The Effects of Dimension Ratio on the Micropolar Peridynamic Model

2010 ◽  
Author(s):  
Y. Ferhat ◽  
I. Ozkol
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Displacement Field ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Elastic Behavior ◽  
Displacement Fields ◽  
Peridynamic Theory ◽  
Peridynamic Model ◽  
Central Forces

The aim of this study is to investigate the capability of the micropolar peridynamic theory to analyze elastic behavior of plates with various length and width. Since the quantities such as stress and strain are related to displacement field, only the displacement fields of these structures are computed using the micropolar peridynamic model while Poisson’s ratios are kept constant. The results are compared both to the analytical solution of the classical elasticity theory and to the solution of displacement based finite element methods. The software package ANSYS is used for FEM results. To compute the displacement field, a programming code is developed using MATHEMATICA. In the peridynamic theory the constitutive model contains only central forces and can be applied only to the materials having 1/4 Poisson’s ratio. It is the biggest shortcoming of the peridynamic theory. To overcome strict Poisson’s ratio limitation of the peridynamic theory, the micropolar peridynamic theory is proposed. The micropolar peridynamic model allows peridynamic moments, in addition to peridynamic central forces, to interact with the particles inside the material horizon. The introduction of the moments to the theory allows us to deal with the materials having Poisson’s ratio different from 1/4. This modification can be seen as the generalization of the peridynamic theory. Furthermore, the micropolar peridynamic theory can be easily implemented using the finite element methods. This provides easy application of the boundary conditions to the physical model in hand. In this work, by applying the micropolar peridynamic theory, we observed that the displacement fields of the plates are strongly affected by dimensional ratio of the plates. However, it is naturally expected that the micropolar and classical theories should give the same results, at least to a certain extend. This strong dependability on the dimensions of the structure can be a significant shortcoming of the micropolar peridynamic theory.

scholarly journals A Hybrid Artificial Intelligence Model to Predict the Elastic Behavior of Sandstone Rocks

2019 ◽  
Vol 11 (19) ◽  
pp. 5283 ◽  
Author(s):  
Gowida ◽  
Moussa ◽  
Elkatatny ◽  
Ali
Keyword(s):  
Poisson’S Ratio ◽  
Accurate Determination ◽  
Oil And Gas Industry ◽  
Poisson's Ratio ◽  
Elastic Behavior ◽  
Percentage Error ◽  
Ann Model ◽  
Field Development ◽  
Well Completion

Rock mechanical properties play a key role in the optimization process of engineering practices in the oil and gas industry so that better field development decisions can be made. Estimation of these properties is central in well placement, drilling programs, and well completion design. The elastic behavior of rocks can be studied by determining two main parameters: Young’s modulus and Poisson’s ratio. Accurate determination of the Poisson’s ratio helps to estimate the in-situ horizontal stresses and in turn, avoid many critical problems which interrupt drilling operations, such as pipe sticking and wellbore instability issues. Accurate Poisson’s ratio values can be experimentally determined using retrieved core samples under simulated in-situ downhole conditions. However, this technique is time-consuming and economically ineffective, requiring the development of a more effective technique. This study has developed a new generalized model to estimate static Poisson’s ratio values of sandstone rocks using a supervised artificial neural network (ANN). The developed ANN model uses well log data such as bulk density and sonic log as the input parameters to target static Poisson’s ratio values as outputs. Subsequently, the developed ANN model was transformed into a more practical and easier to use white-box mode using an ANN-based empirical equation. Core data (692 data points) and their corresponding petrophysical data were used to train and test the ANN model. The self-adaptive differential evolution (SADE) algorithm was used to fine-tune the parameters of the ANN model to obtain the most accurate results in terms of the highest correlation coefficient (R) and the lowest mean absolute percentage error (MAPE). The results obtained from the optimized ANN model show an excellent agreement with the laboratory measured static Poisson’s ratio, confirming the high accuracy of the developed model. A comparison of the developed ANN-based empirical correlation with the previously developed approaches demonstrates the superiority of the developed correlation in predicting static Poisson’s ratio values with the highest R and the lowest MAPE. The developed correlation performs in a manner far superior to other approaches when validated against unseen field data. The developed ANN-based mathematical model can be used as a robust tool to estimate static Poisson’s ratio without the need to run the ANN model.

