CMES-Vol. 90, No. 5, 2013

Open Access

ARTICLE

A Three-Dimensional Constitutive Equation And Finite Element Method Implementation for Shape Memory Polymers
Guanghui Shi¹, Qingsheng Yang^1,2, Xiaoqiao He^3,4, Kim Meow Liew³
CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.5, pp. 339-358, 2013, DOI:10.3970/cmes.2013.090.339
Abstract In order to describe the thermomechanical deformation and shape memory effect of shape memory polymers (SMPs), a three-dimensional thermomechanical constitutive model that considers elastic, viscoelastic strain and thermal expansion is proposed for isotropic SMPs. A three-dimensional finite element procedure is developed by implementing the proposed constitutive model into the user material subroutine (UMAT) in ABAQUS program. Numerical examples are used to compare it with existing experimental data in a one dimensional case and to demonstrate the thermomechanical behavior of SMPs with 3D deformation. It is shown that the present constitutive theory and the finite element method can effectively simulate the… More >

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ARTICLE

Numerical solution of nonlinear fractional integral differential equations by using the second kind Chebyshev wavelets
Yiming Chen¹, Lu Sun¹, Xuan Li¹, Xiaohong Fu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.5, pp. 359-378, 2013, DOI:10.3970/cmes.2013.090.359
Abstract By using the differential operator matrix and the product operation matrix of the second kind Chebyshev wavelets, a class of nonlinear fractional integral-differential equations is transformed into nonlinear algebraic equations, which makes the solution process and calculation more simple. At the same time, the maximum absolute error is obtained through error analysis. It also can be used under the condition that no exact solution exists. Numerical examples verify the validity of the proposed method. More >

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ARTICLE

Fracture & Fatigue Analyses: SGBEM-FEM or XFEM? Part 2: 3D Solids
Leiting Dong^1,2, Satya N. Atluri^1,3
CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.5, pp. 379-413, 2013, DOI:10.3970/cmes.2013.090.379
Abstract The SGBEM-FEM alternating method is compared with the recently popularized XFEM, for analyzing mixed-mode fracture and fatigue growth of 3D nonplanar cracks in complex solid and structural geometries. A large set of 3D examples with different degrees of complexity is analyzed by the SGBEM-FEM alternating method, and the numerical results are compared with those obtained by XFEM available in the open literature. It is clearly shown that: (a) SGBEM-FEM alternating method gives extremely high accuracy for the stress intensity factors; but the XFEM gives rather poor computational results, even for the most simple 3D cracks; (b) while SGBEM-FEM alternating method… More >

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