Analytical solution for Young's modulus of concrete with aggregate aspect ratio effect

2015 ◽  
Vol 67 (18) ◽  
pp. 963-971
Author(s):  
Jianjun Zheng ◽  
Xinzhu Zhou ◽  
Linzhu Sun
Keyword(s):  
Aspect Ratio ◽  
Analytical Solution ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Ratio Effect

scholarly journals Analytical Solution of a Circular Opening considering Nonuniform Pressure and Its Engineering Application

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Peng Wu ◽  
Yanlong Chen ◽  
Liang Chen ◽  
Xianbiao Mao ◽  
Wei Zhang
Keyword(s):  
Analytical Solution ◽  
Plastic Zone ◽  
Young’S Modulus ◽  
Lateral Pressure ◽  
Young's Modulus ◽  
Pressure Coefficient ◽  
Surrounding Rock ◽  
Engineering Practice ◽  
Circular Opening ◽  
Lateral Pressure Coefficient

Based on the Mohr–Coulomb criterion, a new analytical solution of a circular opening under nonuniform pressure was presented, which considered rock dilatancy effect and elastic-brittle-plastic failure characteristics. In the plastic zone, the attenuation of Young’s modulus was considered using a radius-dependent model (RDM), and solution of the radius and radial displacement of plastic zone was obtained. The results show that many factors have important impact on the response of the surrounding rock, including lateral pressure coefficient, dilation coefficient, buried depth, and Young’s modulus attenuation. Under nonuniform pressure condition, the distribution of plastic zone and deformation around the opening show obvious nonuniform characteristic: with the increasing of lateral pressure coefficient, the range of plastic zone and deformation decrease gradually at side, while they increase at roof and floor, and the location of the maximum value of support and surrounding rock response curve transfers from side to roof. Based on the analytical results and engineering practice, an optimization method of support design was proposed for the circular opening under nonuniform pressure.

Effects of cross-sessional area and aspect ratio coupled with orientation on mechanical properties and deformation behavior of Cu nanowires

2021 ◽  
Author(s):  
Hui Cao ◽  
Wenke Chen ◽  
Zhiyuan Rui ◽  
Changfeng Yan
Keyword(s):  
Mechanical Properties ◽  
Aspect Ratio ◽  
Yield Stress ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Cu Nanowires ◽  
The Cross

Abstract Metal nanomaterials exhibit excellent mechanical properties compared with corresponding bulk materials and have potential applications in various areas. Despite a number of studies of the size effect on Cu nanowires mechanical properties with square cross-sectional, investigations of them in rectangular cross-sectional with various sizes at constant volume are rare, and lack of multifactor coupling effect on mechanical properties and quantitative investigation. In this work, the dependence of mechanical properties and deformation mechanisms of Cu nanowires/nanoplates under tension on cross-sessional area, aspect ratio of cross-sectional coupled with orientation were investigated using molecular dynamics simulations and the semi-empirical expressions related to mechanical properties were proposed. The simulation results show that the Young’s modulus and the yield stress sharply increase with the aspect ratio except for the <110>{110}{001} Cu nanowires/nanoplates at the same cross-sectional area. And the Young’s modulus increases while the yield stress decreases with the cross-sectional area of Cu nanowires. However, both of them increase with the cross-sectional area of Cu nanoplates. Besides, the Young’s modulus increases with the cross-sectional area at all the orientations. The yield stress shows a mildly downward trend except for the <111> Cu nanowires with increased cross-sectional area. For the Cu nanowires with a small cross-sectional area, the surface force increases with the aspect ratio. In contrast, it decreases with the aspect ratio increase at a large cross-sectional area. At the cross-sectional area of 13.068 nm2, the surface force decreases with the aspect ratio of the <110> Cu nanowires while it increases at other orientations. The surface force is a linearly decreasing function of the cross-sectional area at different orientations. Quantitative studies show that Young’s modulus and yield stress to the aspect ratio of the Cu nanowires satisfy exponent relationship. In addition, the main deformation mechanism of Cu nanowires is the nucleation and propagation of partial dislocations while it is the twinning-dominated reorientation for Cu nanoplates.

