Evaluation Of Effective Material Properties Research Articles

Peridynamic micromechanical model for damage mechanisms in composites

This study presents a novel three-dimensional (3D) micromechanical peridynamic (PD) model to establish relationships between microstructural features such as shape, size and distribution of fibers, damage initiation, and size-effect relationships. It specifically permits to investigate the effective elastic properties and damage mechanisms in composites. It enables the application of pure strain, pure stress and mixed stress–strain constraints while including the effect of temperature change. Also, it permits the evaluation of effective material properties from a single load case. Periodic boundary conditions are applied naturally by completing the interaction domain using material points from the opposite side of microstructure. Also, this 3D PD micromechanical model does not require any surface correction for both homogenization and dehomogenization. Complex heterogeneous microstructures of composites are constructed and analyzed by state-based PD. Material variability is taken into consideration during the progressive damage analysis to capture more realistic failure mechanisms. Peridynamic predictions recover results available in the literature; thus, verifying the accuracy and effectiveness of the present micromechanical model.

Computational Evaluation of Thermal Response of Open-Cell Foam With Circular Pore

Abstract The evaluation of effective material properties in heterogeneous materials (e.g., composites or multicomponent structures) is critically relevant to a wide spectrum of applications, including nuclear power, electronic packaging, flame retardants, hypersonics, and gas turbine power. The work described in this paper is centered around the numerical assessment of the thermal behavior of porous materials obtained from finite element thermal modeling and simulation. Two-dimensional, steady-state analyses were performed on unit cells with centered, circular pores using a second-order accurate Galerkin finite element method (FEM). The effective thermal conductivities of the porous systems were examined, encompassing a range of porosities from 4.9% to 60.1%. The geometries of the models were generated based on ordered circular pores for each modeled porosity level. The system response quantity (SRQ) under investigation was the dimensionless effective thermal conductivity across the unit cell. The dimensionless effective thermal conductivity was compared across all simulated cases, producing a trend between porosity and effective thermal conductivity. In the presented investigation, the method of manufactured solutions (MMS) was used to perform code verification, and the grid convergence index (GCI) was employed to estimate discretization uncertainty as solution verification. Code verification concluded an approximately second order accurate Galerkin FEM solver. It was found that the introduction of porosity to the unit cell material structure reduces effective thermal conductivity, as anticipated. Numerical results obtained in this study are compared to an analytical solution and to a sample of empirical data. This approach can be readily generalized to study a wide variety of porous solids from ranging from structures at the nanoscale—such as nanocarbon tubes—to structures at macrolevel scales—such as geological features.

Microstructure modelling using the scaled boundary finite element method

AbstractAn automatic approach for the evaluation of effective material properties is presented. It is based on the scaled boundary finite element method (SBFEM). The SBFEM facilitates the use of structured meshes on highly heterogeneous domains. These meshes are obtained automatically from image data. Two examples illustrate the potential of the proposed methodology.

Evaluation of effective material properties in magneto-electro-elastic composite materials

The meshless local integral equation method is developed to analyze general two-dimensional boundary value problems in size-dependent magnetoelectroelastic solids. A consistent theory is developed for size dependent magnetoelectroelasticity. The strain gradients are considered in the constitutive equations for electric displacement and magnetic induction. The governing equations are derived with the corresponding boundary conditions using the variational principle. The local integral equations are subsequently derived and the meshless moving least square (MLS) numerical method is implemented to solve these equations.

Analysis of particles loaded fiber composites for the evaluation of effective material properties with the variation of shape and size

The effective material properties are predicted for composites with different shape and size of inclusions such as cylindrical fibers, spherical and elliptical particles and cylindrical fibers with hemispherical ends. The analysis is based on a numerical homogenization technique using finite element method in connection with three-dimensional representative volume element models. Investigations are carried out to study the influence of various parameters like volume fraction, aspect ratio and particle distribution. Results are discussed and compared.

On numerical evaluation of effective material properties for composite structures with rhombic fiber arrangements

This paper deals with unidirectional fiber reinforced composites with rhombic fiber arrangements. It is assumed, that there is a periodic structure on micro level, which can be taken by homogenization as a representative volume element (RVE) for the composite, where the composite phases have isotropic or transversely isotropic material characterizations. A special procedure is developed to handle the primary non-rectangular periodicity with common numerical homogenization techniques based on FE-models. Due to appropriate boundary conditions applied to the RVE elastic effective macroscopic coefficients are derived. Results are listed and compared with other publications and good agreements are shown. Furthermore new results are presented, which exhibit the special orthotropic behavior of such composites caused by the rhombic fiber arrangement.

