Energy Resolved Neutron Imaging for Strain Reconstruction Using the Finite Element Method

A novel pulsed neutron imaging technique based on the finite element method is used to reconstruct the residual strain within a polycrystalline material from Bragg edge strain images. This technique offers the possibility of a nondestructive analysis of strain fields with a high spatial resolution. The finite element approach used to reconstruct the strain uses the least square method constrained by the conditions of equilibrium. This inclusion of equilibrium makes the problem well-posed. The procedure is developed and verified by validating for a cantilevered beam problem. It is subsequently demonstrated by reconstructing the strain from experimental data for a ring-and-plug sample, measured at the spallation neutron source RADEN at J-PARC in Japan. The reconstruction is validated by comparison with conventional constant wavelength strain measurements on the KOWARI diffractometer at ANSTO in Australia. It is also shown that the addition of a Tikhonov regularisation scheme further improves the reconstruction.

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Increasing the Solution Accuracy in the Numerical Modeling of Boundary Value Problems Using Finite Element Method Based on Hankel Shape Functions

International Journal of Applied Mechanics ◽

10.1142/s1758825119500625 ◽

2019 ◽

Vol 11 (07) ◽

pp. 1950062

Author(s):

S. Farmani ◽

M. Ghaeini-Hessaroeyeh ◽

S. Hamzehei-Javaran

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Boundary Value Problems ◽

Numerical Solutions ◽

Boundary Value ◽

The Finite Element Method ◽

Shape Functions ◽

Element Approach ◽

Solution Accuracy ◽

Element Method

A new finite element approach is developed here for the modeling of boundary value problems. In the present model, the finite element method (FEM) is reformulated by new shape functions called spherical Hankel shape functions. The mentioned functions are derived from the first and second kind of Bessel functions that have the properties of both of them. These features provide an improvement in the solution accuracy with number of elements which are equal or lower than the ones used by the classic FEM. The efficiency and accuracy of the suggested model in the potential problems are examined by several numerical examples. Then, the obtained results are compared with the analytical and numerical solutions. The comparisons indicate the high accuracy of the present method.

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Finite element approach to Bragg edge neutron strain tomography

ANZIAM Journal ◽

10.21914/anziamj.v60i0.14054 ◽

2020 ◽

Vol 60 ◽

Author(s):

Riya Aggarwal ◽

Mike Meylan ◽

Bishnu Lamichhane ◽

Chris Wensrich

Keyword(s):

