Micromechanical approach to viscoelastic stress analysis of a pin-loaded hole in unidirectional laminated PMC

2021 ◽  
pp. 096739112110473
Author(s):  
Arash Reza ◽  
Mohammad Shishesaz ◽  
Hamid M Sedighi
Keyword(s):  
Micromechanical Model ◽  
Viscoelastic Behavior ◽  
Tensile Load ◽  
Laminated Composite ◽  
Integral Form ◽  
Equilibrium Equations ◽  
Stress Strain Relation ◽  
The Laplace Transform ◽  
The Time Domain ◽  
Comparison Of The Results

This paper aims to investigate the effect of viscoelastic behavior of polymer matrix of unidirectional fiber-reinforced laminated composite on stress distribution around the pin-loaded hole under tensile loading. The Laplace transform is used to prevent the integral form of matrix governing stress-strain relation. Applying a micromechanical model, all equilibrium equations for the fibers are written analytically in the Laplace domain. The numerical algorithm of Gaver–Stehfest is implemented, and the governing equations were solved at any given time to extract the concerned results in the time domain. The obtained results are validated against the Finite Element Method results obtained through ANSYS software. Moreover, a comparison of the results of this study at the time equal zero with elastic solutions of other references showed a good agreement. The results revealed that in the long term, the maximum tensile load in the intact fiber around the pinhole was enlarged and the tensile load in fibers far from the pinhole slightly was decreased. Moreover, the location of the maximum axial load that had occurred on pinhole edges was moved slightly toward the center over time.

A Truly Generalized Plane Strain Meshless Model for Combined Normal and Shear Loading of Fiber Reinforced Materials

2010 ◽  
Author(s):  
Eisa Ahmadi ◽  
M. M. Aghdam
Keyword(s):  
Direct Method ◽  
Micromechanical Model ◽  
Computation Time ◽  
Integral Form ◽  
Shear Loading ◽  
Interface Condition ◽  
Fiber Reinforced ◽  
Equilibrium Equations ◽  
Normal Loading ◽  
Fiber Reinforced Materials

A truly meshless method based on the integral form of equilibrium equations is formulated. A micromechanical model is developed to study micro-stresses in normal and shear loading of unidirectional fiber reinforced composites. A small repeating area of composite including a fiber surrounded by matrix called representative volume element (RVE) is considered as solution domain. A direct method is proposed for enforcement of the appropriate periodic boundary conditions for shear and normal loading. Especially transverse shear loading is considered in this analysis. Fully bonded interface condition is investigated and the continuity of displacements and traction is imposed to the fiber-matrix interface. Comparison of the predicted results shows excellent agreement with results in available literature. Results of this study also revealed that the presented model can provide highly accurate predictions with respectively small number of nodes and small computation time without the complexity of mesh generation.

Analytical Expressions for the Relaxation Moduli of Linear Viscoelastic Composites With Periodic Microstructure

1995 ◽  
Vol 62 (3) ◽  
pp. 786-793 ◽  
Author(s):  
R. Luciano ◽  
E. J. Barbero
Keyword(s):  
Laplace Transform ◽  
Viscoelastic Behavior ◽  
Relaxation Functions ◽  
Periodic Microstructure ◽  
The Matrix ◽  
The Laplace Transform ◽  
Linear Viscoelastic ◽  
The Time Domain ◽  
Viscoelastic Composites ◽  
Long Fibers

In this paper the viscoelastostatic problem of composite materials with periodic microstructure is studied. The matrix is assumed linear viscoelastic and the fibers elastic. The correspondence principle in viscoelasticity is applied and the problem in the Laplace domain is solved by using the Fourier series technique and assuming the Laplace transform of the homogenization eigenstrain piecewise constant in the space. Formulas for the Laplace transform of the relaxation functions of the composite are obtained in terms of the properties of the matrix and the fibers and in function of nine triple series which take into account the geometry of the inclusions. The inversion to the time domain of the relaxation and the creep functions of composites reinforced by long fibers is carried out analytically when the four-parameter model is used to represent the viscoelastic behavior of the matrix. Finally, comparisons with experimental results are presented.

Analysis of micro-stresses in the SiC/Ti metal matrix composite using a truly local meshless method

2009 ◽  
Vol 224 (8) ◽  
pp. 1567-1577 ◽  
Author(s):  
I Ahmadi ◽  
M M Aghdam
Keyword(s):  
Meshless Method ◽  
Metal Matrix ◽  
Interpolation Method ◽  
Micromechanical Model ◽  
Integral Form ◽  
Interface Condition ◽  
Computational Time ◽  
Equilibrium Equations ◽  
Normal Loading ◽  
Domain Integration

