Yongfeng Zhang¹, Hanchen Huang^1,2, Satya N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.3, pp. 215-226, 2008, DOI:10.3970/cmes.2008.035.215

Abstract Molecular dynamics simulations reveal the asymmetrical yield strength of twinned copper nanowires under tension and compression. The simulation results show that the strength of nanowires depends on loading conditions, morphologies, and twin spacing. Under tensile loading condition the Schmidt factor of the leading partial is larger than that under compression. Effectively, the yield strength under tension is smaller than that under compression. When the cross-section is circular in morphology, dislocation nucleation requires larger stress, and the asymmetry of yield strength depends on the nucleation stress. When the cross section is square in morphology, dislocation nucleation requires smaller stress, and the… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.3, pp. 161-180, 2006, DOI:10.3970/cmes.2006.012.161

Abstract Materials' internal spacetime may bear certain similarities with the external spacetime of special relativity theory. Previously, it is shown that material hardening and anisotropy may cause the internal spacetime curved. In this paper we announce the third mechanism of mixed-control to cause the curvedness of internal spacetime. To tackle the mixed-control problem for a Prager kinematic hardening material, we demonstrate two new formulations. By using two-integrating factors idea we can derive two Lie type systems in the product space of M^m+1⊗Mⁿ⁺¹. The Lie algebra is a direct sum of so(m,1)⊕so(n,1), and correspondingly the symmetry group is a direct product of… More >

Bhaskar Kumar¹, Sanjay Mittal^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.2, pp. 95-122, 2009, DOI:10.3970/cmes.2009.053.095

Abstract The steady flow past a circular cylinder is investigated. Symmetry conditions are imposed along the centerline of the flow field. The variation of the structure of the recirculation zone with the Reynolds number is studied. The effect of the location of lateral boundary on the flow is analyzed and compared with results from earlier studies. The eddy length varies linearly with Re. Three kinds of solutions, based on eddy structure, are found for different location of the lateral boundary. Global linear stability analysis has been carried out in a translating frame to determine the convective modes for flow past a… More >

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 on which the… More >

Yoshitaka Suetake¹, Masashi Iura², S. N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 329-336, 2003, DOI:10.3970/cmes.2003.004.329

Abstract The objective of this paper is to examine the symmetry of the tangent operator for nonlinear shell theories with the finite rotation field. As well known, it has been stated that since the rotation field carries the Lie group structure, not a vector space one, the tangent operator incorporating the rotation field does not become symmetric. In this paper, however, it is shown that by adopting a rotation vector as a variable, the symmetry can be achieved in the Lagrangean (material) description. First, we present a general concept for the problem. Next, we adopt the finitely deformed thick shell problem… More >

J. P. Agnantiaris¹, D. Polyzos^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 197-212, 2003, DOI:10.3970/cmes.2003.004.197

Abstract A Boundary Element Method (BEM), for the three-dimensional solution of both non-axisymmetric and axisymmetric coupled acoustic-elastic problems in the frequency domain, is presented. The present BEM makes use of the Burton and Miller integral equation for infinite acoustic spaces, while elastic structures are dealt with the standard boundary integral equation of elastodynamics. The axisymmetric formulation involves the use of the fast Fourier transform algorithm. Highly accurate numerical algorithms are used for the evaluation of singular integrals, while nearly singular integrals are treated, also with high accuracy, through the use of practical numerical techniques, for both the axisymmetric and non-axisymmetric cases.… More >

F. Mechighel^1,2, M. El Ganaoui¹, M. Kadja², B. Pateyron³, S. Dost⁴

FDMP-Fluid Dynamics & Materials Processing, Vol.5, No.4, pp. 313-330, 2009, DOI:10.3970/fdmp.2009.005.313

Abstract A numerical study has been carried out to investigate the three-dimen -sional buoyant flow in a parallelepiped box heated from below and partially from the two sidewalls (a configuration commonly used for solidification problems and crystal growth systems). Attention has been paid, in particular, to phenomena of symmetry breaking and transition to unsteady non-symmetric convection for a low Prandtl number fluid (Pr=0.01). The influence of an applied horizontal magnetic field on the stability properties of the flow has been also considered. Results obtained may be summarized as follows: In the absence of magnetic field and for relatively small values of… More >

Ran Wang¹, Xuegang Yuan^1,2, Hongwu Zhang¹, Jing Zhang³, Na Lv^2,*

CMC-Computers, Materials & Continua, Vol.55, No.2, pp. 345-357, 2018, DOI:10.3970/cmc.2018.00233

Abstract In this paper, a nonlinear wave equation with variable coefficients is studied, interestingly, this equation can be used to describe the travelling waves propagating along the circular rod composed of a general compressible hyperelastic material with variable cross-sections and variable material densities. With the aid of Lou’s direct method1, the nonlinear wave equation with variable coefficients is reduced and two sets of symmetry transformations and exact solutions of the nonlinear wave equation are obtained. The corresponding numerical examples of exact solutions are presented by using different coefficients. Particularly, while the variable coefficients are taken as some special constants, the nonlinear… More >

J. Naqui¹, F. Martín¹

CMC-Computers, Materials & Continua, Vol.39, No.3, pp. 267-288, 2014, DOI:10.3970/cmc.2014.039.267

Abstract Metamaterial resonators are electrically small resonant particles useful for the implementation of effective media metamaterials. In this paper, some applications of metamaterial resonators (such as the split ring resonator -SRR-, the complementary split ring resonator -CSRR-, the folded stepped impedance resonator -SIR-, and the electric LC resonator), that exploit the symmetry properties of transmission lines loaded with such symmetric particles, are reviewed. This covers differential (balanced) lines with common mode suppression, linear and angular displacement sensors (including alignment sensors), angular velocity sensors, and radiofrequency barcodes. Advantages and drawbacks as compared to existing implementations are also discussed. More >

S. Patala¹, C.A. Schuh¹

CMC-Computers, Materials & Continua, Vol.17, No.1, pp. 1-18, 2010, DOI:10.3970/cmc.2010.017.001

Abstract Recent advances in microstructural characterization have made it possible to measure grain boundaries and their networks in full crystallographic detail. Statistical studies of the complete boundary space using full crystallographic parameters (misorientations and boundary plane inclinations) are limited because the topology of the parameter space is not understood (especially for homophase grain boundaries). This paper addresses some of the complexities associated with the group space of grain boundaries, and resolves the topology of the complete boundary space for systems of two-dimensional crystals. Although the space of homophase boundaries is complicated by the existence of a `no-boundary' singularity, i.e., no boundary… More >