Periodic boundary conditions for FE analyses of a representative volume element for composite laminates with one cracked ply and delaminations

2018 ◽  
Vol 201 ◽  
pp. 932-941 ◽  
Author(s):  
L. Maragoni ◽  
P.A. Carraro ◽  
M. Quaresimin
Keyword(s):  
Boundary Conditions ◽  
Representative Volume Element ◽  
Composite Laminates ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Volume Element ◽  
Representative Volume

A Micromechanics Model for Thermoelastic Properties of Plain Weave Fabric Composites

1994 ◽  
Vol 116 (4) ◽  
pp. 517-523 ◽  
Author(s):  
H. T. Hahn ◽  
R. Pandey
Keyword(s):  
Representative Volume Element ◽  
Composite Laminates ◽  
Volume Element ◽  
Thermoelastic Properties ◽  
Micromechanics Model ◽  
Plain Weave ◽  
Representative Volume ◽  
Thermal Expansion Coefficients ◽  
Weave Fabric ◽  
Effective Thermal Expansion

A micromechanics model is presented to predict thermoelastic properties of composites reinforced with plain weave fabrics. A representative volume element is chosen for analysis and the fiber architecture is described by a few simple functions. Equations are developed to calculate various phase fractions from geometric parameters that can be measured on a cross section. Effective elastic moduli and effective thermal expansion coefficients are determined under the assumption of uniform strain inside the representative volume element. The resulting model is similar to the classical laminated theory, and hence is easier to use than other models available in the literature. An experimental correlation is provided for a number of Nicalon SiC/CVI SiC and Graphite/CVI SiC composite laminates.

Comparison of Full Field and Single Inclusion Approaches to Homogenization of Composites with Non-Ellipsoidal Pores

2014 ◽  
Vol 627 ◽  
pp. 309-312
Author(s):  
Igor Tsukrov ◽  
Borys Drach ◽  
Anton Trofimov
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Numerical Results ◽  
Finite Element Simulations ◽  
Full Field ◽  
Representative Volume ◽  
Single Inclusion

This paper compares two approaches to predict the overall mechanical properties of solids with irregularly shaped pores. The first approach involves direct finite element simulations of representative volume elements containing arrangements of irregularly shaped pores subjected to periodic boundary conditions. The second approach utilizes numerical results for individual defect shapes in a micromechanical scheme. Several realizations of parallel and randomly oriented distributions of defects are considered. It is determined that the Mori-Tanaka micromechanical scheme provides good correlation with the full field finite element simulations.

scholarly journals Design of Reinforcement in Nano- and Microcomposites

Materials ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1474 ◽  
Author(s):  
Małgorzata Chwał ◽  
Aleksander Muc
Keyword(s):  
Boundary Conditions ◽  
Representative Volume Element ◽  
Optimization Problems ◽  
Volume Element ◽  
Numerical Homogenization ◽  
Representative Volume ◽  
Material Optimization ◽  
Design Variables ◽  
Element Shape ◽  
Dimensional Optimization

The application of numerical homogenization and optimization in the design of micro- and nanocomposite reinforcement is presented. The influence of boundary conditions, form of a representative volume element, shape and distribution of reinforcement are distinguished as having the crucial influence on a design of the reinforcement. The paper also shows that, in the optimization problems, the distributions of any design variables can be expressed by n-dimensional curves. It applies not only to the tasks of optimizing the shape of the edge of the structure or its mid-surface but also dimensional optimization or topology/material optimization. It is shown that the design of reinforcement may be conducted in different ways and 2D approaches may be expanding to 3D cases.

scholarly journals Influence of Boundary Conditions on Numerical Homogenization of High Performance Concrete

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 1009
Author(s):  
Arkadiusz Denisiewicz ◽  
Mieczysław Kuczma ◽  
Krzysztof Kula ◽  
Tomasz Socha
Keyword(s):  
Experimental Data ◽  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Representative Volume Element ◽  
High Performance ◽  
High Performance Concrete ◽  
Volume Element ◽  
Numerical Homogenization ◽  
Representative Volume

