scholarly journals Random Stiffness Tensor of Particulate Composites with Hyper-Elastic Matrix and Imperfect Interface

Materials ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 6676
Author(s):  
Damian Sokołowski ◽  
Marcin Kamiński
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Analytical Method ◽  
Volume Fraction ◽  
Effective Stiffness ◽  
Particulate Composites ◽  
Stiffness Tensor ◽  
The Matrix ◽  
Hyper Elastic

The main aim of this study is determination of the basic probabilistic characteristics of the effective stiffness for inelastic particulate composites with spherical reinforcement and an uncertain Gaussian volume fraction of the interphase defects. This is determined using a homogenization method with a cubic single-particle representative volume element (RVE) of such a composite and the finite element method solution. A reinforcing particle is spherical, located centrally in the RVE, surrounded by the thin interphase of constant thickness, and remains in an elastic reversible regime opposite to the matrix, which is hyper-elastic. The interphase defects are represented as semi-spherical voids, which are placed on the outer surface of this particle. The interphase is modeled as hyper-elastic and isotropic, whose effective stiffness is calculated by the spatial averaging of hyper-elastic parameters of the matrix and of the defects. A constitutive relation of the matrix is recovered experimentally by its uniaxial stretch. The 3D homogenization problem solution is based upon a numerical determination of strain energy density in the given RVE under specific uniaxial and biaxial stretches as well as under shear deformations. The analytical relation of the effective composite stiffness to the input uncertain parameter is recovered via the response function method, using a polynomial basis and an optimized order. Probabilistic calculations are completed using three concurrent approaches, namely the iterative stochastic finite element method (SFEM), Monte Carlo simulation and by the semi-analytical method. Previous papers consider the composite fully elastic, which limits the applicability of the resulting effective stiffness tensor computed therein. The current study voids this assumption and defines the composite as fully hyper-elastic, thus extending applicability of this tensor to strains up to 0.25. The most important research finding is that (1) the effective stiffness tensor is sensitive to random interface defects in its hyper-elastic range, (2) its resulting randomness is not close to Gaussian, (3) the semi-analytical method is not perfectly suited to stochastic calculations in this region of strains, as opposed to the linear elastic region, and (4) that the increase in random dispersion of defects volume fraction has a much higher effect on the stochastic characteristics of this stiffness tensor than fluctuation of the strain.

scholarly journals Predictive Computational Model for Damage Behavior of Metal-Matrix Composites Emphasizing the Effect of Particle Size and Volume Fraction

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2143
Author(s):  
Shaimaa I. Gad ◽  
Mohamed A. Attia ◽  
Mohamed A. Hassan ◽  
Ahmed G. El-Shafei
Keyword(s):  
Finite Element ◽  
Metal Matrix Composites ◽  
Metal Matrix ◽  
Volume Fraction ◽  
Particulate Composites ◽  
Aluminum Matrix Composites ◽  
Matrix Composites ◽  
Zone Method ◽  
Stress Strain ◽  
The Matrix

In this paper, an integrated numerical model is proposed to investigate the effects of particulate size and volume fraction on the deformation, damage, and failure behaviors of particulate-reinforced metal matrix composites (PRMMCs). In the framework of a random microstructure-based finite element modelling, the plastic deformation and ductile cracking of the matrix are, respectively, modelled using Johnson–Cook constitutive relation and Johnson–Cook ductile fracture model. The matrix-particle interface decohesion is simulated by employing the surface-based-cohesive zone method, while the particulate fracture is manipulated by the elastic–brittle cracking model, in which the damage evolution criterion depends on the fracture energy cracking criterion. A 2D nonlinear finite element model was developed using ABAQUS/Explicit commercial program for modelling and analyzing damage mechanisms of silicon carbide reinforced aluminum matrix composites. The predicted results have shown a good agreement with the experimental data in the forms of true stress–strain curves and failure shape. Unlike the existing models, the influence of the volume fraction and size of SiC particles on the deformation, damage mechanism, failure consequences, and stress–strain curve of A359/SiC particulate composites is investigated accounting for the different possible modes of failure simultaneously.

scholarly journals Hysteretic Behavior of Random Particulate Composites by the Stochastic Finite Element Method

Materials ◽  
2019 ◽  
Vol 12 (18) ◽  
pp. 2909 ◽  
Author(s):  
Damian Sokołowski ◽  
Marcin Kamiński
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cyclic Stretch ◽  
Hysteretic Behavior ◽  
Particulate Composites ◽  
Strain History ◽  
Stochastic Finite Element Method ◽  
Stochastic Finite Element ◽  
The Matrix ◽  
Element Method

Hysteretic behavior of random particulate composite was analyzed using the stochastic finite element method and three independent probabilistic formulations, i.e., generalized iterative stochastic perturbation technique of the tenth order, Monte-Carlo simulation, and semi-analytical method. This study was based on computational homogenization of the representative volume element (RVE), and its main focus was to demonstrate an influence of random stress in constitutive relation to the matrix on the deformation energies stored in the effective (homogenized) medium. This was done numerically for an increasing uncertainty of random matrix admissible stress with a Gaussian probability density function, for which the relations to the energies of the entire composite were approximated via the weighted least squares method algorithm. This composite was made of two phases, a hyper-elastic matrix exhibiting hysteretic behavior and a linear elastic spherical reinforcing particle located centrally in the RVE. The RVE was subjected to a cyclic stretch with an increasing amplitude, and computations of deformation energies were carried out using the finite element method system ABAQUS. A stress–strain history of the homogenized medium has been presented for the extreme and for the mean mechanical properties of the matrix to illustrate the random hysteresis of the given composite. The first four probabilistic moments and coefficients of the RVE deformation energy were determined and have been presented in addition to the input statistical scattering of the admissible stresses.