Evaluation of effective material properties of spiral wound gasket through homogenization

In this paper, a homogenization methodology is proposed to determine the material properties of spiral wound gaskets (SWGs) using finite element analysis through representative volume elements (RVE) of the gaskets. The constituents of this RVE are described by elasto-plastic material properties. The RVE are subjected to six load cases and the volume averaged responses are analyzed simultaneously to predict the anisotropic properties. The mechanical behaviour is simplified to an orthotropic material model with Hill’s plasticity model and the properties are verified with micro-mechanical simulation and experimental results available in the literature. Reasonable agreement is obtained between the results. Formulae for elastic properties are also derived by a simplified analytical method based on lamination theory and compared with those obtained from homogenization.

Evaluation of effective material properties of randomly distributed short cylindrical fiber composites using a numerical homogenization technique

Evaluation of effective material properties of randomly distributed short cylindrical fiber composites using a numerical homogenization technique

Evaluation of influence of interphase material parameters on effective material properties of three phase composites

In this paper, evaluation of effective material properties of different types of three phase composites (reinforcement, matrix and in between interphase) using numerical homogenization techniques (representative volume element (RVE) approach) based on finite element method is presented. The influence of interphase parameters like stiffness and volume fraction of interphase on effective material properties of transversely randomly distributed uni-directional fiber composites and randomly distributed spherical particle composites is studied. The RVEs, required for transversely randomly distributed uni-directional fiber composites and randomly distributed spherical particle composites, are generated using a modified random sequential adsorption (RSA) algorithm with periodicity on opposite boundary surfaces. The numerical results are compared with analytical methods like asymptotic homogenization method for regular arrangement of uni-directional fiber composites.

Numerical Evaluation of Effective Material Properties of Transversely Randomly Distributed Unidirectional Piezoelectric Fiber Composites

This article presents a method for the evaluation of effective material properties of transversely randomly distributed unidirectional piezoelectric fiber composites using homogenization techniques based on the finite element method (FEM) and representative volume element (RVE) method. Modified random sequential adsorption (RSA) algorithm is used to generate three-dimensional (3D) RVE models of transversely randomly distributed unidirectional fiber composites. Numerical studies are carried out to estimate the influence of diameter and arrangement of fibers on the effective material properties. Using different diameters of fibers, RVE models are generated up to 80% volume fraction. All effective material properties of transversely randomly distributed unidirectional piezoelectric fiber composites are evaluated and comparisons are made with regular packing like square and hexagonal arrangement of piezoelectric fiber composites.

Meshless method for nonlinear heat conduction analysis of nano-composites

Carbon nanotubes (CNTs) may become ideal reinforcing materials for high-performance nano-composites due their exceptional properties. Still, much work is needed to be done before the potentials of CNT based composites can be fully realized. The evaluation of effective material properties of nano-composites is one of many difficult tasks. Simulations using continuum mechanics approach can play a significant role in the analysis of these composites. In the present work, nonlinear heat conduction analysis of CNT based composites has been carried out using continuum mechanics approach. Element free Galerkin method has been applied as a numerical tool. Thermal conductivities of nanotube and polymer matrix are assumed to vary quadratically with temperature. Picard and quasi-linearization schemes have been utilized to obtain the solution of a system of nonlinear equations. Cylindrical representative volume element has been used to evaluate the thermal properties of nano-composites. Present simulations show that the temperature dependent matrix thermal conductivity has a significant effect on the equivalent thermal conductivity of the composite, whereas temperature dependent nanotube thermal conductivity has a small effect on the equivalent thermal conductivity of the composite. The results obtained by Picard method have been found almost similar with those obtained by quasi-linearization approach.

Numerical evaluation of effective material properties of randomly distributed short cylindrical fibre composites

The aim of presenting this paper is to evaluate the effective material properties of randomly distributed short fibre (RDSF) and transversely randomly distributed short fibre (TRDSF) composites with change in volume fraction, and aspect ratio of fibres. A numerical homogenization technique based on the finite element method (FEM) is used to evaluate the effective material properties with periodic boundary conditions. A modified random sequential adsorption algorithm (RSA) is applied to generate the three-dimensional unite cell models of randomly distributed short cylindrical fibre composites. The developed numerical homogenization technique is used to calculate effective material properties in order to systematically evaluate different material systems. The numerical results are also compared and verified with different analytical methods.

