L. Gornet¹, S. Marguet², G. Marckmann³

CMC-Computers, Materials & Continua, Vol.4, No.2, pp. 63-74, 2006, DOI:10.3970/cmc.2006.004.063

Abstract The purpose of the present study is to determine the components of the effective elasticity tensor and the failure properties of Nomex^® honeycomb cores. In order to carry out this study, the NidaCore software, a program dedicated to Nomex®Cores predictions, has been developed using the Finite Element tool Cast3M-CEA. This software is based on periodic homogenization techniques and on the modelling of structural instability phenomena. The homogenization of the periodic microstructure is realized thanks to a strain energy approach. It assumes the mechanical equivalence between the microstructures of a RVE and a similar homogeneous macroscopic volume.… More >

Łukasz Kaczmarczyk¹

CMC-Computers, Materials & Continua, Vol.4, No.2, pp. 55-62, 2006, DOI:10.3970/cmc.2006.004.055

Abstract In recent years the multiscale computational homogenisation has been extensively developed. Such micro-macro modelling does not require any constitutive assumptions at the macro-level. The multi-scale computational homogenisation has also been extended for the second order continuum at the macro level Kouznetsova V.G., Geers M.G.D., and Brekelmans V.A.M (2004). The second-order framework is based on incorporation of the gradient of macroscopic deformation in micro to macro multiscale transition. The introduction of the secondorder continuum at macro-scale takes into account the size effect and gives more accurate results in case of insufficient scale separation. The general framework 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 >

G. Q. Xie^1,2, S. Y. Long^1,3

CMC-Computers, Materials & Continua, Vol.4, No.1, pp. 11-20, 2006, DOI:10.3970/cmc.2006.004.011

Abstract The concept of the micropolar theory is employed to investigate vibration behaviors of carbon nanotubes. The constitutive relation has been deduced from the two-dimensional analysis of the microstructure of the carbon nanotube. Van der Waals interactions are simulated by a weak spring model. Hamilton's principle is employed to obtain dynamics equations of the multi-walled carbon nanotube. Numerical examples for both single-walled and double-walled carbon nanotubes are presented and the significant difference in vibration behaviors between them has been distinguished. Numerical results show that fundamental frequencies for the cantilever single-walled carbon nanotube decreases with increase of More >

D.L. Young^1,2, C.C. Tsai³, Y.C. Lin¹, C.S. Chen⁴

CMC-Computers, Materials & Continua, Vol.4, No.1, pp. 1-10, 2006, DOI:10.3970/cmc.2006.004.001

Abstract This paper describes the method of fundamental solutions (MFS) to solve eigenfrequencies of plate vibrations by utilizing the direct determinant search method. The complex-valued kernels are used in the MFS in order to avoid the spurious eigenvalues. The benchmark problems of a circular plate with clamped, simply supported and free boundary conditions are studied analytically as well as numerically using the discrete and continuous versions of the MFS schemes to demonstrate the major results of the present paper. Namely only true eigenvalues are contained and no spurious eigenvalues are included in the range of direct More >

T. Nishioka¹, S. Tchouikov¹, T. Fujimoto¹

CMC-Computers, Materials & Continua, Vol.3, No.3, pp. 147-154, 2006, DOI:10.3970/cmc.2006.003.147

Abstract In this study, phenomena of multiple branching of dynamically propagating crack are investigated numerically. The complicated paths of cracks propagating in a material are simulated by moving finite element method based on Delaunay automatic triangulation (MFEM BODAT), which was extended for such problems. For evaluation of fracture parameters for propagating and branching cracks switching method of the path independent dynamic J integral was used. Using these techniques the generation phase simulation of multiple dynamic crack branching was performed. Various dynamic fracture parameters, which are almost impossible to obtain by experimental technique alone, were accurately evaluated. More >

G. Haasemann¹, M. Kästner¹ and V. Ulbricht¹

CMC-Computers, Materials & Continua, Vol.3, No.3, pp. 131-146, 2006, DOI:10.3970/cmc.2006.003.131

Abstract Novel textile reinforced composites provide an extremely high adaptability and allow for the development of materials whose features can be adjusted precisely to certain applications. A successful structural and material design process requires an integrated simulation of the material behavior, the estimation of the effective properties which need to be assigned to the macroscopic model and the resulting features of the component. In this context two efficient modelling strategies - the Binary Model (Carter, Cox, and Fleck (1994)) and the Extended Finite Element Method (X-FEM) (Moës, Cloirec, Cartraud, and Remacle (2003)) - are used to… More >

X.G. Yuan¹, R.J. Zhang²

CMC-Computers, Materials & Continua, Vol.3, No.3, pp. 119-130, 2006, DOI:10.3970/cmc.2006.003.119

Abstract In this paper, the problem of cavity formation and motion in an incompressible transversely isotropic nonlinearly elastic solid sphere, which is subjected to a uniform radial tensile dead load on its surface, is examined in the context of nonlinear elastodynamics. The strain energy density associated with the nonlinearly elastic material may be viewed as the generalized forms of some known material models. It is proved that some determinate conditions must be imposed on the form of the strain energy density such that the surface tensile dead load has a finite critical value. Correspondingly, as the More >

Hamid Sharifi¹ and Augustin Gakwaya¹

CMC-Computers, Materials & Continua, Vol.3, No.2, pp. 77-96, 2006, DOI:10.3970/cmc.2006.003.077

Abstract In this paper, an object-oriented modeling of solid material constitutive behavior using the UML notation is presented. Material properties are first classified into large and small deformation kinematical models. In the small deformation package, we keep classes such as Elastic, ElastoPlastic, ViscoElastic and ViscoPlastic. In the large deformation package, we store classes such as ElastoPlastic, HyperElastic, HyperPlastic, HyperViscoElastic, HyperViscoPlastic and so on. The hierarchical structure, the association relationships as well as key attributes and methods of these classes are presented. We used a C++ implementation of the above model for developing HyperElastic, HyperElastoPlastic and Contact More >

P. B. Wang¹, Z. H. Yao^1,2, T. Lei¹

CMC-Computers, Materials & Continua, Vol.3, No.2, pp. 65-76, 2006, DOI:10.3970/cmc.2006.003.065

Abstract The fast multipole method (FMM) is applied to the dual boundary element method (DBEM) for the analysis of finite solids with large numbers of microcracks. The application of FMM significantly enhances the run-time and memory storage efficiency. Combining multipole expansions with local expansions, computational complexity and memory requirement are both reduced to O(N), where N is the number of DOFs (degrees of freedom). This numerical scheme is used to compute the effective in-plane bulk modulus of 2D solids with thousands of randomly distributed microcracks. The results prove that the IDD method, the differential method, and the More >