Finite element analysis of flexible functionally graded beams with variable Poisson’s ratio

2016 ◽  
Vol 33 (8) ◽  
pp. 2421-2447 ◽  
Author(s):  
João Paulo Pascon
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Poisson’S Ratio ◽  
Scientific Literature ◽  
Functionally Graded ◽  
Poisson's Ratio ◽  
Transverse Strain ◽  
Thickness Direction ◽  
Element Analysis ◽  
Content Type

Purpose The purpose of this paper is to deal with large deformation analysis of plane beams composed of functionally graded (FG) elastic material with a variable Poisson’s ratio. Design/methodology/approach The material is assumed to be linear elastic, with a Poisson’s ratio varying according to a power law along the thickness direction. The finite element used is a plane beam of any-order of approximation along the axis, and with four transverse enrichment schemes, which can describe constant, linear, quadratic and cubic variation of the strain along the thickness direction. Regarding the constitutive law, five materials are adopted: two homogeneous limiting cases, and three intermediate FG cases. The effect of both finite element kinematics and distribution of Poisson’s ratio on the mechanical response of a cantilever is investigated. Findings In accordance with the scientific literature, the second scheme, in which the transverse strain is linearly variable, is sufficient for homogeneous long (or thin) beams under bending. However, for FG short (or moderate thick) beams, the third scheme, in which the transverse strain variation is quadratic, is needed for a reliable strain or stress distribution. Originality/value In the scientific literature, there are several studies regarding nonlinear analysis of functionally graded materials (FGMs) via finite elements, analysis of FGMs with constant Poisson’s ratio, and geometrically linear problems with gradually variable Poisson’s ratio. However, very few deal with finite element analysis of flexible beams with gradually variable Poisson’s ratio. In the present study, a reliable formulation for such beams is presented.

scholarly journals Direct Determination of Dynamic Elastic Modulus and Poisson’s Ratio of Timoshenko Rods

Vibration ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 157-173 ◽  
Author(s):  
Guadalupe Leon ◽  
Hung-Liang Chen
Keyword(s):  
Exact Solution ◽  
Finite Element ◽  
Elastic Constants ◽  
Frequency Ratio ◽  
Poisson’S Ratio ◽  
Direct Determination ◽  
Poisson's Ratio ◽  
Torsional Mode ◽  
Bending Mode ◽  
Resonance Frequencies

In this paper, the exact solution of the Timoshenko circular beam vibration frequency equation under free-free boundary conditions was determined with an accurate shear shape factor. The exact solution was compared with a 3-D finite element calculation using the ABAQUS program, and the difference between the exact solution and the 3-D finite element method (FEM) was within 0.15% for both the transverse and torsional modes. Furthermore, relationships between the resonance frequencies and Poisson’s ratio were proposed that can directly determine the elastic constants. The frequency ratio between the 1st bending mode and the 1st torsional mode, or the frequency ratio between the 1st bending mode and the 2nd bending mode for any rod with a length-to-diameter ratio, L/D ≥ 2 can be directly estimated. The proposed equations were used to verify the elastic constants of a steel rod with less than 0.36% error percentage. The transverse and torsional frequencies of concrete, aluminum, and steel rods were tested. Results show that using the equations proposed in this study, the Young’s modulus and Poisson’s ratio of a rod can be determined from the measured frequency ratio quickly and efficiently.

Young's Modulus and Poisson's Ratio Estimation Based on PSO Constriction Factor Method Parameters Evaluation

2019 ◽  
Vol 9 (2) ◽  
pp. 33-46
Author(s):  
George Lucas Dias ◽  
Ricardo Rodrigues Magalhães ◽  
Danton Diego Ferreira ◽  
Bruno Henrique Groenner Barbosa
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Young’S Modulus ◽  
Cantilever Beam ◽  
Poisson’S Ratio ◽  
Inverse Analysis ◽  
Young's Modulus ◽  
Poisson's Ratio ◽  
Factor Method ◽  
Constriction Factor

The knowledge of materials' mechanical properties in design during product development phases is necessary to identify components and assembly problems. These are problems such as mechanical stresses and deformations which normally cause plastic deformation, early fatigue or even fracture. This article is aimed to use particle swarm optimization (PSO) and finite element inverse analysis to determine Young's Modulus and Poisson's ratio from a cantilever beam, manufactured in ASTM A36 steel, subjected to a load of 19.6 N applied to its free end. The cantilever beam was modeled and simulated using a commercial FEA software. Constriction Factor Method (PSO variation) was used and its parameters were analyzed in order to improve errors. PSO results indicated Young's Modulus and Poisson's ratio errors of around 1.9% and 0.4%, respectively, when compared to the original material properties. Improvement in the data convergence and a reduction in the number of PSO iterations was observed. This shows the potentiality of using PSO along with Finite Element Inverse Analysis for mechanical properties evaluation.