A generalized plane strain micromechanical model is developed for the analysis of unidirectional fibre-reinforced composites subjected to various combined normal loading conditions. Based on the integral form of the equilibrium equations, a truly meshless method is presented to obtain the solution for the governing equations of the problem. By employing the integral form of equilibrium equations for each sub-domain, the domain integration is eliminated from the formulation and the computational time is considerably reduced. The solution domain includes a quarter of the fibre surrounded by the corresponding matrix known as the representative volume element (RVE). The appropriate boundary conditions are imposed on the RVE using a direct interpolation method. The continuity of displacements and reciprocity of traction are imposed on the fibre—matrix interface based on the fully bonded interface condition. The presented model is used to predict the micro-stresses in the SiC/Ti metal matrix composites. Comparison of the CPU time between the presented model and the conventional meshless local Petrov—Galerkin model shows significant reduction of computational time. The results also revealed that the presented model can provide highly accurate predictions with a relatively small number of nodes. Comparison of the predicted results shows excellent agreement with available experimental and finite-element studies.

scholarly journals Semi-analytical static analysis of nonlocal strain gradient laminated composite nanoplates in hygrothermal environment

2021 ◽  
Vol 43 (5) ◽  
Author(s):  
Giovanni Tocci Monaco ◽  
Nicholas Fantuzzi ◽  
Francesco Fabbrocino ◽  
Raimondo Luciano
Keyword(s):  
Thin Plate ◽  
Strain Gradient ◽  
Plate Theory ◽  
Laminated Composite ◽  
Equilibrium Equations ◽  
Thin Plate Theory ◽  
Bending Behavior ◽  
Hygrothermal Environment ◽  
Load Types ◽  
Novel Applications

AbstractIn this work, the bending behavior of nanoplates subjected to both sinusoidal and uniform loads in hygrothermal environment is investigated. The present plate theory is based on the classical laminated thin plate theory with strain gradient effect to take into account the nonlocality present in the nanostructures. The equilibrium equations have been carried out by using the principle of virtual works and a system of partial differential equations of the sixth order has been carried out, in contrast to the classical thin plate theory system of the fourth order. The solution has been obtained using a trigonometric expansion (e.g., Navier method) which is applicable to simply supported boundary conditions and limited lamination schemes. The solution is exact for sinusoidal loads; nevertheless, convergence has to be proved for other load types such as the uniform one. Both the effect of the hygrothermal loads and lamination schemes (cross-ply and angle-ply nanoplates) on the bending behavior of thin nanoplates are studied. Results are reported in dimensionless form and validity of the present methodology has been proven, when possible, by comparing the results to the ones from the literature (available only for cross-ply laminates). Novel applications are shown both for cross- and angle-ply laminated which can be considered for further developments in the same topic.

The study of the nonlinear vibration of S-S and C-C laminated composite conical shells on elastic foundations through an approximate method

2021 ◽  
pp. 095440622110214
Author(s):  
Shahin Mohammadrezazadeh ◽  
Ali Asghar Jafari
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Vibration ◽  
Approximate Method ◽  
Laminated Composite ◽  
Vertex Angle ◽  
Nonlinear Frequency ◽  
Conical Shells ◽  
Elastic Foundations ◽  
Vibration Responses ◽  
Comparison Of The Results

This paper investigates the nonlinear vibration responses of laminated composite conical shells surrounded by elastic foundations under S-S and C-C boundary conditions via an approximate approach. The laminated composite conical shells are modeled based on classical shell theory of Love employing von Karman nonlinear theory. Nonlinear vibration equation of the conical shells is extracted by handling Lagrange method. The linear and nonlinear vibration responses are obtained via an approximate method which combines Lindstedt-Poincare method with modal analysis. The validation of this study is carried out through the comparison of the results of this study with results of published literature. The effects of several parameters including the constants of elastic foundations, boundary conditions, total thickness, length, large edge radius and semi-vertex angle on the values of fundamental linear frequency and curves of amplitude parameter versus nonlinear frequency ratio for laminated composite conical shells with both S-S and C-C boundary conditions are investigated.

Hygrothermal Buckling Response of Laminated Composite Plates with Random Material Properties: Micro-Mechanical Model

2011 ◽  
Vol 110-116 ◽  
pp. 113-119 ◽  
Author(s):  
Rajesh Kumar ◽  
Dharamveer Singh
Keyword(s):  
Material Properties ◽  
Plate Theory ◽  
Perturbation Technique ◽  
Micromechanical Model ◽  
Laminated Composite ◽  
Composite Plates ◽  
Second Order Statistics ◽  
Operational Life ◽  
Safety And Reliability ◽  
Random Material Properties

The aim of this paper is to find out the randomness in the material properties on the buckling of laminated composite plate needed for the economy, safety and reliability of the structures and components in their operational life especially for sensitive Aerospace Engineering applications in hygrothermal environments. Micromechanical model has been taken for the analysis .The used methodology is a C0 finite element method based on higher-order shear deformation plate theory for deriving the standard eigenvalue problem. A Taylor series based mean-centered first order perturbation technique is used to find out the second order statistics of the hygrothermal buckling loads under different sets of environmental conditions..The numerical results for deterministic parameters are compared and validated with available literature and random parameters with independent Monte Carlo Simulation. The result shows that the plate is significantly affected by the hygrothermal buckling load.

