A Monte Carlo Finite Element Method for Determining the Young’s Modulus of Polymer Nanocomposites Using Nanoindentation Data

2007 ◽  
Author(s):  
A. Kontsos ◽  
P. D. Spanos
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Monte Carlo ◽  
Young’S Modulus ◽  
Polymer Nanocomposites ◽  
Young's Modulus ◽  
Statistical Processing ◽  
Spectral Representation Method ◽  
Representation Method ◽  
Element Method

This article presents a Monte Carlo finite element method (MCFEM) for determining the Young’s modulus (YM) of polymer nanocomposites (PNC) using Nanoindentation (NI) data. The method treats actual NI data as measurements of the local YM of PNC; it further assesses the effect of the nonhomogeneous dispersion of carbon nanotubes in polymers on the statistical variations observed in experimental NI data. First the method simulates numerically NI data by developing a random field and a multiscale homogenization model. Subsequently, the MCFEM applies the spectral representation method to generate a population of samples of local YM values. These local values are then used in conjunction with a stochastic finite element scheme to derive estimates for the YM of PNC. The statistical processing of the ensemble of FE solutions yields overall YM values that agree well with corresponding results reported in the literature.

Apparent Young's modulus of human radius using inverse finite element method

2006 ◽  
Vol 39 ◽  
pp. S19
Author(s):  
M.R. Bosisio ◽  
M. Talmant ◽  
W. Skalli ◽  
P. Laugier ◽  
D. Mitton
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Inverse Finite Element Method ◽  
Element Method

scholarly journals A Stochastic Galerkin Cell-based Smoothed Finite Element Method (SGCS–FEM)

2019 ◽  
Vol 17 (08) ◽  
pp. 1950054
Author(s):  
Tittu Varghese Mathew ◽  
Lars Beex ◽  
Stéphane PA Bordas ◽  
Sundararajan Natarajan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Numerical Study ◽  
Mesh Size ◽  
Statistical Characteristics ◽  
Smoothed Finite Element Method ◽  
Element Method

In this paper, the cell-based smoothed finite element method is extended to solve stochastic partial differential equations with uncertain input parameters. The spatial field of Young’s Modulus and the corresponding stochastic results are represented by Karhunen-Loéve expansion and polynomial chaos expansion, respectively. Young’s Modulus of structure is considered to be random for stochastic static as well as free vibration problems. Mathematical expressions and the solution procedure are articulated in detail to evaluate the statistical characteristics of responses in terms of the static displacements and the free vibration frequencies. The feasibility and the effectiveness of the proposed SGCS–FEM method in terms of accuracy and lower demand on the mesh size in the solution domain over that of conventional FEM for stochastic problems are demonstrated by carefully chosen numerical examples. From the numerical study, it is inferred that the proposed framework yields accurate results.

scholarly journals Modelling of Nanoindentation of TiAlN and TiN Thin Film Coatings for Automotive Bearing

2019 ◽  
Vol 8 (3) ◽  
pp. 7194-7199
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Yield Strength ◽  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Poisson's Ratio ◽  
The Finite Element Method ◽  
Element Method

Bearings are critical components for the transmission of motion in machines. Automotive components, especially bearings, will wear out over a certain period of time because they are constantly subjected to high levels of stress and friction. Studies have proven that coatings can extend the lifespan of bearings. Hence, it is necessary to conduct studies on coatings for bearings, particularly the mechanical and wear properties of the coating material. This detailed study focused on the mechanical properties of single-coatings of TiN and TiAIN using the finite element method (FEM). The mechanical properties that can be obtained from nano-indentation experiments are confined to just the Young’s modulus and hardness. Therefore, nanoindentation simulations were conducted together with the finite element method to obtain more comprehensive mechanical properties such as the yield strength and Poisson’s ratio. In addition, various coating materials could be examined by means of these nanoindentation simulations, as well the effects of those parameters that could not be controlled experimentally, such as the geometry of the indenter and the bonding between the coating and the substrate. The simulations were carried out using the ANSYS Mechanical APDL software. The mechanical properties such as the Young’s modulus, yield strength, Poisson’s ratio and tangent modulus were 370 GPa, 19 GPa, 0.21 and 10 GPa, respectively for the TiAlN coating and 460 GPa, 14 GPa, 0.25 and 8 GPa, respectively for the TiN coating. The difference between the mechanical properties obtained from the simulations and experiments was less than 5 %.

