Z. D. Han¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 5-20, 2003, DOI:10.3970/cmes.2003.004.005

Abstract Using the directly derived non-hyper singular integral equations for displacement gradients [as in Okada, Rajiyah, and Atluri (1989a)], simple and straight-forward derivations of weakly singular traction BIE's for solids undergoing small deformations are presented. A large number of ``intrinsic properties'' of the fundamental solutions in elasticity are developed, and are used in rendering the tBIE and dBIE to be only weakly-singular, in a very simple manner. The solutions of the weakly singular tBIE and dBIE through either global Petrov-Galerkin type ``boundary element methods'', or, alternatively, through the meshless local Petrov-Galerkin (MLPG) methods, are discussed. As special cases, the Galerkin type… More >

Frédéric Gibou¹, Chohong Min², Hector D. Ceniceros³

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.1, pp. 37-48, 2007, DOI:10.3970/fdmp.2007.003.037

Abstract We describe two finite difference schemes for simulating incompressible flows on nonuniform meshes using quadtree/octree data structures. The first one uses a cell-centered Poisson solver that yields first-order accurate solutions, while producing symmetric linear systems. The second uses a node-based Poisson solver that produces second-order accurate solutions and second-order accurate gradients, while producing nonsymmetric linear systems as the basis for a second-order accurate Navier-Stokes solver. The grids considered can be non-graded, i.e. the difference of level between two adjacent cells can be arbitrary. In both cases semi-Lagrangian methods are used to update the intermediate fluid velocity in a standard projection… More >

Marcello Lappa¹

FDMP-Fluid Dynamics & Materials Processing, Vol.1, No.3, pp. 213-234, 2005, DOI:10.3970/fdmp.2005.001.213

Abstract The physical properties of many emulsions and metal alloys strongly depend on the multiphase morphology which is controlled to a great degree by particle-particle interaction during the related processing. In the present article significant effort is devoted to illustrate the philosophy of modeling for these phenomena and some insights into the physics. Within such a context working numerical techniques that have enjoyed a widespread use over recent years are presented and/or reviewed. Finally a focused and critical comparison of these possible approaches is reported illustrating advantages and disadvantages, strengths and weaknesses, past history and future directions. More >

Chih-Ping Wu^1,2, Kuan-Hao Chiu², Yung-Ming Wang²

CMC-Computers, Materials & Continua, Vol.8, No.2, pp. 93-132, 2008, DOI:10.3970/cmc.2008.008.093

Abstract The article is to present an overview of various three-dimensional (3D) analytical approaches for the analysis of multilayered and functionally graded (FG) piezoelectric plates and shells. The reported 3D approaches in the literature are classified as four different approaches, namely, Pagano's classical approach, the state space approach, the series expansion approach and the asymptotic approach. Both the mixed formulation and displacement-based formulation for the 3D analysis of multilayered piezoelectric plates are derived. The analytical process, based on the 3D formulations, for the aforementioned approaches is briefly interpreted. The present formulations of multilayered piezoelectric plates can also be used for the… More >

S. Smaoui¹, A. Ben Hamida¹, I. Djeran-Maigre², H. Dumontet¹

CMC-Computers, Materials & Continua, Vol.4, No.3, pp. 153-162, 2006, DOI:10.3970/cmc.2006.004.153

Abstract An iterative homogenization approach is proposed in order to predict the nonlinear hydro-mechanical behaviour of porous media. This process is coupled to classical and modified secant extended methods and linear homogenization predictive schemes. At convergence of the iterative process, same equivalent behaviour is obtained for any secant method, any simplified homogenization used for the linear comparison material and for any initial porosity of the media. An application to the study of the nonlinear behaviour of clayey sediments is presented. The model parameters quantification is based on oedometric experimental results for different clays. More >

H. T. Liu¹, Z. D. Han¹, A. M. Rajendran², S. N. Atluri³

CMC-Computers, Materials & Continua, Vol.4, No.1, pp. 43-54, 2006, DOI:10.3970/cmc.2006.004.043

Abstract The Rajendran-Grove (RG) ceramic damage model is a three-dimensional internal variable based constitutive model for ceramic materials, with the considerations of micro-crack extension and void collapse. In the present paper, the RG ceramic model is implemented into the newly developed computational framework based on the Meshless Local Petrov-Galerkin (MLPG) method, for solving high-speed impact and penetration problems. The ability of the RG model to describe the internal damage evolution and the effective material response is investigated. Several numerical examples are presented, including the rod-on-rod impact, plate-on-plate impact, and ballistic penetration. The computational results are compared with available experiments, as well… More >

Hamad F. Al-Harbi¹, Marko Knezevic^1,2, Surya R. Kalidindi^1,3

CMC-Computers, Materials & Continua, Vol.15, No.2, pp. 153-172, 2010, DOI:10.3970/cmc.2010.015.153

Abstract In recent work, we have demonstrated the viability and computational advantages of DFT-based spectral databases for facilitating crystal plasticity solutions in face-centered cubic (fcc) metals subjected to arbitrary deformation paths. In this paper, we extend and validate the application of these novel ideas to body-centered cubic (bcc) metals that exhibit a much larger number of potential slip systems. It was observed that the databases for the bcc metals with a larger number of slip systems were more compact compared to those obtained previously for fcc metals with a smaller number of slip systems. Furthermore, we demonstrate in this paper that… More >