scholarly journals 4D Printing of NiTi Auxetic Structure with Improved Ballistic Performance

Micromachines ◽  
2020 ◽  
Vol 11 (8) ◽  
pp. 745
Author(s):  
Hany Hassanin ◽  
Alessandro Abena ◽  
Mahmoud Ahmed Elsayed ◽  
Khamis Essa
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Analytical Model ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
4D Printing ◽  
Auxetic Structures ◽  
Negative Poisson's Ratio ◽  
The Impact ◽  
Auxetic Structure

Auxetic structures have attracted attention in energy absorption applications owing to their improved shear modulus and enhanced resistance to indentation. On the other hand, four-dimensional (4D) printing is an emerging technology that is capable of 3D printing smart materials with additional functionality. This paper introduces the development of a NiTi negative-Poisson’s-ratio structure with superelasticity/shape memory capabilities for improved ballistic applications. An analytical model was initially used to optimize the geometrical parameters of a re-entrant auxetic structure. It was found that the re-entrant auxetic structure with a cell angle of −30° produced the highest Poisson’s ratio of −2.089. The 4D printing process using a powder bed fusion system was used to fabricate the optimized NiTi auxetic structure. The measured negative Poisson’s ratio of the fabricated auxetic structure was found in agreement with both the analytical model and the finite element simulation. A finite element model was developed to simulate the dynamic response of the optimized auxetic NiTi structure subjected to different projectile speeds. Three stages of the impact process describing the penetration of the top plate, auxetic structure, and bottom plate have been identified. The results show that the optimized auxetic structures affect the dynamic response of the projectile by getting denser toward the impact location. This helped to improve the energy absorbed per unit mass of the NiTi auxetic structure to about two times higher than that of the solid NiTi plate and five times higher than that of the solid conventional steel plate.

FINITE ELEMENT ANALYSIS OF MECHANICAL DEFORMATION OF CHONDROCYTE TO 2D SUBSTRATE AND 3D SCAFFOLD

2015 ◽  
Vol 15 (05) ◽  
pp. 1550077 ◽  
Author(s):  
JINJU CHEN ◽  
D. L. BADER ◽  
D. A. LEE ◽  
M. M. KNIGHT
Keyword(s):  
Mechanical Properties ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Poisson’S Ratio ◽  
Glass Plate ◽  
Mechanical Deformation ◽  
Poisson's Ratio ◽  
3D Scaffold ◽  
Element Analysis ◽  
Cell Functions

The mechanical properties of cells are important in regulation of many aspects of cell functions. The cell may respond differently to a 2D plate and a 3D scaffold. In this study, the finite element analysis (FEA) was adopted to investigate mechanical deformation of chondrocyte on a 2D glass plate and chondrocyte seeded in a 3D scaffold. The elastic properties of the cell differ in these two different compression tests. This is because that the cell sensed different environment (2D plate and 3D construct) which can alter its structure and mechanical properties. It reveals how the apparent Poisson's ratio of a cell changes with the applied strain depends on its mechanical environment (e.g., the elastic moduli and Poisson's ratios of the scaffold and extracellular matrix) which regulates cell mechanics. In addition, the elastic modulus of the nucleus also plays a significant role in the determination of the Poisson's ratio of the cell for the cells seeded scaffold. It also reveals the intrinsic Poisson's ratio of the cell cannot be obtained by extrapolating the measured apparent Poisson's ratio to zero strain, particularly when scaffold's Poisson's ratio is quite different from the cell.

