrounding matrix, and the CNT/polymer interface. The carbon-carbon bonds of the CNT are modeled using Timoshenko beams, whilst three-dimensional solid elements are used for the surrounding matrix. Through the application of four loading conditions, the RVEs are homogenized into transversely isotropic equivalent fibers by equating the associated strain energies. Secondly, the equivalent fibers are employed in a micromechanics approach to estimate the macroscopic response of non-dilute composites. This is performed using both the analytical Mori-Tanaka model and a computational RVE model with a hexagonal packing geometry. A wide spectrum of single- and multi-walled carbon nanotubes are studied, as well as two different polymeric matrices. Furthermore, the so-called efficiency parameters, imperative for the application of the simplified extended rule of mixtures, are characterized by polynomial expressions for practical filler contents. Finally, detailed parametric analyses are also provided to give insight into the sensitivity of the macroscopic response of CNT-reinforced polymer composites to microstructural features such as filler volume fraction, chirality or aspect ratio.

Determination of Metamaterial Parameters by Means of a Homogenization Approach Based on Asymptotic Analysis

Abstract: Owing to additive manufacturing techniques, a structure at millimeter length scale (macroscale) can be produced by using a lattice substructure at micrometer length scale (microscale). Such a system is called a metamaterial at the macroscale as the mechanical characteristics deviate from the characteristics at the microscale. As a remedy, metamaterial is modeled by using additional parameters; we intend to determine them. A homogenization approach based on the asymptotic analysis establishes a connection between these different characteristics at micro- and macroscales. A linear elastic first order theory at the microscale is related to a linear elastic second order theory at the macroscale. Relation for parameters at the macroscale is derived by using the equivalence of energy at macro- and microscales within a so-called Representative Volume Element (RVE). Determination of parameters are succeeded by solving a boundary value problem with the Finite Element Method (FEM). The proposed approach guarantees that the additional parameters vanish if the material is purely homogeneous, in other words, it is fully compatible with conventional homogenization schemes based on spatial averaging techniques. Moreover, the proposed approach is reliable as it ensures that such resolved additional parameters are not sensitive to choices of RVE consisting in the repetition of smaller RVEs but depend upon the intrinsic size of the structure.

A consistently coupled multiscale mechanical–electrochemical battery model with particle interaction and its validation

Abstract: As an inherent multiscale structure, a continuum scale battery electrode is composed of many microscale particles. Currently it is generally assumed that each particle is isolated while the stress in a particle only affects solid diffusion. The lack of mechanical interaction between particles and effect of stress on the electrochemical reaction rate makes mechanics and electrochemistry uncoupled at the continuum scale: an applied continuum scale stress in the electrode has no effect on the spatial distribution of electrochemical reaction in the electrode and vice versa. This paper first presents a multiscale model that couples mechanics and electrochemistry consistently at the microscopic and continuum scales. The microscopic particle stress is a superposition of the intra-particle concentration gradient-induced stress and the particle interaction stress, with the latter being related to the continuum scale stress through a representative volume element. The electrochemical charge transfer kinetics is generalized with the stress effect. Diffusion in a particle is described by a chemical potential that includes stress and phase transition. In a parallel effort, we develop a direct three-dimensional particle network model, which consists of realistic active material particles. Unlike the multiscale model, there is no scale separation and homogenization in the particle network model: all particles are modeled explicitly with fully coupled three-dimensional mechanical-electrochemical equations and the finite element method. The results from the particle network model are accurate and can serve as a standard, but the size of particle network that can be calculated is limited due to high computational cost. Comparison of results from the multiscale model and from the particle network model shows that the multiscale model gives good, satisfying accuracy while reducing the computational cost dramatically in comparison to the three-dimensional particle network model. The multiscale model is a power tool to address various coupled problems in the electrode, from inter-particle crack growth to electrode structure design for high performance and long cycle life.

Efficient generator of random fiber distribution with diverse volume fractions by random fiber removal

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.

On micromechanics approach to stiffness and strength of unidirectional composites

Abstract: The purposes of this paper are sixfold. First, any micromechanics model for predicting elastic property (stiffness) of a composite is applicable to a reasonable prediction of a composite strength, ...

Failure of chopped carbon fiber Sheet Molding Compound (SMC) composites under uniaxial tensile loading: Computational prediction and experimental analysis

Abstract: This paper presents a computational framework to predict the tensile failure of chopped carbon fiber SMC composites based on the Representative Volume Element (RVE) model. In the framework, a conforming mesh-based reconstruction algorithm is developed to generate mesostructure RVE models of SMC based on the statistical characteristics. Moreover, constitutive models are proposed for the three phases in SMC composites: fiber chip, matrix, and interface. The model predictions are validated by coupon-level experimental tests on SMC samples of various chip orientation distributions. The meso-scale failure mechanism and failure strength predicted by the RVE models are in good agreement with the experimental results. The presented study demonstrates the capability of the present modeling framework in the design of composites materials with complex micro- and meso- structure.