Residual Stress in an Autofrettaged Tube Taking Bauschinger Effect as a Function of the Prior Plastic Strain

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Xiaoping Huang ◽  
Torgeir Moan
Keyword(s):  
Residual Stress ◽  
Stress Distribution ◽  
Analytical Solution ◽  
Plastic Strain ◽  
Young’S Modulus ◽  
Bauschinger Effect ◽  
Young's Modulus ◽  
Residual Stress Distribution ◽  
Present Solution ◽  
Stress Dependent

Autofrettage is a practical method for increasing the elastic carrying capacity and the fatigue life of thick-walled cylinders such as cannon and high-pressure tubular reactor. Many analytical and numerical solutions for determining the residual stress distribution in an autofrettaged tube have been reported. It is still difficult to model the Bauchinger effect, which is dependent on the prior plasticity in an analytical solution. The reduced Young’s modulus during unloading affects residual stress distribution. However, until now this effect has not been considered in any analytical model. In this paper, an autofrettage analytical solution considering Young’s modulus and the reverse yield stress dependent on the prior plasticity, based on the actual tensile-compressive curve of the material and the von Mises yield criterion, has been proposed. New model incorporates the Bauschinger effect factor and the unloading modulus variation as a function of prior plastic strain, and hence of the radius. Thereafter it assumes a fixed nonlinear unloading profile. The comparison of predicted residual stress distribution by the present solution with that of fixed unloading curve model, and test results shows that the present solution gives accurate prediction of residual stress distribution of an autofrettaged tube. This analytical procedure for the cylinder permits an excellent representation of various pressure vessel steels.

Analytical Solution and Experimental Study of Effective Young's Modulus of Selective Laser Melting-Fabricated Lattice Structure With Triangular Unit Cells

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Jie Niu ◽  
Hui Leng Choo ◽  
Wei Sun ◽  
Sui Him Mok
Keyword(s):  
Analytical Solution ◽  
Young’S Modulus ◽  
Selective Laser Melting ◽  
Triangular Lattice ◽  
Young's Modulus ◽  
Numerical Results ◽  
Lattice Structures ◽  
Shape Parameters ◽  
Laser Melting ◽  
Unit Cells

Research on materials, design, processing, and manufacturability of parts produced by additive manufacturing (AM) has been investigated significantly in the past. However, limited research on tensile behavior of cellular lattice structures by AM was carried out. In this paper, effective tensile Young's modulus, E*, of triangular lattice structures was determined. Firstly, analytical solution was derived based on Euler–Bernoulli beam theory. Then, numerical results of E* were obtained by finite element analysis (FEA) for triangular lattice structures classified by three shape parameters. The effects of side length, L, beam thickness, t, and height, h, on E* were investigated individually. FEA results revealed that there is a relationship between E* and the relative density and shape parameters. Among them, t has the most significant effect on E*. Numerical results were also compared with the results from modified general function for cellular structures and modified formula for triangular honeycomb. The E* predicted by the proposed analytical solution shows the best agreement with the numerical results. Finally, tensile tests were carried out using AlSi10 Mg triangular lattice structures manufactured by selective laser melting (SLM) process. The experimental results show that both analytical and numerical solutions are able to predict E* with good accuracy. In the future, the proposed solution can be used to design lightweight structures with triangular unit cells.

Predicting the Young’s modulus of intercalated and exfoliated polymer/clay nanocomposites

e-Polymers ◽  
2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Vadoud Molajavadi ◽  
Hamid Garmabi
Keyword(s):  
Aspect Ratio ◽  
Young’S Modulus ◽  
Surface Area ◽  
High Aspect Ratio ◽  
Young's Modulus ◽  
Clay Nanocomposites ◽  
High Modulus ◽  
Proposed Model ◽  
Theoretical Predictions ◽  
New Equation

AbstractThe Halpin-Tsai equations were used for the composites with low level content of reinforcements, which contain lamellar shape, high modulus and high aspect ratio. These characteristics of reinforcements were taken into consideration to simplify the Halpin-Tsai equations. The effect of different parameters on the longitudinal Young’s modulus of well aligned polymer/clay nanocomposites was investigated for both exfoliated and intercalated microstructures. It was shown that the applied simplification had negligible effect on the prediction of the Halpin-Tsai model. For the intercalated structures with a high number of platelets per stack (n), increase in the gallery spacing did not influence the predicted modulus values. In an intercalated structure, the surface area of a stack, as the interface of fillermatrix, is n times lower than that of the exfoliated state. By considering the effect of the degree of exfoliation in the proposed model, a new equation was developed to predict the modulus enhancement in the nanocomposites filled with Montmorillonite (MMT). The theoretical predictions were supported by the experimental results.

