Youping Chen¹, James D Lee², Azim Esk,arian¹

CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.1, pp. 35-44, 2004, DOI:10.3970/cmes.2004.005.035

Abstract This paper addresses the need of theories and simulations for material body of mesoscopic and microscopic sizes. An overview of polar theories is presented. The micropolar theory proposed by Eringen is introduced and compared with other polar theories. Constitutive equations of micropolar thermo-visco-elastic solid are derived. Finite element analyses have been performed for a few sample problems with wide range of length scales. Based on the discussion, comparison and computer simulations, the unique feature and applicability of micropolar theory are demonstrated. More >

H.J. Bohm¨ ¹, W. Han^1,2, A. Eckschlager^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.1, pp. 5-20, 2004, DOI:10.3970/cmes.2004.005.005

Abstract Three-dimensional periodic micromechanical models are used for studying the mechanical behavior of discontinuously reinforced ductile matrix composites. The models are based on unit cells that contain a number of randomly positioned and, where applicable, randomly oriented spherical, spheroidal or cylindrical reinforcements. The Finite Element method is used to resolve the microscale stress and strain fields and to predict the homogenized responses under overall uniaxial tensile loading in the elastic and elastoplastic regimes. Periodicity boundary conditions are employed in the analyses.\\ The main emphasis of the contribution is put on studying the microscale stresses in the reinforcements, which are evaluated in… More >

R. Allena^*,†

Molecular & Cellular Biomechanics, Vol.11, No.3, pp. 185-208, 2014, DOI:10.3970/mcb.2014.011.185

Abstract Confined migration is a crucial phenomenon during embryogenesis, immune response and cancer. Here, a two-dimensional finite element model of a HeLa cell migrating across constricted–curved micro-channels is proposed. The cell is modelled as a continuum with embedded cytoplasm and nucleus, which are described by standard Maxwell viscoelastic models. The decomposition of the deformation gradient is employed to define the cyclic active strains of protrusion and contraction, which are synchronized with the adhesion forces between the cell and the substrate. The micro-channels are represented by two rigid walls and exert an additional viscous force on the cell boundaries. Five configurations have… More >

Wei Huang^∗,†, Qinlian Zhou^†,‡, Jian Gao^‡, R. T. Yen^‡,§,¶

Molecular & Cellular Biomechanics, Vol.8, No.2, pp. 105-122, 2011, DOI:10.3970/mcb.2011.008.105

Abstract A continuum model was introduced to analyze the pressure-flow relationship for steady flow in human pulmonary circulation. The continuum approach was based on the principles of continuum mechanics in conjunction with detailed measurement of vascular geometry, vascular elasticity and blood rheology. The pulmonary arteries and veins were considered as elastic tubes and the "fifth-power law" was used to describe the pressure-flow relationship. For pulmonary capillaries, the "sheet-flow" theory was employed and the pressure-flow relationship was represented by the "fourth-power law". In this paper, the pressure-flow relationship for the whole pulmonary circulation and the longitudinal pressure distribution along the streamlines were… More >

V.K. Tewary¹, M. D. Vaudin²

CMC-Computers, Materials & Continua, Vol.25, No.3, pp. 265-290, 2011, DOI:10.3970/cmc.2011.025.265

Abstract A semicontiuum Green's-function-based model is proposed for analysis of averaged mechanical characteristics of Si_xGe_{1 - x}. The atomistic forces in the model are distributed at discrete lattice sites, but the Green's function is approximated by the continuum GF in the far field and by the averaged lattice GF in the near field. Averaging is achieved by replacing Si and Ge atoms by identical hypothetical atoms that are x fraction Si and (1-x) fraction Ge. The parameters of the model are derived using the atomistic model from the interatomic potential between the hypothetical atoms. The interatomic potential is obtained from the… More >

Salvatore Brischetto¹

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.4, pp. 305-327, 2015, DOI:10.3970/cmes.2015.104.305

Abstract This paper proposes the free vibration analysis of Double-Walled Carbon NanoTubes (DWCNTs). A continuum elastic three-dimensional shell model is used for natural frequency investigation of simply supported DWCNTs. The 3D shell method is compared with beam analyses to show the applicability limits of 1D beam models. The effect of van der Waals interaction between the two cylinders is shown for different Carbon NanoTube (CNT) lengths and vibration modes. Results give the van der Waals interaction effect in terms of frequency values. In order to apply the 3D shell continuum model, DWCNTs are defined as two concentric isotropic cylinders (with an… More >

Dan Dumitriu¹, Ligia Munteanu¹, Cornel Brişan², Veturia Chiroiu¹, Rǎzvan-Vlad Vasiu², Octavian Melinte¹, Victor Vlǎdǎreanu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.2, pp. 159-173, 2013, DOI:10.3970/cmes.2013.094.159

Abstract The continuum modeling of tire/road vibro-contact dynamics is developed in this paper by assuming continuum relationship between the contact force and the deformation. An important aspect of this model is that the damping depends on the indentation. In the continuum approach, no difference is made between impact and contact, and the friction law can be other than the Coulomb’s law. Since the road is rocky, a bristle model was chosen to take into account the effect of the road irregularities. The identification of the contact domain is performed by checking the minimum distance between bodies. More >

Jian Hua Rong^1,2,3, Zhi Jun Zhao⁴, Yi Min Xie⁵, Ji Jun Yi^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.3, pp. 211-231, 2013, DOI:10.3970/cmes.2013.090.211

Abstract Similar periodic structures have been widely used in engineering. In order to obtaining the optimal similar periodic structures, a topology optimization method of similar periodic structures with multiple displacement constraints is proposed in this paper. Firstly, in the proposed method, the design domain is divided into sub-domains. Secondly, a penalty term considering discrete conditions of density variables is introduced into the objective function, and the reciprocal density exponents of structural elements are taken as design variables. A topological optimization model of a similar periodic continuum structure with the objective function being the structural mass and the constraint functions being structural… More >

Xianqiao Wang¹, James D. Lee²

CMES-Computer Modeling in Engineering & Sciences, Vol.69, No.3, pp. 199-222, 2010, DOI:10.3970/cmes.2010.069.199

Abstract This paper presents an atom-based continuum (ABC) method aiming at a seamless transition from the atomistic to the continuum description of multi-element crystalline solids (which has more than one kind of atom in the unit cell). Contrary to many concurrent multiscale approaches, ABC method is naturally suitable for the analysis of multi-element crystals within a finite element (FE) framework. Taking both efficiency and accuracy into account, we adopt a cluster-based summation rule for atomic force calculations in the FE formulations. Single-crystals MgO, BaTiO₃ and Cu under mechanical loading are modeled and simulated. With a coarse-grained mesh, ABC method is shown… More >

Zheng Juan^1,2,3, Long Shuyao^1,2, Xiong Yuanbo^1,2, Li Guangyao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.2, pp. 137-154, 2008, DOI:10.3970/cmes.2008.034.137

Abstract In this paper, the meshless radial point interpolation method (RPIM) is applied to carry out a topology optimization design for the continuum structure. Considering the relative density of nodes as a design variable, and the minimization of compliance as an objective function, the mathematical formulation of the topology optimization design is developed using the SIMP (solid isotropic microstructures with penalization) interpolation scheme. The topology optimization problem is solved by the optimality criteria method. Numerical examples show that the proposed approach is feasible and efficient for the topology optimization design for the continuum structure, and can effectively overcome the checkerboard phenomenon. More >