The Arithmetic Mean Theorem of Eshelby Tensor for Exterior Points Outside the Rotational Symmetrical Inclusion

In 1957, Eshelby proved that the strain field within a homogeneous ellipsoidal inclusion embedded in an infinite isotropic media is uniform, when the eigenstrain prescribed in the inclusion is uniform. This property is usually referred to as the Eshelby property. Although the Eshelby property does not hold for the non-ellipsoidal inclusions, in recent studies we have successfully proved that the arithmetic mean of Eshelby tensors at N rotational symmetrical points inside an N-fold rotational symmetrical inclusion is constant and equals the Eshelby tensor for a circular inclusion, when N⩾3 and N≠4. The property is named the quasi-Eshelby property or the arithmetic mean theorem of Eshelby tensors for interior points. In this paper, we investigate the elastic field outside the inclusion. By the Green formula and the knowledge of complex variable functions, we prove that the arithmetic mean of Eshelby tensors at N rotational symmetrical points outside an N-fold rotational symmetrical inclusion is equal to zero, when N⩾3 and N≠4. The property is referred to as the arithmetic mean theorem of Eshelby tensors for exterior points. Due to the quality of the Green function for plane strain problems, the fourfold rotational symmetrical inclusions are excluded from possessing the arithmetic mean theorem. At the same time, by the method proposed in this paper, we verify the quasi-Eshelby property which has been obtained in our previous work. As corollaries, two more special properties of Eshelby tensor for N-fold rotational symmetrical inclusions are presented which may be beneficial to the evaluation of effective material properties of composites. Finally, the circular inclusion is used to test the validity of the arithmetic mean theorem for exterior points by using the known solutions.

Computational evaluation of effective material properties of composites reinforced by randomly distributed spherical particles

The aim of presenting this paper is to evaluate the effective material properties of spherical particle reinforced composites for different volume fractions up to 60%. A numerical homogenization technique based on the finite element method (FEM) with representative volume element (RVE) was used to evaluate the effective material properties with periodic boundary conditions. The numerical approach is based on the FEM and it allows the extension of the composites with arbitrary geometrical inclusion configurations, providing a powerful tool for fast calculation of their effective material properties. Modified random sequential adsorption algorithm (RSA) was used to generate the three-dimensional RVE models of randomly distributed spherical particles. The effective material properties obtained using the numerical homogenization techniques were compared with different analytical methods and good agreement was achieved. Several investigations had been conducted to estimate the influence of the size of spherical particles and of the RVE on effective material properties of spherical particle reinforced composites.

Evaluation of effective material properties of composite materials using special FEM

In the present paper, a novel method using the special 2D finite element method (FEM) and the concept of equivalent homogeneous materials has been employed to evaluate the effective material properties of composites. Special 2D finite elements containing an internal defect or reinforcement have been well developed in order to greatly simplify the numerical modeling of composites. It can assure the high precision especially in the vicinity of defects or reinforcements in composite materials. Some numerical examples will be provided to demonstrate the validity and versatility of the proposed method by comparing the existing results from other literatures.

Application of GPS Tensors to Fiber Reinforced Composites

In this paper we propose a pair of two new tensors called GPS tensors S and D for the concentric cylindrical inclusion problem. GPS tensor S relates the strain in the inclusion constrained by the matrix of finite radius to the uniform transformation strain (eigenstrain), whereas tensor D relates the strain in the matrix to the same eigenstrain. The tensorial form of relationship to the inclusion problem allows us to derive explicit expressions for a larger class of transformation problems, including thermal residual stress problems. Since GPS tensors take the fiber volume fraction into account explicitly, we are able to study the effect of matrix properties and fiber volume fraction on the spatial distribution of thermal residual stress. GPS tensors are also used in the evaluation of effective material properties by using the self-consistent method. Very good agreement between analytical results using GPS tensors and experimental data is observed for graphite/epoxy and glass/epoxy composites.

On the Determination of Effective Elastic-Plastic Properties for the Equivalent Solid Plate Analysis of Tube Sheets

Practical procedures are described for the evaluation of effective material properties for use in elastic-plastic analyses of perforated plates involving the equivalent solid plate approach. The finite-element method is used to generate numerical solutions that permit these properties to be determined for a given penetration pattern and given base metal properties. An example is treated for the triangular penetration pattern. The results are illustrative of the anisotropy of the equivalent solid material.