Numerical homogenization of coiled carbon nanotube reinforced shape memory polymer nanocomposites

Abstract: Shape memory polymers (SMPs) are a group of smart materials that, by applying an external stimulation such as the temperature, retrieve their permanent shape from a temporary one. SMP nanocomposites have been developed to improve the mechanical, thermal, electrical, and magnetic properties of SMPs for potential applications in e.g. medical equipment, sensors, actuators, and drug delivery systems. In this research, SMP is reinforced with Coiled carbon nanotubes (CCNT) due to its geometric properties which let material tolerate higher strains and improve thermomechanical properties of SMP. In this paper, the effect of addition of CCNT on thermomechanical response of SMP under large deformations is numerically investigated. Employing a thermo-visco-hyperelastic constitutive model for SMP, a cubic representative volume element is realized using Monte Carlo algorithm. The effect of inclusion's geometry (e.g. spring length or aspect ratio, pitch or number of coils of CCNT), volume fraction, as well as their distribution on the thermomechanical properties of SMP/CCNT composite in two stress- and shape recovery processes in different heating rates and pre-strains is studied using Finite Element technique. Results reveal that increasing the volume fraction up to 0.6%, leads to a 15% rise in the effective stress in the nanocomposite. Increasing the spring length of the CCNT, the strain recovery of the nanocomposite increases about 8%. It is shown that when the mechanical loading is parallel to the CCNTs orientation, the stress is about 25% larger than when the loading is perpendicular to the unidirectional CCNTs. But for the strain recovery, the orientation does not play an important role in the strain recovery.

Estimating Young's modulus of graphene/polymer composites using stochastic multi-scale modeling

Abstract: A stochastic multi-scale approach is developed for predicting elastic properties of graphene/polymer nanocomposites. All scales of nano, micro, meso and macro are travelled through a bottom-up approach using appropriate method at each scale. For each scale, separate representative volume element (RVE) is defined capturing effective parameters of that scale. Categorized under the hierarchical multi-scale modeling, the outputs of each scale are fed into the next upper scale as input data. Semi-continuum modeling is performed at the nano and micro scales, while micromechanical model is adapted for the upper scales of meso and macro. The developed modeling is implemented stochastically to address the randomness in graphene size, volume fraction, orientation, wrinkle and also formation of agglomerated particles. Therefore, stochastic multi-scale modeling is conducted accounting for process-induced uncertainties. Results show a very good agreement with experimental data available on open literature. The novelty of this research is twofold: (1) Developing of a full-range multi-scale modeling for graphene reinforced polymers starting from nano-scale and lasting to the uppermost scale of macro, (2) Full stochastic implementation of developed modeling accounting for non-deterministic parameters induced during processing graphene reinforced polymer.

3D micromechanical simulation of the mechanical behavior of an in-situ Al3Ti/A356 composite

Abstract: The mechanical behavior of an in-situ Al3Ti/A356 composite was studied by three-dimensional (3D) micromechanical simulation with microstructure-based Representative Volume Element (RVE) models. A series of 3D RVEs were automatically generated with A356 matrix and icosahedron shaped Al3Ti particles as representative of various microstructures. Ductile damage of matrix and brittle damage of Al3Ti particles were considered, while perfect interfacial bonding between Al3Ti and Al matrix was assumed. Simulation results were validated by experimental stress-strain curves. Furthermore, the effects of the particle size, volume fraction and distribution of Al3Ti on mechanical properties were simulated by controlling the corresponding parameters in RVEs. The simulation results show that the refinement of particles improves the yield strength and elongation. However, the increase of volume fraction or clustering of the particles reduces the elongation evidently. Additionally, the Young's modulus, yield strength and elongation of the Al3Ti/A356 composite were predicted from different RVE models. The prediction shows that the Young's modulus follows the calculation of Tsai-Halpin equation. The yield strengths are close to the micromechanical approach considering both load bearing and coefficient of thermal expansion (CTE) mismatch strengthening contribution. The relationship between elongation and the properties of the Al3Ti particles is set up by a polynomial fitting, which is generally in agreement with reported experimental results.

Numerically-aided 3D printed random isotropic porous materials approaching the Hashin-Shtrikman bounds

Abstract: The present study introduces a methodology that allows to combine 3D printing, experimental testing, numerical and analytical modeling to create random closed-cell porous materials with statistically controlled and isotropic overall elastic properties that are extremely close to the relevant Hashin-Shtrikman bounds. In this first study, we focus our experimental and 3D printing efforts to isotropic random microstructures consisting of single-sized (i.e. monodisperse) spherical voids embedded in a homogeneous solid matrix. The 3D printed specimens are realized by use of the random sequential adsorption method. A detailed FE numerical study allows to define a cubic representative volume element (RVE) by combined periodic and kinematically uniform (i.e. average strain or affine) boundary conditions. The resulting cubic RVE is subsequently assembled to form a standard dog-bone uniaxial tension specimen, which is 3D printed by use of a photopolymeric resin material. The specimens are then tested at relatively small strains by a proper multi-step relaxation procedure to obtain the effective elastic properties of the porous specimens.