Machine Learning ◽

Finite Element Method ◽

Finite Element ◽

Gaussian Processes ◽

Elastic Strain ◽

Neutron Imaging ◽

The Finite Element Method ◽

Neutron Transmission ◽

Ray Transform ◽

Element Method

A number of techniques and applications in neutron imaging that exploit wavelength resolved measurements have been developed recently. One such technique, known as energy resolved neutron imaging, receives ample attention because of its capability to not only visualise but to also quantify physical attributes with spatial resolution. The objective of this article is to develop a reconstruction algorithm for elastic strain tomography from Bragg edge neutron transmission strain images obtained from a pulsed neutron beam with high resolution. This technique has several advantages over those using monochromatic neutron beams from continuous sources; for example, finer wavelength resolution. In contrast to the conventional radon based computed tomography, wherein neutron transmission revolves around the inversion of the longitudinal ray transform that has uniqueness issues, the reconstruction in the proposed algorithm is based on the least squares approach, constrained by an equilibrium formulated through the finite element method. References B. Abbey, S. Y. Zhang, W. J. J. Vorster, and A. M. Korsunsky. Feasibility study of neutron strain tomography. Proc. Eng., 1\penalty 0 (1):185–188, 2009. doi:10.1016/j.proeng.2009.06.043. R. Aggarwal, M. H. Meylan, B. P. Lamichhane, and C. M. Wensrich. Energy resolved neutron imaging for strain reconstruction using the finite element method. J. Imag., 6(3):13, 2020. doi:10.3390/jimaging6030013. J. N. Hendriks, A. W. T. Gregg, C. M. Wensrich, A. S. Tremsin, T. Shinohara, M. Meylan, E. H. Kisi, V. Luzin, and O. Kirsten. Bragg-edge elastic strain tomography for in situ systems from energy-resolved neutron transmission imaging. Phys. Rev. Mat., 1:053802, 2017. doi:10.1103/PhysRevMaterials.1.053802. C. Jidling, J. Hendriks, N. Wahlstrom, A. Gregg, T. B. Schon, C. Wensrich, and A. Wills. Probabilistic modelling and reconstruction of strain. Nuc. Inst. Meth. Phys. Res. B, pages 141–155, 2018. doi:10.1016/j.nimb.2018.08.051. W. R. B. Lionheart and P. J. Withers. Diffraction tomography of strain. Inv. Prob., 31:045005, 2015. doi:10.1088/0266-5611/31/4/045005. C. E. Rasmussen and C. K. I. Williams. Gaussian processes for machine learning. MIT Press, 2006. URL https://mitpress.mit.edu/books/gaussian-processes-machine-learning. C. M. Wensrich, E. Kisi, V. Luzin, and O. Kirstein. Non-contact measurement of the stress within granular materials via neutron diffraction. AIP Conf. Proc., 1542:441–444, 2013. doi:10.1063/1.4811962. R. Woracek, J. Santisteban, A. Fedrigo, and M. Strobl. Diffraction in neutron imaging–-a review. Nuc. Inst. Meth. Phys. Res. A, 878:141–158, 2018. doi:10.1016/j.nima.2017.07.040.

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2D Meshless Solution of Elastoplastic with Damage Problem

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.504-506.413 ◽

2012 ◽

Vol 504-506 ◽

pp. 413-418 ◽

Cited By ~ 1

Author(s):

Zohra Sendi ◽

Carl Labergère ◽

Khemais Saanouni ◽

Hedi Belhadj Salah

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Computing Time ◽

Least Square ◽

Ductile Damage ◽

Isotropic Hardening ◽

The Finite Element Method ◽

Time Step ◽

Moving Least Square ◽

Element Method

The Finite Element Method (FEM) is today the most widely used in numerical simulation of forming processes, due essentially to the continuous improvement of the FEM over the years and the simplicity of its implementation. However, this method has some limitations such as the distortion of elements under large inelastic deformation and the influence of the mesh on the results in several applications. The simulation of metal forming process with large plastic strain is a classical example where the successive remeshing is often the proposed solution in this case. But the remeshing raises the problems of precision and computing time. In this context and in order to avoid the remeshing process, a Meshless method is experimented in the solving of an elastoplastic problem coupled to the isotropic ductile damage. An Element Free Galerkin (EFG) method based on Moving Least Square (MLS) concept is considered in this proposal. A two-dimensional Mechanical problem was studied and solved by a Dynamic-Explicit resolution scheme where the material behaviour is based on an isotropic hardening fully coupled to ductile damage model. In a first step a parametric study is conducted in order to find the most influent parameters on the accuracy of the results. The effect of the number of nodes, of support nodes, of quadrature points, the effect of the time-step and the support domain size are analysed and optimal values are found. In a second step, the meshless results are compared with those of the finite element method and some concluding remarks relative to the accuracy and the computing time are given.

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Simulation of tuning graphene plasmonic behaviors by ferroelectric domains for self-driven infrared photodetector applications

Nanoscale ◽

10.1039/c9nr06508c ◽

2019 ◽

Vol 11 (43) ◽

pp. 20868-20875 ◽

Cited By ~ 1

Author(s):

Junxiong Guo ◽

Yu Liu ◽

Yuan Lin ◽

Yu Tian ◽

Jinxing Zhang ◽

...

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Interfacial Effect ◽

Infrared Photodetector ◽

The Finite Element Method ◽

Ferroelectric Domains ◽

Element Method

We propose a graphene plasmonic infrared photodetector tuned by ferroelectric domains and investigate the interfacial effect using the finite element method.

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