Challenge problems for the benchmarking of micromechanics analysis: Level I initial results

2017 ◽  
Vol 52 (1) ◽  
pp. 61-80 ◽  
Author(s):  
Hamsasew M Sertse ◽  
Johnathan Goodsell ◽  
Andrew J Ritchey ◽  
R Byron Pipes ◽  
Wenbin Yu
Keyword(s):  
Composite Materials ◽  
Resource Constraints ◽  
Effective Properties ◽  
Constitutive Relations ◽  
Short Fiber ◽  
Local Fields ◽  
Element Analysis ◽  
Software Packages ◽  
Weave Fabric ◽  
Level I

Because of composite materials’ inherent heterogeneity, the field of micromechanics provides essential tools for understanding and analyzing composite materials and structures. Micromechanics serves two purposes: homogenization or prediction of effective properties and dehomogenization or recovery of local fields in the original heterogeneous microstructure. Many micromechanical tools have been developed and codified, including commercially available software packages that offer micromechanical analyses as stand-alone tools or as part of an analysis chain. With the increasing number of tools available, the practitioner must determine which tool(s) provides the most value for the problem at hand given budget, time, and resource constraints. To date, simple benchmarking examples have been developed in an attempt to address this challenge. The present paper presents the benchmark cases and results from the Micromechanical Simulation Challenge hosted by the Composites Design and Manufacturing HUB. The challenge is a series of comprehensive benchmarking exercises in the field of micromechanics against which such tools can be compared. The Level I challenge problems consist of six microstructure cases, including aligned, continuous fibers in a matrix, with and without an interphase; a cross-ply laminate; spherical inclusions; a plain-weave fabric; and a short-fiber microstructure with “random” fiber orientation. In the present phase of the simulation challenge, the material constitutive relations are restricted to linear thermoelastic. Partial results from DIGIMAT-MF, ESI VPS, MAC/GMC, finite volume direct averaging method, Altair MDS, SwiftComp, and 3D finite element analysis are reported. As the challenge is intended to be ongoing, the full results are hosted and updated online at www.cdmHUB.org .

scholarly journals Internal resonances and relaxation memory kernels in composites

2019 ◽  
Vol 378 (2162) ◽  
pp. 20190106
Author(s):  
Elena Cherkaev
Keyword(s):  
Composite Materials ◽  
Spectral Measure ◽  
Effective Properties ◽  
Constitutive Relations ◽  
Relaxation Times ◽  
Internal Variables ◽  
Fading Memory ◽  
Relaxation Kernel ◽  
Internal Resonances ◽  
Materials With Memory

In heterogeneous composite materials, the behaviour of the medium on larger scales is determined by the microgeometry and properties of the constituents on finer scales. To model the influence of the microlevel processes in composite materials, they are described as materials with memory in which the constitutive relations between stress and strain are given as time-domain convolutions with some relaxation kernel. The paper reveals the relationship between the viscoelastic relaxation kernel and the spectral measure in the Stieltjes integral representation of the effective properties of composites. This spectral measure contains all information about the microgeometry of the material, thus providing a link between the relaxation kernel and the microstructure of the composite. We show that the internal resonances of the microstructure determine the characteristic relaxation times of the fading memory kernel and can be used to introduce a set of internal variables that captures dissipation at the microscale. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.

Optimization Design for the Interface Modulus of Csf/Al Composite

2008 ◽  
Vol 575-578 ◽  
pp. 859-863
Author(s):  
Guo Xing Tang ◽  
G.A. Zhang ◽  
H.B. Wu ◽  
Wen Tong Tian ◽  
Hun Guo
Keyword(s):  
Composite Materials ◽  
Strain Distribution ◽  
Optimization Design ◽  
Fiber Strength ◽  
Short Fiber ◽  
Stress Strain ◽  
Element Analysis ◽  
The Matrix ◽  
Bond Interface ◽  
Base Composite

Short fiber reinforced Al-base composite can be manufactured various parts by plastic working. Elastic modulus has a large influence on the parts among the composite system. In the paper, model of finite-element analysis has been established. The influences of interface modulus on the law of stress-strain distribution, the strength and the modulus for the composite materials have been simulated by ANSYS in the condition of strong-bond, medium-bond and weak-bond interface. The results show that the stress-strain distribution is non-uniform, moreover the force on the fiber is greatly higher than that of the matrix within the composite materials; the strength of the composite materials is improved with the increasing of the interface modulus, but the increasing will be limited by the strength of fiber. Therefore the relation of ideal interface modulus with the fiber strength has been proposed. 70GPa of the interface modulus is thought to be better for M40 short fiber.