Poisson's ratio of plywood measured by tension test

Holzforschung ◽  
2009 ◽  
Vol 63 (5) ◽  
Author(s):  
Hiroshi Yoshihara
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Poisson’S Ratio ◽  
Tension Test ◽  
Experimental Results ◽  
Poisson's Ratio ◽  
Element Analysis ◽  
Young’S Moduli ◽  
Tension Tests ◽  
Finite Element Calculations

Abstract In this research, Poisson's ratio of plywood as obtained by a tension test was examined by varying the width of the specimen. The tension tests were conducted on five-plywood of lauan (Shorea sp.) with various widths, and Young's moduli and Poisson's ratios of the specimens were measured. Finite element calculations were independently conducted. A comparison of the experimental results with those of finite element analysis revealed that Young's modulus could be obtained properly when the width of the plywood strip varied. In contrast, the width of the plywood strip should be large enough to determine Poisson's ratio properly.

scholarly journals Promising Bialkali Bismuthides Cs(Na, K)2Bi for High-Performance Nanoscale Electromechanical Devices: Prediction of Mechanical and Anisotropic Elastic Properties under Hydrostatic Tension and Compression and Tunable Auxetic Properties

Nanomaterials ◽  
2021 ◽  
Vol 11 (10) ◽  
pp. 2739
Author(s):  
Shahram Yalameha ◽  
Zahra Nourbakhsh ◽  
Ali Ramazani ◽  
Daryoosh Vashaee
Keyword(s):  
Elastic Properties ◽  
Poisson’S Ratio ◽  
High Performance ◽  
Hydrostatic Compression ◽  
Poisson's Ratio ◽  
Elastic Behavior ◽  
Hydrostatic Tension ◽  
Tension And Compression ◽  
Electromechanical Devices ◽  
Anisotropic Elastic

Using first-principles calculations, we predict highly stable cubic bialkali bismuthides Cs(Na, K)2Bi with several technologically important mechanical and anisotropic elastic properties. We investigate the mechanical and anisotropic elastic properties under hydrostatic tension and compression. At zero pressure, CsK2Bi is characterized by elastic anisotropy with maximum and minimum stiffness along the directions of [111] and [100], respectively. Unlike CsK2Bi, CsNa2Bi exhibits almost isotropic elastic behavior at zero pressure. We found that hydrostatic tension and compression change the isotropic and anisotropic mechanical responses of these compounds. Moreover, the auxetic nature of the CsK2Bi compound is tunable under pressure. This compound transforms into a material with a positive Poisson’s ratio under hydrostatic compression, while it holds a large negative Poisson’s ratio of about −0.45 along the [111] direction under hydrostatic tension. An auxetic nature is not observed in CsNa2Bi, and Poisson’s ratio shows completely isotropic behavior under hydrostatic compression. A directional elastic wave velocity analysis shows that hydrostatic pressure effectively changes the propagation pattern of the elastic waves of both compounds and switches the directions of propagation. Cohesive energy, phonon dispersion, and Born–Huang conditions show that these compounds are thermodynamically, mechanically, and dynamically stable, confirming the practical feasibility of their synthesis. The identified mechanisms for controlling the auxetic and anisotropic elastic behavior of these compounds offer a vital feature for designing and developing high-performance nanoscale electromechanical devices.

Analysis on the influence of Poisson’s ratio on brittle fracture by applying uni-bond dual-parameter peridynamic model

2019 ◽  
Vol 222 ◽  
pp. 106685 ◽  
Author(s):  
Xiaohua Huang ◽  
Shuang Li ◽  
Yanli Jin ◽  
Dong Yang ◽  
Guoshao Su ◽  
...  
Keyword(s):  
Brittle Fracture ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Peridynamic Model

Using multi-dimensional contact mechanics experiments to measure Poisson's ratio of porous low-k films

2003 ◽  
Vol 766 ◽  
Author(s):  
B. N. Lucas ◽  
J. C. Hay ◽  
W. C. Oliver
Keyword(s):  
Integrated Circuits ◽  
Contact Mechanics ◽  
Poisson’S Ratio ◽  
Mechanical Response ◽  
Contact Stiffness ◽  
Poisson's Ratio ◽  
Elastic Behavior ◽  
Structural Effects ◽  
Potential Influence ◽  
Low K

AbstractUsing a new multi-dimensional contact mechanics system, it was recently shown that the experimentally measured tangential to normal stiffness ratio of a contact can be described as a function of the bulk Poisson's ratio of the material as predicted by Mindlin [1-3]. This system has been utilized to measure the normal and tangential elastic contact stiffness of a series of porous low-k films, with increasing starting porogen content. These results indicate a transition from a material-controlled elastic behavior to a structure-controlled elastic behavior as the porosity of the film is increased. These structural effects and their potential influence on the mechanical response to forces imposed on integrated circuits are discussed. The experimental details and apparatus are introduced and described.

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