scholarly journals Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems

2021 ◽  
Author(s):  
Changkun Wei ◽  
Jiaqing Yang ◽  
Bo Zhang
Keyword(s):  
Time Domain ◽  
Electromagnetic Scattering ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Scattering Problems ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Time Domain Electromagnetic ◽  
Numer Anal ◽  
The Time Domain

In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the $L^2$-norm and $L^{\infty}$-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3) (2020), 1918-1940).

scholarly journals Thermoelastic Diffusion Multicomponent Half-Space under the Effect of Surface and Bulk Unsteady Perturbations

2019 ◽  
Vol 24 (1) ◽  
pp. 26 ◽  
Author(s):  
Sergey Davydov ◽  
Andrei Zemskov ◽  
Elena Akhmetova
Keyword(s):  
Half Space ◽  
Green's Functions ◽  
Green’S Functions ◽  
Local Equilibrium ◽  
Linear Equations ◽  
Integral Form ◽  
External Effects ◽  
Thermoelastic Diffusion ◽  
One Dimensional ◽  
The Laplace Transform

This article presents an algorithm for solving the unsteady problem of one-dimensional coupled thermoelastic diffusion perturbations propagation in a multicomponent isotropic half-space, as a result of surface and bulk external effects. One-dimensional physico-mechanical processes, in a continuum, have been described by a local-equilibrium model, which included the coupled linear equations of an elastic medium motion, heat transfer, and mass transfer. The unknown functions of displacement, temperature, and concentration increments were sought in the integral form, which was a convolution of the surface and bulk Green’s functions and external effects functions. The Laplace transform on time and the Fourier sine and cosine transforms on the coordinate were used to find the Green’s functions. The obtained Green’s functions was analyzed. Test calculations were performed on the examples of some technological processes.

Viscoelastic behavior of epoxy resin reinforced with shape-memory-alloy wires

2020 ◽  
pp. 1045389X2097549
Author(s):  
Niloufar Bagheri ◽  
Mahmood M Shokrieh ◽  
Ali Saeedi
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Epoxy Resin ◽  
Volume Fraction ◽  
Niti Alloy ◽  
Micromechanical Model ◽  
Viscoelastic Behavior ◽  
Mechanical Analysis ◽  
Reinforced Polymer ◽  
Small Volume Fraction

The effect of NiTi alloy long wires on the viscoelastic behavior of epoxy resin was investigated by utilizing the dynamic mechanical analysis (DMA) and a novel micromechanical model. The present model is capable of predicting the viscoelastic properties of the shape-memory-alloy (SMA) reinforced polymer as a function of the SMA volume fraction, initial martensite volume fraction, pre-strain level in wires, and the temperature variations. The model was verified by conducting experiments. Good agreement between the theoretical and experimental results was achieved. A parametric study was also performed to investigate the effect of SMA parameters. According to the results, by the addition of a small volume fraction of SMA, the storage modulus of the composite increases significantly, especially at higher temperatures. Moreover, applying a 4% pre-strain caused a 10% increase in the maximum value of the loss factor of the SMA reinforced epoxy in comparison with the 0% pre-strained SMA reinforced epoxy.

Stress analysis of smart composite plate structures

2020 ◽  
pp. 095440622097544
Author(s):  
Aniket Chanda ◽  
Utkarsh Chandel ◽  
Rosalin Sahoo ◽  
Neeraj Grover
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Laminated Composite ◽  
Composite Plates ◽  
Higher Order ◽  
Hyperbolic Function ◽  
Solution Technique ◽  
Shear Stresses ◽  
Laminated Composite Plates ◽  
Equilibrium Equations

In the present study, the electro-mechanical responses of smart laminated composite plates with piezoelectric materials are derived using a two-dimensional (2 D) displacement-based non-polynomial higher-order shear deformation theory. The kinematics of the mathematical model incorporates the deformation of laminates which account for the effects of transverse shear deformation and a non-linear variation of the in-plane displacements using inverse sine hyperbolic function of the thickness coordinate. The equilibrium equations are obtained using the minimization of energy principle known as the principle of minimum potential energy (PMPE) which is also based on a variational approach and the solutions are obtained using Navier’s solution technique for diaphragm supported smart laminated composite plates. The responses obtained in the form of deflection and stresses are compared with three dimensional (3 D) solutions and also with different polynomial and non-polynomial based higher-order theories in the literature. The transverse shear stresses are obtained using 3 D equilibrium equations of elasticity to enhance the accuracy of the present results. Various examples are numerically solved to establish the efficiency of the present model.

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