scholarly journals Numerical Estimation of Effective Mechanical Properties for Reinforced Plexiglas in the Two-Dimensional Case

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Vladimir Levin ◽  
Ignatiy Vdovichenko ◽  
Anatoly Vershinin ◽  
Maksim Yakovlev ◽  
Konstantin Zingerman
Keyword(s):  
Mechanical Properties ◽  
Cross Section ◽  
Effective Properties ◽  
Strain Tensor ◽  
Finite Strains ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Numerical Estimation ◽  
Wire Cross Section ◽  
Effective Mechanical Properties

The paper describes an algorithm for numerical estimation of effective mechanical properties in two-dimensional case, considering finite strains. The algorithm is based on consecutive application of different boundary conditions to representative surface elements (RSEs) in terms of displacements, solution of elastic boundary value problem for each case, and averaging the stress field obtained. Effective properties are estimated as a quadratic dependence of the second Piola-Kirchhoff stress tensor upon the Green strain tensor. The results of numerical estimation of effective mechanical properties of plexiglas, reinforced with steel wire, are presented at finite strains. Numerical calculations were performed with the help of CAE Fidesys using the finite element method. The dependence of the effective properties of reinforced plexiglas upon the concentration of wires and the shape of wire cross section is investigated. In particular, it was found that the aspect ratio of reinforcing wire cross section has the most significant impact on effective moduli characterizing the material properties in the direction of larger side of the cross section. The obtained results allow one to estimate the influence of nonlinear effects upon the mechanical properties of the composite.

scholarly journals Rank-one convexity implies polyconvexity for isotropic, objective and isochoric elastic energies in the two-dimensional case

2017 ◽  
Vol 147 (3) ◽  
pp. 571-597 ◽  
Author(s):  
Robert J. Martin ◽  
Ionel-Dumitrel Ghiba ◽  
Patrizio Neff
Keyword(s):  
Energy Function ◽  
Strain Tensor ◽  
Dimensional Case ◽  
Logarithmic Strain ◽  
Two Dimensional ◽  
Rank One ◽  
Isotropic Functions ◽  
Deviatoric Part ◽  
Convexity Conditions ◽  
Quasi Convexity

We show that, in the two-dimensional case, every objective, isotropic and isochoric energy function that is rank-one convex on GL+(2) is already polyconvex on GL+(2). Thus, we answer in the negative Morrey's conjecture in the subclass of isochoric nonlinear energies, since polyconvexity implies quasi-convexity. Our methods are based on different representation formulae for objective and isotropic functions in general, as well as for isochoric functions in particular. We also state criteria for these convexity conditions in terms of the deviatoric part of the logarithmic strain tensor.

Misestimation of the ITZ Thickness around Non-Spherical Aggregates

2021 ◽  
Vol 1036 ◽  
pp. 432-441
Author(s):  
Ming Qi Li ◽  
Hui Su Chen
Keyword(s):  
Mechanical Properties ◽  
Cross Section ◽  
Linear Analysis ◽  
Interfacial Transition Zone ◽  
High Porosity ◽  
Two Dimensional ◽  
One Dimensional ◽  
3D Microstructure ◽  
Porosity And Permeability ◽  
Very High

The ITZ (interfacial transition zone) in concrete has very high porosity and permeability, which affects concrete’s macroscopic mechanical properties and transport properties. Two-dimensional (2D) areal analysis and one-dimensional (1D) linear analysis are usually used to study ITZ’s microstructure. However, 3D microstructure is difficult to be characterized by 1D and 2D information. For example, 2D cross-section planes do not always intercept both the ITZ and the corresponding aggregate, which causes some ITZ regions are ignored by researchers. Therefore, ITZ’s volume and thickness will be misestimated, and leads to the misestimation of the diffusivity. In this paper, the effect of aggregate’s shape on the misestimation of ITZ thickness t is studied. The results reveal that the misestimation increases with the increasing sphericity s of aggregates.

On the Effective Mechanical Properties of Fluid-Saturated Composites: A Homogenization Approach

2010 ◽  
Vol 654-656 ◽  
pp. 2273-2276
Author(s):  
Lian Hua Ma ◽  
Bernard F. Rolfe ◽  
Qing Sheng Yang ◽  
Chun Hui Yang
Keyword(s):  
Mechanical Properties ◽  
Effective Properties ◽  
Micromechanical Model ◽  
Fluid Pressure ◽  
Fluid Phase ◽  
Homogenization Theory ◽  
Small Scale ◽  
Multi Scale ◽  
Homogenization Approach ◽  
Effective Mechanical Properties

Composites containing saturated fluid are widely distributed in nature, such as saturated rocks, colloidal materials and biological cells. In the study to determine effective mechanical properties of fluid-saturated composites, a micromechanical model and a multi-scale homogenization-based model are developed. In the micromechanical model the internal fluid pressure is generated by applying eigenstrains in the domain of the fluid phase and the explicit expressions of effective bulk modulus and shear modulus are obtained. Meanwhile a multi-scale homogenization theory is employed to develop the homogenization-based model on determination of effective properties at the small scale in a unit cell level. Applying the two proposed approaches, the effects of the internal pressure of hydrostatic fluid on effective properties are further investigated.