Comparison of the Models to Predict the Effective Young's Modulus of Hybrid Composites Reinforced with Multi-Shape Inclusions

2013 ◽  
Vol 290 ◽  
pp. 15-20
Author(s):  
Dong Mei Luo ◽  
Hong Yang ◽  
Qiu Yan Chen ◽  
Ying Long Zhou
Keyword(s):  
Aspect Ratio ◽  
Young’S Modulus ◽  
Hybrid Composites ◽  
Young's Modulus ◽  
Controlling Factors ◽  
Isotropic Matrix ◽  
Mechanical Models ◽  
Multi Phase

In this paper, two kinds of micro-mechanical models are utilized to predict the effective Young's modulus for hybrid composites including fiber-like, spherical and needle inclusions in an isotropic matrix. The two models of Multi-Phase Mori-Tanaka Model (MP model) and Multi-Step Mori-Tanaka Model (MS model) are proposed by the authors in a series of interrelated research. The results show that the shape and the Young’s modulus of inclusion, aspect ratio of fiber-like inclusion are the controlling factors to influence the Young's modulus, and MP model is more rational to predict the effective Young’s modulus of hybrid composites reinforced with multi-shape inclusions.

An Axisymmetric Boundary Integral Model for Assessing Elastic Cell Properties in the Micropipette Aspiration Contact Problem

2002 ◽  
Vol 124 (5) ◽  
pp. 586-595 ◽  
Author(s):  
Mansoor A. Haider ◽  
Farshid Guilak
Keyword(s):  
Aspect Ratio ◽  
Contact Problem ◽  
Young’S Modulus ◽  
Cell Response ◽  
Cell Model ◽  
Young's Modulus ◽  
Boundary Integral ◽  
Micropipette Aspiration ◽  
Spherical Cell ◽  
Curvature Parameter

The micropipette aspiration technique has been used extensively in recent years to measure the mechanical properties of living cells. In the present study, a boundary integral formulation with quadratic elements is used to predict the elastic equilibrium response in the micropipette aspiration contact problem for a three-dimensional incompressible spherical continuum cell model (Young’s modulus E). In contrast to the halfspace model [19], the spherical cell model accounts for nonlinearities in the cell response which result from a consideration of geometric factors including the finite cell dimension (radius R), curvature of the cell boundary, evolution of the cell-micropipette contact region and curvature of the edges of the micropipette (inner radius a, edge curvature radius ε). The efficiency of the boundary element method facilitates the quantification of cell response as a function of the scaled pressure p/E, for the range of parameters a/R=0.4-0.7,ε/a=0.02-0.08, in terms of two measures that can be quantified using video microscopy. These are the aspiration length, which measures projection of the cell into the micropipette, and a characteristic strain, which measures stretching along the symmetry axis. For both measures of cell response, the resistance to aspiration is found to decrease with increasing values of the aspect ratio a/R and curvature parameter ε/a, and the nonlinearities in the cell response are most pronounced in the earlier portion of the aspiration test. The aspiration length is found to exhibit less sensitivity to the aspect ratio a/R than to the curvature parameter ε/a, whereas the characteristic strain, which provides a more realistic measure of overall cell stiffness, exhibits sensitivity to the aspect ratio a/R. The resistance to aspiration in the spherical cell model is initially less than that of the half space model but eventually exceeds the halfspace prediction and the deviation between the two models increases as the parameter ε/a decreases. Adjustment factors for the Young’s modulus E, as predicted by the halfspace model, are presented and the deviation from the spherical cell model is found to be as large as 35%, when measured locally on the response curve. In practice, the deviation will be less than the maximum figure but its precise value will depend on the number of data points available in the experiment and the specific curve-fitting procedure. The spherical cell model allows for efficient and more realistic simulations of the micropipette aspiration contact problem and quantifies two observable measures of cell response that, using video microscopy, can facilitate the determination of Young’s modulus for various cell populations while, simultaneously, providing a means of evaluating the validity of continuum cell models. Furthermore, this numerical model may be readily extended to account for more complex geometries, inhomogeneities in cellular properties, or more complex constitutive descriptions of the cell.

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