Chein-Shan Liu¹

CMC-Computers, Materials & Continua, Vol.10, No.1, pp. 97-116, 2009, DOI:10.3970/cmc.2009.010.097

Abstract A new numerical method is proposed for solving the delay ordinary differential equations (DODEs) under multiple time-varying delays or state-dependent delays. The finite difference scheme is used to approximate the ODEs, which together with the initial conditions constitute a system of nonlinear algebraic equations (NAEs). Then, a Fictitious Time Integration Method (FTIM) is used to solve these NAEs. Numerical examples confirm that the present approach is highly accurate and efficient with a fast convergence. More >

CMC-Computers, Materials & Continua, Vol.10, No.1, pp. 65-96, 2009, DOI:10.3970/cmc.2009.010.065

Abstract This work proposed an alternative formulation for the prediction of martensite start temperature (Ms) of Fe-Mn-Si shape memory alloys (SMAs) depending on the various compositions and heat treatment techniques by using Neural Network (NN) and genetic programming (GP) soft computing techniques. The training and testing patterns of the proposed NN and GP formulations are based on well established experimental results from the literature. The NN and GP based formulation results are compared with experimental results and found to be quite reliable with a very high correlation (R2=0.955 for GEP and 0.999 for NN). More >

J. Ghanbari¹, R. Naghdabadi^1,2

CMC-Computers, Materials & Continua, Vol.10, No.1, pp. 41-64, 2009, DOI:10.3970/cmc.2009.010.041

Abstract Continuum-based modeling of nanostructures is an efficient and suitable method to study the behavior of these structures when the deformation can be considered homogeneous. This paper is concerned about multiscale nonlinear tensorial constitutive modeling of carbon nanostructures based on the interatomic potentials. The proposed constitutive model is a tensorial equation relating the second Piola-Kirchhoff stress tensor to Green-Lagrange strain tensor. For carbon nanotubes, some modifications are made on the planar representative volume element (RVE) to account for the curved atomic structure resulting a non-planar RVE. Using the proposed constitutive model, the elastic behavior of the graphene sheet and carbon nanotube… More >

E.J. Sapountzakis¹, V.G. Mokos²

CMC-Computers, Materials & Continua, Vol.10, No.1, pp. 1-40, 2009, DOI:10.3970/cmc.2009.010.001

Abstract In this paper the boundary element method is employed to develop a displacement solution for the general transverse shear loading problem of composite beams of arbitrary constant cross section. The composite beam (thin or thick walled) consists of materials in contact, each of which can surround a finite number of inclusions. The materials have different elasticity and shear moduli and are firmly bonded together. The analysis of the beam is accomplished with respect to a coordinate system that has its origin at the centroid of the cross section, while its axes are not necessarily the principal bending ones. The transverse… More >

S. Straface¹, S. Troisi, V. Gagliardi

CMC-Computers, Materials & Continua, Vol.3, No.3, pp. 155-166, 2006, DOI:10.3970/cmc.2006.003.155

Abstract The present work shows an alternative to the classical methods to solve the Richards' Equation (RE), used to model flow in unsaturated porous media. This alternative is named Cell Method (CM). The CM is based on a preliminary reformulation of the mathematical model in a partially discrete form, which preserves as much as possible the physical and geometrical content of the original problem, and is made possible by the existence and properties of a common mathematical structure of field theories. The goal is to maintain the focus, both in the modelling and discretization steps, on the physics of the problem.… 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 model materials which exhibit a… 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 surface tensile dead load exceeds… More >

B.B. Karki¹, D. Bhattarai¹, L. Stixrude²

CMC-Computers, Materials & Continua, Vol.3, No.3, pp. 107-118, 2006, DOI:10.3970/cmc.2006.003.107

Abstract Computer modeling of liquid phase poses tremendous challenge: It requires a relatively large simulation size, long simulation time and accurate interatomic interaction and as such, it produces massive amounts of data. Recent advances in hardware and software have made it possible to accurately simulate the liquid phase. This paper reports the details of methodology used in the context of liquid simulations and subsequent analysis of the output data. For illustration purpose, we consider the results for the liquid phases of two geophysically relevant materials, namely MgO and MgSiO₃. The simulations are performed using the parallel first-principles molecular dynamics (FPMD) technique… 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 applications in the Diffpack environment. More >