Effective Mechanical Properties of Carbon-Carbon Composites

2014 ◽  
Author(s):  
Aswathi Sudhir ◽  
Abhilash M. Nagaraja ◽  
Suhasini Gururaja
Keyword(s):  
Mechanical Properties ◽  
Effective Properties ◽  
Leading Edge ◽  
Carbon Composites ◽  
Length Scales ◽  
Heterogeneous Microstructure ◽  
Specific Strength ◽  
C Fibers ◽  
Exit Nozzle ◽  
Effective Mechanical Properties

In recent times, composite materials have gained mainstream acceptance as a structural material of choice due to their tailorability and improved thermal, specific strength/stiffness and durability performance [1–3]. For high temperature applications, which include exit nozzle for rockets, leading edge for missiles, nose cones, brake pads etc. Carbon-Carbon composites (C/C composite) are found suitable [4–6]. Mechanical property estimation of C/C composites is challenging due to their highly heterogeneous microstructure. The highly heterogeneous microstructure consists of woven C-fibers, C-matrix, irregularly shaped voids, cracks and other inclusions. Predicting the mechanical behavior of complex hierarchical materials like C/C composites is of interest which forms the motivation for the present work. A systematic study to predict the effective mechanical properties of C/C composite using numerical homogenization has been undertaken in this work. The Micro-Meso-Macro (MMM) principle of ensemble averages for estimating the effective properties of the composite has been adopted. The hierarchical length scales in C/C composites were identified as micro (single fiber with matrix), meso (fabric) and macro (laminate). Comparisons have been made with mechanical testing of C/C composites at different length scales.

EVALUATION OF EFFECTIVE MECHANICAL PROPERTIES OF NANOCOMPOSITES REINFORCED WITH SINUSOIDAL CARBON NANOTUBES

NANO ◽  
2012 ◽  
Vol 07 (05) ◽  
pp. 1250041 ◽  
Author(s):  
HOSSEIN GOLESTANIAN ◽  
MAHDIEH HAMEDI
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Effective Properties ◽  
Theory Of Elasticity ◽  
Interface Strength ◽  
Reinforced Polymers ◽  
Reinforced Polymer ◽  
Elastic Interface ◽  
Longitudinal Modulus ◽  
Effective Mechanical Properties

Carbon nanotubes (CNTs) possess exceptional mechanical properties and are therefore suitable candidates for use as reinforcements in composite materials. Substantial improvements in mechanical properties of polymers have been attained through the addition of small amounts of CNTs. The CNTs, however, form complicated shapes and do not usually appear as straight reinforcements when introduced in polymer matrices. In this paper, theory of elasticity of anisotropic materials and finite element method (FEM) are used to determine effective mechanical properties of sinusoidal-nanotube reinforced polymers. The effects of CNT shape, orientation, and CNT distribution on nanocomposite effective properties are investigated by modeling different CNT-reinforced polymers. Also, the effects of interface strength on nanocomposite properties are investigated using an elastic interface model. The results indicate that even a slight nanotube curvature significantly reduces the reinforcing efficiency of sinusoidal — nanotubes compared to straight nanotubes. Also, in-plane isotropy was observed in the results obtained from the random CNT reinforced polymer. Finally, increasing the interface strength results in higher nanocomposite longitudinal modulus.

scholarly journals Homogenization of Heterogeneous Tissue Scaffold: A Comparison of Mechanics, Asymptotic Homogenization, and Finite Element Approach

2005 ◽  
Vol 2 (1) ◽  
pp. 17-29 ◽  
Author(s):  
Z. Fang ◽  
C. Yan ◽  
W. Sun ◽  
A. Shokoufandeh ◽  
W. Regli
Keyword(s):  
Mechanical Properties ◽  
Tissue Engineering ◽  
Finite Element ◽  
Effective Properties ◽  
Tissue Scaffolds ◽  
Homogenization Theory ◽  
Tissue Scaffold ◽  
Finite Element Approach ◽  
Element Approach ◽  
Effective Mechanical Properties

Actual prediction of the effective mechanical properties of tissue scaffolds is very important for tissue engineering applications. Currently common homogenization methods are based on three available approaches: standard mechanics modeling, homogenization theory, and finite element methods. Each of these methods has advantages and limitations. This paper presents comparisons and applications of these approaches for the prediction of the effective properties of a tissue scaffold. Derivations and formulations of mechanics, homogenization, and finite element approach as they relate to tissue engineering are described. The process for the development of a computational algorithm, finite element implementation, and numerical solution for calculating the effective mechanical properties of porous tissue scaffolds are also given. A comparison of the results based upon these different approaches is presented. Parametric analyses using the homogenization approach to study the effects of different scaffold materials and pore shapes on the properties of the scaffold are conducted, and the results of the analyses are also presented.

The Numerical Analysis of Contaminant Migration from Sanitary Landfill Sites

1977 ◽  
Vol 12 (1) ◽  
pp. 233-255
Author(s):  
J.F. Sykes ◽  
A.J. Crutcher
Keyword(s):  
Contaminant Transport ◽  
Cross Section ◽  
Element Model ◽  
Sanitary Landfill ◽  
Saturated Porous Media ◽  
Two Dimensional ◽  
Contaminant Migration ◽  
Southern Ontario ◽  
Galerkin Finite Element ◽  
Chloride Concentrations

Abstract A two-dimensional Galerkin finite element model for flow and contaminant transport in variably saturated porous media is used to analyze the transport of chlorides from a sanitary landfill located in Southern Ontario. A representative cross-section is selected for the analysis. Predicted chloride concentrations are presented for the cross section at various horizon years.

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