scholarly journals Predicting the mechanical properties of lightweight aggregate concrete using finite element method

2020 ◽  
Vol 13 (4) ◽  
Author(s):  
Aldemon Lage Bonifácio ◽  
Julia Castro Mendes ◽  
Michèle Cristina Resende Farage ◽  
Flávio de Souza Barbosa ◽  
Anne-Lise Beaucour
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Compressive Strength ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Lightweight Aggregate ◽  
Numerical Results ◽  
Lightweight Aggregate Concrete ◽  
Percentage Error ◽  
Element Method

Abstract The compressive strength (fc) and Young’s modulus (Ec) of concretes are properties of great importance in civil engineering problems. To this day, despite the relevance of the subject, concretes are still designed based on charts and empirical formulae. This scenario is even more imprecise for lightweight aggregate concretes (LWAC), which contain less design methodologies and case studies available in the literature. In this sense, the present work presents a numerical simulation for predicting the properties of LWAC’s specimens using the Finite Element Method. The material was considered as biphasic, comprising lightweight aggregates and the enveloping mortar. Each phase was modelled with its own compressive strength, tensile strength and Young’s modulus. The achieved numerical results for fc and Ec were compared with their experimental counterparts, obtained from the literature. In total, 48 concrete formulations were assessed. Numerical results showed fair agreement with the experimental data. In general, the Mean Absolute Percentage Error (MAPE) was lower for the shale aggregates for both Young's modulus (1.75% versus 4.21% of expanded clay) and compressive strength (4.19% versus 9.89% of expanded clay). No clear trend of error was identified in relation to the aggregate proportion or to the mortar types, in which the MAPE varied from 2.36% to 8.13%. In conclusion, the simplification to spherical aggregates has shown satisfactory results, as has the adoption of a 2D model, which require less computational resources. Results encourage further applications with more complex geometrical aspects to improve the mix design and safety of LWAC.

scholarly journals Simulation of Implants and Fixators using Finite Element Method

2020 ◽  
Vol 8 (5) ◽  
pp. 2900-2904
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Titanium Implants ◽  
Human Bone ◽  
Element Analysis ◽  
Element Method

Finte Element Analysis (FEA) of implants and fixators were carried out in this paper. Various implants and fixators were carried these fixators were used for various fractures occurring in the human bone. The implants and fixators were modeled and analysed using FEA software called ANYSWorkBench. These results were analysed, it is found titanium implants are more suitable for implants and fixators due to its rigidity and strength and young’s modulus very near tom the young’s modulus of the bone.

scholarly journals The numerical calculations of influence of underpinning on foundations settlement

2013 ◽  
Vol 35 (4) ◽  
pp. 47-64 ◽  
Author(s):  
Krzysztof Górski ◽  
Rajmund Leszek Ignatowicz ◽  
Jędrzej Wierzbicki ◽  
Robert Mazur ◽  
Jakub Mazurkiewicz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Numerical Calculations ◽  
Technological Parameters ◽  
Jet Grouting ◽  
Element Method

Abstract The paper presents numerical calculations of the influence of implementation technology for underpinning the footing on settlement, with the use of finite element method. Three cases of underpinning methods were taken for calculations, depending on the diameter of the jet grouting column and the order of works. The intensity of settlement of the base of the footing foundation is significantly influenced by the growth of Young’s modulus and the jet grouting column with time, until its complete curing and reaching final technological parameters.

scholarly journals The Elastic Property of Bulk Silicon Nanomaterials through an Atomic Simulation Method

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Jixiao Tao ◽  
Yuzhou Sun
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Property ◽  
Young’S Modulus ◽  
Silicon Nanowires ◽  
Young's Modulus ◽  
Poisson Ratio ◽  
Bulk Silicon ◽  
Atomic Simulation ◽  
Element Method

This paper reports a systematic study on the elastic property of bulk silicon nanomaterials using the atomic finite element method. The Tersoff-Brenner potential is used to describe the interaction between silicon atoms, and the atomic finite element method is constructed in a computational scheme similar to the continuum finite element method. Young’s modulus and Poisson ratio are calculated for[100],[110], and[111] silicon nanowires that are treated as three-dimensional structures. It is found that the nanowire possesses the lowest Young’s modulus along the[100] direction, while the[110] nanowire has the highest value with the same radius. The bending deformation of[100] silicon nanowire is also modeled, and the bending stiffness is calculated.

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