CMES-Vol. 56, No. 1, 2010

Open Access

ARTICLE

Size Effects and Mesh Independence in Dynamic Fracture Analysis of Brittle Materials
Letícia Fleck Fadel Miguel¹, Ignacio Iturrioz², Jorge Daniel Riera³
CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.1, pp. 1-16, 2010, DOI:10.3970/cmes.2010.056.001
Abstract Numerical predictions of the failure load of large structures, accounting for size effects, require the adoption of appropriate constitutive relations. These relations depend on the size of the elements and on the correlation lengths of the random fields that describe material properties. The authors proposed earlier expressions for the tensile stress-strain relation of concrete, whose parameters are related to standard properties of the material, such as Young's modulus or specific fracture energy and to size. Simulations conducted for a typical concrete showed that as size increases, the effective stress-strain diagram becomes increasingly linear, with a sudden rupture, while at the… More >

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A High-Order Time and Space Formulation of the Unsplit Perfectly Matched Layer for the Seismic Wave Equation Using Auxiliary Differential Equations (ADE-PML)
R. Martin¹, D. Komatitsch^1,2, S. D. Gedney³, E. Bruthiaux^1,4
CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.1, pp. 17-42, 2010, DOI:10.3970/cmes.2010.056.017
Abstract Unsplit convolutional perfectly matched layers (CPML) for the velocity and stress formulation of the seismic wave equation are classically computed based on a second-order finite-difference time scheme. However it is often of interest to increase the order of the time-stepping scheme in order to increase the accuracy of the algorithm. This is important for instance in the case of very long simulations. We study how to define and implement a new unsplit non-convolutional PML called the Auxiliary Differential Equation PML (ADE-PML), based on a high-order Runge-Kutta time-stepping scheme and optimized at grazing incidence. We demonstrate that when a second-order time-stepping… More >

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Dynamic Stress Intensity Factors of Mode I Crack Problem for Functionally Graded Layered Structures
Sheng-Hu Ding^1,2, Xing Li², Yue-Ting Zhou^2,3
CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.1, pp. 43-84, 2010, DOI:10.3970/cmes.2010.056.043
Abstract In this paper, the crack-tip fields in bonded functionally graded finite strips are studied. Different layers may have different nonhomogeneity properties in the structure. A bi-parameter exponential function was introduced to simulate the continuous variation of material properties. The problem was reduced as a system of Cauchy singular integral equations of the first kind by Laplace and Fourier integral transforms. Various internal cracks and edge crack and crack crossing the interface configurations are investigated, respectively. The asymptotic stress field near the tip of a crack crossing the interface is examined and it is shown that, unlike the corresponding stress field… More >

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The Lie-Group Shooting Method for Computing the Generalized Sturm-Liouville Problems
Chein-Shan Liu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.1, pp. 85-112, 2010, DOI:10.3970/cmes.2010.056.085
Abstract We propose a novel technique, transforming the generalized SturmLiouville problem: w'' + q(x,λ)w = 0, a₁(λ)w(0) + a₂(λ)w'(0) = 0, b₁(λ)w(1) + b₂(λ)w'(1) = 0 into a canonical one: y'' = f, y(0) = y(1) = c(λ). Then we can construct a very effective Lie-group shooting method (LGSM) to compute eigenvalues and eigenfunctions, since both the left-boundary conditions y(0) = c(λ) and y'(0) = A(λ) can be expressed explicitly in terms of the eigen-parameter λ. Hence, the eigenvalues and eigenfunctions can be easily calculated with better accuracy, by a finer adjusting of λ to match the right-boundary condition y(1) =… More >

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