Computer-aided Analysis of Micromechanics and Damage of Composite Materials Based on Multiscale Homogenization Method

2013 ◽  
Vol 1535 ◽  
Author(s):  
Yuriy I. Dimitrienko ◽  
Alexandr P. Sokolov ◽  
Yulia V. Shpakova
Keyword(s):  
Finite Element ◽  
Composite Materials ◽  
Effective Properties ◽  
Homogenization Method ◽  
Software System ◽  
Computational Results ◽  
Composite Construction ◽  
Element Analysis ◽  
Object Oriented Design ◽  
Multiscale Homogenization

ABSTRACTResults of finite element analysis of linked two and three scale levels tasks are presented. Fields of components of stress concentration tensor function for several models of unit cells of textile composite materials are presented too. Comparison of experimental and computational results of obtained effective properties was carried out and results of this research are introduced. The basis of this phenomenological approaches was made by Prof. N.S. Bahvalov and Prof. B.E. Pobedriya in 80's and finally this method was renovated by Prof. Yu.I. Dimitrienko at Bauman Moscow State Technical University at «Computational mathematics and mathematical physics» department. Computational procedures and program implementation was made using object-oriented design and C/C++ language by A.P. Sokolov. All computational results have been performed using new-developed distributed high-perfomance software system GCD. Multiscale homogenization method was applied for single macroscopic level of composite construction and several connected microscopic levels. The task of stress-strain determination of composite construction was stated automatically by means of automatically defined plan based on certain computational problems. Architecture of software system and finite-element subsystem were developed too. Several practically important tasks were solved and some of its results are attached.

The Effective Properties of Composite Materials With Constant Reinforcement Density by the Linear Mori-Tanaka Method

1994 ◽  
Vol 116 (3) ◽  
pp. 428-437 ◽  
Author(s):  
J. R. Zuiker ◽  
G. J. Dvorak
Keyword(s):  
Composite Materials ◽  
Volume Fraction ◽  
Effective Properties ◽  
Functionally Graded ◽  
Local Fields ◽  
Original Form ◽  
Constant Field ◽  
Inhomogeneous Materials ◽  
Reinforcement Density ◽  
Variable Reinforcement

In its original form, the Mori-Tanaka method estimates constant overall properties of statistically homogeneous composite materials subjected to uniform overall stresses, strain or temperature changes, from averages of local fields in the phases. To permit applications involving large overall stress and/or temperature gradients, and functionally graded materials with a variable reinforcement density, the method has been extended to linearly variable overall and local fields by Zuiker and Dvorak (Composites Engineering, Vol. 4, 19–35, 1994) as a first step toward application of the method to statistically inhomogeneous materials with variable reinforcement density. Here, the effective properties are examined in detail. Non-zero components of the stiffness matrix are shown to satisfy invariance requirements and to vary with reinforcement volume fraction and size of the representative volume. It is shown that the linear and constant field approaches provide different estimates of overall properties for small representative volumes, but nearly identical estimates for large volumes.

scholarly journals Introduction to Macroscopic Optimal Design in the Mechanics of Composite Materials and Structures

2021 ◽  
Vol 5 (2) ◽  
pp. 36
Author(s):  
Aleksander Muc
Keyword(s):  
Composite Materials ◽  
Composite Structures ◽  
Constitutive Relations ◽  
A Priori ◽  
Chemical Properties ◽  
Composite Plates ◽  
Failure Criteria ◽  
Lagrange Equations ◽  
Homogenization Methods ◽  
Mechanics Of Composite Materials

The main goal of building composite materials and structures is to provide appropriate a priori controlled physico-chemical properties. For this purpose, a strengthening is introduced that can bear loads higher than those borne by isotropic materials, improve creep resistance, etc. Composite materials can be designed in a different fashion to meet specific properties requirements.Nevertheless, it is necessary to be careful about the orientation, placement and sizes of different types of reinforcement. These issues should be solved by optimization, which, however, requires the construction of appropriate models. In the present paper we intend to discuss formulations of kinematic and constitutive relations and the possible application of homogenization methods. Then, 2D relations for multilayered composite plates and cylindrical shells are derived with the use of the Euler–Lagrange equations, through the application of the symbolic package Mathematica. The introduced form of the First-Ply-Failure criteria demonstrates the non-uniqueness in solutions and complications in searching for the global macroscopic optimal solutions. The information presented to readers is enriched by adding selected review papers, surveys and monographs in the area of composite structures.

scholarly journals Image-based semi-multiscale finite element analysis using elastic subdomain homogenization

Meccanica ◽  
2021 ◽  
Author(s):  
J. Jansson ◽  
K. Salomonsson ◽  
J. Olofsson
Keyword(s):  
Finite Element ◽  
Analytical Method ◽  
Effective Properties ◽  
Reference Model ◽  
Computational Time ◽  
Component Level ◽  
Element Analysis ◽  
Model Fidelity ◽  
Multiscale Finite Element ◽  
Anisotropic Elastic

