CMES-Vol. 6, No. 3, 2004

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Crack-Path Analysis for Brittle and Non-Brittle Cracks: A Cell Method Approach
E. Ferretti¹
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 227-244, 2004, DOI:10.3970/cmes.2004.006.227
Abstract Defining the crack path in brittle and non-brittle crack is not easy, due to several unknowns. If the direction of crack propagation can be computed by means of one of the existing criteria, it is not known whether this direction will remain constant during crack propagation. A crack initiation leads to an enhanced stress field at crack tip. During propagation, the enhanced tip stress field propagates into the solid, locally interacting with the pre-existing stress field. This interaction can lead to modifications of the propagation direction, depending on the domain and crack geometry. Moreover, trajectory… More >

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Nucleation and Propagation of Deformation Twin in Polysynthetically Twinned TiAl
L. G. Zhou¹, L. M. Hsiung², Hanchen Huang¹
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 245-252, 2004, DOI:10.3970/cmes.2004.006.245
Abstract Using molecular dynamics simulations, we study the deformation of polysynthetically twinned (PST) TiAl at room temperature. The simulation cell is pre-strained and thermodynamically relaxed to zero stress, so that no dislocations pre-exist in γ−α₂ interfaces. A uniaxial compression is then applied along one 1/6<112] direction. Our results show that interfacial dislocation pairs nucleate at the γ−α₂ interface under the compression. The glide and agglomeration of these dislocations lead to the nucleation of deformation twins from the interface. Based on our studies, twins may nucleate without pre-existing interfacial dislocations. Further we have monitored the propagation of the More >

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A Meshless Method for the Laplace and Biharmonic Equations Subjected to Noisy Boundary Data
B. Jin^1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 253-262, 2004, DOI:10.3970/cmes.2004.006.253
Abstract In this paper, we propose a new numerical scheme for the solution of the Laplace and biharmonic equations subjected to noisy boundary data. The equations are discretized by the method of fundamental solutions. Since the resulting matrix equation is highly ill-conditioned, a regularized solution is obtained using the truncated singular value decomposition, with the regularization parameter given by the L-curve method. Numerical experiments show that the method is stable with respect to the noise in the data, highly accurate and computationally very efficient. More >

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Asymptotic Postbuckling Analysis of Composite and Sandwich Structures via the Assumed Strain Solid Shell Element Formulation
Jihan Kim¹, Yong Hyup Kim¹, Sung Won Lee²
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 263-276, 2004, DOI:10.3970/cmes.2004.006.263
Abstract The Koiter's asymptotic method is combined with the assumed strain solid shell element formulation for postbuckling analysis of composite and sandwich structures. The assumed strain solid shell element is free of locking and the small angle assumption, and it allows multiple plies through the element thickness. While laminated composite structures are modeled with single element through the thickness, sandwich structures are modeled with three elements stacked through the thickness to model the face sheets and the core independently. The Koiter's method is used to trace initial postbuckling path. Subsequently, the Koiter's method is switched to More >

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Lie Group Symmetry Applied to the Computation of Convex Plasticity Constitutive Equation
C.-S. Liu^1,2, C.-W. Chang¹
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 277-294, 2004, DOI:10.3970/cmes.2004.006.277
Abstract This paper delivers several new types of representations of the convex plasticity equation and realizes them by numerical discretizations. In terms of the Gaussian unit vector and the Weingarten map techniques in differential geometry, we prove that the plastic equation exhibits a Lie group symmetry. We convert the nonlinear constitutive equations to a quasilinear equations system X = AX, X ∈ Mⁿ⁺¹, A ∈ so(n,1) in local. In this way the inherent symmetry of the constitutive model of convex plasticity is brought out. The underlying structure is found to be a cone in the Minkowski space Mⁿ⁺¹ More >

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Calculation of J-Integral and Stress Intensity Factors using the Material Point Method
Y. Guo¹, J. A. Nairn¹
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 295-308, 2004, DOI:10.3970/cmes.2004.006.295
Abstract The Material Point Method (MPM), which is a particle-based, meshless method that discretizes material bodies into a collection of material points (the particles), is a new method for numerical analysis of dynamic solid mechanics problems. Recently, MPM has been generalized to include dynamic stress analysis of structures with explicit cracks. This paper considers evaluation of crack-tip parameters, such as J-integral and stress intensity factors, from MPM calculations involving explicit cracks. Examples for both static and dynamic problems for pure modes I and II or mixed mode loading show that MPM works well for calculation of fracture More >

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Meshless Local Petrov-Galerkin Method for Heat Conduction Problem in an Anisotropic Medium
J. Sladek¹, V. Sladek¹, S.N. Atluri²
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 309-318, 2004, DOI:10.3970/cmes.2004.006.309
Abstract Meshless methods based on the local Petrov-Galerkin approach are proposed for solution of steady and transient heat conduction problem in a continuously nonhomogeneous anisotropic medium. Fundamental solution of the governing partial differential equations and the Heaviside step function are used as the test functions in the local weak form. It is leading to derive local boundary integral equations which are given in the Laplace transform domain. The analyzed domain is covered by small subdomains with a simple geometry. To eliminate the number of unknowns on artificial boundaries of subdomains the modified fundamental solution and/or the More >

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