Jin Ma, Yang Liu, Hongbing Lu, Ranga Komanduri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.1, pp. 41-56, 2006, DOI:10.3970/cmes.2006.016.041

Abstract A multiscale simulation technique coupling three scales, namely, the molecular dynamics (MD) at the atomistic scale, the discrete dislocations at the meso scale and the generalized interpolation material point (GIMP) method at the continuum scale is presented. Discrete dislocations are first coupled with GIMP using the principle of superposition (van der Giessen and Needleman (1995)). A detection band seeded in the MD region is used to pass the dislocations to and from the MD simulations (Shilkrot, Miller and Curtin (2004)). A common domain decomposition scheme for each of the three scales was implemented for parallel More >

K. Yashiro¹, Y. Nakashima¹, Y. Tomita¹

CMES-Computer Modeling in Engineering & Sciences, Vol.11, No.2, pp. 73-80, 2006, DOI:10.3970/cmes.2006.011.073

Abstract A simple back force model is proposed for a dislocation cutting into γ' precipitate, taking the work formaking and recovering an anti-phase boundary (APB) into account. The first dislocation, or a leading partial of a superdislocation, is acted upon by a back force whose magnitude is equal to the APB energy. The second dislocation, or a trailing partial of a superdislocation, is attracted by the APB with a force of the same magnitude. The model is encoded in the 3D discrete dislocation dynamics (DDD) code and applied to the cutting behavior of dislocations at a… More >

D. Ballhause¹, M. König¹, B. Kröplin¹

CMC-Computers, Materials & Continua, Vol.4, No.1, pp. 21-30, 2006, DOI:10.3970/cmc.2006.004.021

Abstract The mechanical behaviour of woven fabrics is dominated by the kinematics of the constituents on the microscopic scale. Their macroscopic response usually shows non-linearities which are due to the mobility of the interlaced yarns. The major deformation mechanisms of fabrics, i.e. the crimp interchange in case of biaxial tension and the trellising motion of the yarns in case of shear, reflect the dependency of the macroscopic material behaviour on the microstructural deformation mechanisms.
We present a novel modelling approach for woven fabrics which is capable to represent directly and locally the microstructure and its kinematics… More >

E. Ferretti¹

CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.1, pp. 19-48, 2005, DOI:10.3970/cmes.2005.009.019

Abstract In this study nonlocality is discussed with regard to the differential and discrete formulations. Here, nonlocality is found to be a concept attaining not to the description of the material, but to the governing equations. This has made it possible to discuss the opportunity of introducing nonlocality in the constitutive equations, in order to give respectability to strain-softening damage models. When using the differential formulation, a length scale must be introduced into the material description of a strain-softening modeling, particularly when the size-effect is involved. In the opinion of the Author, this need lies in… More >

P. Castillo², J. Koning³, R. Rieben⁴, D. White⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.4, pp. 331-346, 2004, DOI:10.3970/cmes.2004.005.331

Abstract In this article, we present a computational framework for solving problems arising in electromagnetism. The framework is derived from a modern geometrical approach and is based on differential forms (or p-forms). These geometrical entities provide a natural framework for modeling of physical quantities such as electric potentials, electric and magnetic fields, electric and magnetic fluxes, etc. We have implemented an object oriented class library, called FEMSTER. The library is designed for high order finite element approximations. In addition, it can be expanded by including user-defined data types or by deriving new classes. Finally, the versatility More >

Jun Liu¹, Mauro Ferrari¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.3&4, pp. 421-430, 2003, DOI:10.3970/cmes.2003.004.421

Abstract A microstructure-accounting mechanical field theory approach is applied to the problem of reflection from a granular thin layer embedded between two solid substrates to study the direct relationship of the micro-structural parameters and the overall reflection coefficients of the thin layer. The exact solution for plane wave reflection coefficients is derived under the new theoretical framework giving quantitative relations between the macroscopic reflection coefficients and a set of micro structural/physical parameters including particle size and micromoduli. The model was analyzed using averaged material properties of biological tissue for the granular thin layer. It was demonstrated More >

N. Sukumar¹, J. E. Bolander¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 691-706, 2003, DOI:10.3970/cmes.2003.004.691

Abstract In this paper, we explore the numerical approximation of discrete differential operators on non-uniform grids. The Voronoi cell and the notion of natural neighbors are used to approximate the Laplacian and the gradient operator on irregular grids. The underlying weight measure used in the numerical computations is the {\em Laplace weight function}, which has been previously adopted in meshless Galerkin methods. We develop a difference approximation for the diffusion operator on irregular grids, and present numerical solutions for the Poisson equation. On regular grids, the discrete Laplacian is shown to reduce to the classical finite More >

Enzo TONTI¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 237-258, 2001, DOI:10.3970/cmes.2001.002.237

Abstract We present a new numerical method for the solution of field equations. The essence of the method is to directly provide a discrete formulation of field laws, without using and requiring a differential formulation. It is proved that, for linear interpolation, the stiffness matrix so obtained coincides with the one of the Finite Element Method. For quadratic interpolation, however, the present stiffness matrix differs from that of FEM; moreover it is unsymmetric. It is shown that by using a parabolic interpolation, a convergence of the fourth order is obtained. This is greater than the one More >