Concrete is the most widely used construction material nowadays. We are concerned with the computational modelling and laboratory testing of high-performance concrete (HPC). The idea of HPC is to enhance the functionality and sustainability of normal concrete, especially by its greater ductility as well as higher compressive, tensile, and flexural strengths. In this paper, the influence of three types (linear displacement, uniform traction, and periodic) of boundary conditions used in numerical homogenization on the calculated values of HPC properties is determined and compared with experimental data. We take into account the softening behavior of HPC due to the development of damage (micro-cracks), which finally leads to failure. The results of numerical simulations of the HPC samples were obtained by using the Abaqus package that we supplemented with our in-house finite element method (FEM) computer programs written in Python and the homogenization toolbox Homtools. This has allowed us to better account for the nonlinear response of concrete. In studying the microstructure of HPC, we considered a two-dimensional representative volume element using the finite element method. Because of the random character of the arrangement of concrete’s components, we utilized a stochastic method to generate the representative volume element (RVE) structure. Different constitutive models were used for the components of HPC: quartz sand—linear elastic, steel fibers—ideal elastic-plastic, and cement matrix—concrete damage plasticity. The numerical results obtained are compared with our own experimental data and those from the literature, and a good agreement can be observed.

Modeling of Cementitious Representative Volume Element with Additives

2017 ◽  
Vol 08 (02) ◽  
pp. 1750003 ◽  
Author(s):  
M. M. Shahzamanian ◽  
W. J. Basirun
Keyword(s):  
Finite Element ◽  
Fly Ash ◽  
Boundary Conditions ◽  
Elastic Properties ◽  
Representative Volume Element ◽  
Volume Element ◽  
Type I ◽  
Element Analysis ◽  
Representative Volume ◽  
Mesh Density

CEMHYD3D has been employed to simulate the representative volume element (RVE) of cementitious systems (Type I cement) containing fly ash (Class F) through a voxel-based finite element analysis (FEA) approach. Three-dimensional microstructures composed of voxels are generated for a heterogeneous cementitious material consisting of various constituent phases. The primary focus is to simulate a cementitious RVE containing fly ash and to present the homogenized macromechanical properties obtained from its analysis. Simple kinematic uniform boundary conditions as well as periodic boundary conditions were imposed on the RVE to obtain the principal and shear moduli. Our current work considers the effect of fly ash percentage on the elastic properties based on the mass and volume replacements. RVEs with lengths of 50, 100 and 200[Formula: see text][Formula: see text] at different degrees of hydration are generated, and the elastic properties are modeled and simulated. In general, the elastic properties of a cementitious RVE with fly ash replacement for cement based on mass and volume differ from each other. Moreover, the finite element (FE) mesh density effect is studied. Results indicate that mechanical properties decrease with increasing mesh density.

scholarly journals Systematic study of homogenization and the utility of circular simplified representative volume element

2019 ◽  
Vol 24 (9) ◽  
pp. 2961-2985 ◽  
Author(s):  
Soheil Firooz ◽  
Saba Saeb ◽  
George Chatzigeorgiou ◽  
Fodil Meraghni ◽  
Paul Steinmann ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Representative Volume Element ◽  
Systematic Study ◽  
Linear Displacement ◽  
Volume Element ◽  
Composite Cylinder ◽  
The Finite Element Method ◽  
Numerical Computations ◽  
Various Boundary Conditions ◽  
Representative Volume

Although both computational and analytical homogenization are well-established today, a thorough and systematic study to compare them is missing in the literature. This manuscript aims to provide an exhaustive comparison of numerical computations and analytical estimates, such as Voigt, Reuss, Hashin–Shtrikman, and composite cylinder assemblage. The numerical computations are associated with canonical boundary conditions imposed on either tetragonal, hexagonal, or circular representative volume elements using the finite-element method. The circular representative volume element is employed to capture an effective isotropic material response suitable for comparison with associated analytical estimates. The analytical results from composite cylinder assemblage are in excellent agreement with the numerical results obtained from a circular representative volume element. We observe that the circular representative volume element renders identical responses for both linear displacement and periodic boundary conditions. In addition, the behaviors of periodic and random microstructures with different inclusion distributions are examined under various boundary conditions. Strikingly, for some specific microstructures, the effective shear modulus does not lie within the Hashin–Shtrikman bounds. Finally, numerical simulations are carried out at finite deformations to compare different representative volume element types in the nonlinear regime. Unlike other canonical boundary conditions, the uniform traction boundary conditions result in nearly identical effective responses for all types of representative volume element, indicating that they are less sensitive with respect to the underlying microstructure. The numerical examples furnish adequate information to serve as benchmarks.

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