Determination of the effective stiffness of a unidirectional layer by the finite element method and approximate formulas

2021 ◽  
Vol 87 (3) ◽  
pp. 40-50
Author(s):  
I. P. Olegin ◽  
T. V. Burnysheva ◽  
N. A. Laperdina
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Properties ◽  
Volume Content ◽  
Theory Of Elasticity ◽  
Effective Stiffness ◽  
The Finite Element Method ◽  
Approximate Formulas ◽  
Elastic Characteristics

Layered composites formed by unidirectional layers are widely used in aviation in the most loaded areas of the aircraft. Data on the elastic properties of the layers are required for the strength and stiffness calculation of structural elements made of such materials. There are two possible approaches to address the problem. The first approach is based on solving the problem of micromechanics using methods of the theory of elasticity. The second approach consists in developing a simplified model of a unidirectional layer. Analysis of the model can provide for fairly simple formulas for determination of the effective stiffness of a unidirectional layer. A comparative analysis of the results obtained in both approaches revealed the limits of applicability of approximate formulas derived for evaluating the effective characteristics of the different types of composites depending on the volume content of fibers. The effective elastic characteristics of unidirectional composites are determined by the finite element method in the framework of the linear theory of elasticity. The boundary value problem is solved for a characteristic representative element selected in accordance with the physical and geometric parameters of the medium of an ordered structure. A set of algorithm-programs has been developed under ANSYS environment which automates calculations of the elastic characteristics of materials depending on the volume content of fibers at different ratios of the elastic properties of fibers and binder, and on the parameters of the curvature of the fiber cross-sectional profile. The results obtained by the numerical method are compared with the data obtained experimentally and by approximate formulas.

THE ROLE OF FINITE ELEMENT METHOD IN CIVIL ENGINEERING

2018 ◽  
Vol 5 (02) ◽  
Author(s):  
Er. Hardik Dhull
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Analytical Method ◽  
Civil Engineering ◽  
The Finite Element Method ◽  
Engineering Problems ◽  
Building Components ◽  
Element Method

The finite element method is a numerical method that is used to find solution of mathematical and engineering problems. It basically deals with partial differential equations. It is very complex for civil engineers to study various structures by using analytical method,so they prefer finite element methods over the analytical methods. As it is an approximate solution, therefore several limitationsare associated in the applicationsin civil engineering due to misinterpretationof analyst. Hence, the main aim of the paper is to study the finite element method in details along with the benefits and limitations of using this method in analysis of building components like beams, frames, trusses, slabs etc.

An Analysis of Conventional and Self-Aligned four Terminal Resistor Structures for The Determination of The Contact Resistivity from End Resistance Measurements

1986 ◽  
Vol 71 ◽  
Author(s):  
I. Suni ◽  
M. Finetti ◽  
K. Grahn
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computer Model ◽  
Contact Resistivity ◽  
Experimental Results ◽  
The Finite Element Method ◽  
Model Based ◽  
A Value ◽  
And Diffusion

AbstractA computer model based on the finite element method has been applied to evaluate the effect of the parasitic area between contact and diffusion edges on end resistance measurements in four terminal Kelvin resistor structures. The model is then applied to Al/Ti/n+ Si contacts and a value of contact resistivity of Qc = 1.8×10−7.Ωcm2 is derived. For comparison, the use of a self-aligned structure to avoid parasitic effects is presented and the first experimental results obtained on Al/Ti/n+Si and Al/CoSi2/n+Si contacts are shown and discussed.

Teaching the Finite Element Method As a Design Tool for Mechanical Engineering

1993 ◽  
Author(s):  
T. R. Grimm
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Solution Process ◽  
Thinking Skills ◽  
Design Tool ◽  
Basic Solution ◽  
The Finite Element Method ◽  
The Matrix ◽  
Analysis Of Results ◽  
Element Method

Abstract The importance of the finite element method as an engineering tool for design and analysis is emphasized in a senior level elective course taught at Michigan Technological University. The course emphasizes hands-on experience with computers and the pre- and post-analysis of results to establish confidence in solutions obtained. The students learn by using the finite element method to “solve” several design projects, rather than by being told about the method without significant actual experience. They also learn about the basis of the method, including formation of the matrix equations required and the numerical methods used in their solution. Intelligent use of the method requires that engineers understand both the mechanics of how to apply the method, i.e modeling requirements, and the limitations imposed by the basic solution process. The course provides the students with important experience in using the powerful finite element method as a design tool. It requires a strong background of fundamentals and stimulates the problem solving thinking skills so essential to industry.

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