AbstractIn this paper we present a semi-multiscale methodology, where a micrograph is split into multiple independent numerical model subdomains. The purpose of this approach is to enable a controlled reduction in model fidelity at the microscale, while providing more detailed material data for component level- or more advanced finite element models. The effective anisotropic elastic properties of each subdomain are computed using periodic boundary conditions, and are subsequently mapped back to a reduced mesh of the original micrograph. Alternatively, effective isotropic properties are generated using a semi-analytical method, based on averaged Hashin–Shtrikman bounds with fractions determined via pixel summation. The chosen discretization strategy (pixelwise or partially smoothed) is shown to introduce an uncertainty in effective properties lower than 2% for the edge-case of a finite plate containing a circular hole. The methodology is applied to a aluminium alloy micrograph. It is shown that the number of elements in the aluminium model can be reduced by $$99.89\%$$ 99.89 % while not deviating from the reference model effective material properties by more than $$0.65\%$$ 0.65 % , while also retaining some of the characteristics of the stress-field. The computational time of the semi-analytical method is shown to be several orders of magnitude lower than the numerical one.

scholarly journals Assessing the Flexural Properties of Epoxy Composites with Extremely Low Addition of Cellulose Nanofiber Content

2020 ◽  
Vol 10 (3) ◽  
pp. 1159 ◽  
Author(s):  
Yingmei Xie ◽  
Hiroki Kurita ◽  
Ryugo Ishigami ◽  
Fumio Narita
Keyword(s):  
Mechanical Properties ◽  
Epoxy Resin ◽  
Flexural Modulus ◽  
Strengthening Mechanism ◽  
Short Fiber ◽  
Cellulose Nanofiber ◽  
Resin Matrix ◽  
Element Analysis ◽  
Epoxy Resin Matrix ◽  
The Matrix

Epoxy resins are a widely used common polymer due to their excellent mechanical properties. On the other hand, cellulose nanofiber (CNF) is one of the new generation of fibers, and recent test results show that CNF reinforced polymers have high mechanical properties. It has also been reported that an extremely low CNF addition increases the mechanical properties of the matrix resin. In this study, we prepared extremely-low CNF (~1 wt.%) reinforced epoxy resin matrix (epoxy-CNF) composites, and tried to understand the strengthening mechanism of the epoxy-CNF composite through the three-point flexural test, finite element analysis (FEA), and discussion based on organic chemistry. The flexural modulus and strength were significantly increased by the extremely low CNF addition (less than 0.2 wt.%), although the theories for short-fiber-reinforced composites cannot explain the strengthening mechanism of the epoxy-CNF composite. Hence, we propose the possibility that CNF behaves as an auxiliary agent to enhance the structure of the epoxy molecule, and not as a reinforcing fiber in the epoxy resin matrix.

A FINITE ELEMENT ANALYSIS OF EFFECTIVE THERMOELECTROELASTIC PROPERTIES OF COMPOSITES WITH A DOUBLY PERIODIC ARRAY OF PIEZOELECTRIC FIBERS

2009 ◽  
Vol 23 (06n07) ◽  
pp. 1689-1694 ◽  
Author(s):  
PENG YAN ◽  
CHIPING JIANG
Keyword(s):  
Finite Element ◽  
Effective Properties ◽  
Cell Model ◽  
Periodic Array ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Uniform Temperature Field ◽  
Periodic Microstructures ◽  
Doubly Periodic Array ◽  
Electrical Loads

This work deals with modeling of 1-3 thermoelectroelastic composites with a doubly periodic array of piezoelectric fibers under arbitrary combination of mechanical, electrical loads and a uniform temperature field. The finite element method (FEM) based on a unit cell model is extended to take into account the thermoelectroelastic effect. The FE predictions of effective properties for several typical periodic microstructures are presented, and their influences on effective properties are discussed. A comparison with the Mori-Tanaka method is made to estimate the application scope of micromechanics. The study is useful for the design and assessment of composites.

Analytical and Numerical Predictions of Thermoelastic Properties of Carbon Single-Walled Nanotubes

Aerospace ◽  
2005 ◽  
Author(s):  
Vinod P. Veedu ◽  
Davood Askari ◽  
Mehrdad N. Ghasemi-Nejhad
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Graphene Sheet ◽  
Effective Properties ◽  
Constitutive Models ◽  
Thermoelastic Properties ◽  
Asymptotic Homogenization ◽  
Element Analysis ◽  
Single Walled Nanotubes ◽  
Numerical Predictions

The objective of this paper is to develop constitutive models to predict thermoelastic properties of carbon single-walled nanotubes using analytical, asymptotic homogenization, and numerical, finite element analysis, methods. In our approach, the graphene sheet is considered as a non-homogeneous network shell layer which has zero material properties in the regions of perforation and whose effective properties are estimated from the solution of the appropriate local problems set on the unit cell of the layer. Our goal is to derive working formulas for the entire complex of the thermoelastic properties of the periodic network. The effective thermoelastic properties of carbon nanotubes were predicted using asymptotic homogenization method. Moreover, in order to verify the results of analytical predictions, a detailed finite element analysis is followed to investigate the thermoelastic response of the unit cells and the entire graphene sheet network.

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