CMES-Vol. 97, No. 1, 2014

Open Access

ARTICLE

Eshelby Stress Tensor T: a Variety of Conservation Laws for T in Finite Deformation Anisotropic Hyperelastic Solid & Defect Mechanics, and the MLPG-Eshelby Method in Computational Finite Deformation Solid Mechanics-Part I
Z. D. Han¹, S. N. Atluri^2,3
CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.1, pp. 1-34, 2014, DOI:10.3970/cmes.2014.097.001
Abstract The concept of a stress tensor [for instance, the Cauchy stress σ, Cauchy (1789-1857); the first Piola-Kirchhoff stress P, Piola (1794-1850), and Kirchhoff (1824-1889); and the second Piola-Kirchhoff stress, S] plays a central role in Newtonian continuum mechanics, through a physical approach based on the conservation laws for linear and angular momenta. The pioneering work of Noether (1882-1935), and the extraordinarily seminal work of Eshelby (1916- 1981), lead to the concept of an “energy-momentum tensor” [Eshelby (1951)]. An alternate form of the “energy-momentum tensor” was also given by Eshelby (1975) by taking the two-point deformation gradient tensor as an independent… More >

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How to Select the Value of the Convergence Parameter in the Adomian Decomposition Method
Lei Lu^1,2, Jun-Sheng Duan^2,3
CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.1, pp. 35-52, 2014, DOI:10.3970/cmes.2014.097.035
Abstract In this paper, we investigate the problem of selecting of the convergence parameter c in the Adomian decomposition method. Through the curves of the n-term approximations Φ_n(t;c) versus c for different specified values of n and t, we demonstrate how to determine the value of c such that the decomposition series has a larger effective region of convergence. More >

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Axisymmetric and 3-D Numerical Simulations of the Effects of a Static Magnetic Field on Dissolution of Silicon into Germanium
F. Mechighel^1,2,3, N. Armour⁴, S. Dost⁴, M. Kadja³
CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.1, pp. 53-80, 2014, DOI:10.3970/cmes.2014.097.053
Abstract Numerical simulations were carried out to explain the behavior exhibited in experimental work on the dissolution process of silicon into a germanium melt. The experimental work utilized a material configuration similar to that used in the Liquid Phase Diffusion (LPD) and Melt-Replenishment Czochralski (Cz) growth systems. The experimental dissolution system was modeled by considering axisymmetric and three-dimensional (3-D) domains. In both cases, the governing equations, namely conservation of mass, momentum balance, energy balance, and solute transport balance, were solved using the Finite Element Method.
Measured concentration profiles and dissolution heights from the experiment samples showed that the application of a… More >

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Numerical Solution for the Variable Order Time Fractional Diffusion Equation with Bernstein Polynomials
Yiming Chen¹, Liqing Liu¹, Xuan Li¹ and Yannan Sun¹
CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.1, pp. 81-100, 2014, DOI:10.3970/cmes.2014.097.081
Abstract In this paper, Bernstein polynomials method is proposed for the numerical solution of a class of variable order time fractional diffusion equation. Coimbra variable order fractional operator is adopted, as it is the most appropriate and desirable definition for physical modeling. The Coimbra variable order fractional operator can also be regarded as a Caputo-type definition. The main characteristic behind this approach in this paper is that we derive two kinds of operational matrixes of Bernstein polynomials. With the operational matrixes, the equation is transformed into the products of several dependent matrixes which can also be viewed as the system of… More >

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