L. Dong¹, S. N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.1, pp. 69-118, 2011, DOI:10.3970/cmes.2011.081.069

Abstract In this paper, we explore three different ways of developing T-Trefftz finite elements of quadrilateral as well as polygonal shapes. In all of these three approaches, in addition to assuming an inter-element compatible displacement field along the element boundary, an interior displacement field for each element is independently assumed as a linear combination of T-Trefftz trial functions. In addition, a characteristic length is defined for each element to scale the T-Trefftz modes, in order to avoid solving systems of ill-conditioned equations. The differences between these three approaches are that, the compatibility between the independently assumed… More >

M.A. Argenta¹, A.P. Gebert², E.S. Filho³, B.A. Felizari⁴, M.B. Hecke⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.79, No.3&4, pp. 159-182, 2011, DOI:10.3970/cmes.2011.079.159

Abstract Various methods in the literature proposesequations to calculate the stiffness as a function of density of bone tissue such as apparent density and ash density among others[Helgason, Perilli, Schileo, Taddei, Brynjolfsson and Viceconti, 2008]. Other ones present a value of an equivalent elasticity modulus, obtained by statistical adjustments of curves generated through mechanical compression tests over various specimens[Chevalier, Pahr, Allmer, Charlebois and Zysset, 2007; Cuppone, Seedhom, Berry and Ostell, 2004]. Bone tissue is a material withdifferent behaviors according to the scale of observation. It has a complex composite hierarchical structure, which is responsible for assign More >

K. Jayabal¹, A. Menzel^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.2, pp. 183-208, 2011, DOI:10.3970/cmes.2011.073.183

Abstract Naturally evolving Voronoi discretisation of two-dimensional plane domains renders representative microstructures that turn out to be useful for the modelling and simulation of polycrystalline materials. Hybrid finite element approaches are employed on such polygonal discretisations to solve, for instance, mechanical and electromechanical problems within a finite element context. In view of solving mechanical problems, varying order of polynomial functions are suggested in the literature to sufficiently approximate stresses within the polygonal finite elements. These are, in addition to the order of the approximation functions for the displacements, characterised by the number of edges in the… More >

A. Idesman ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.2, pp. 111-148, 2011, DOI:10.3970/cmes.2011.071.111

Abstract The paper deals with the following issues of existing time-integration methods for a semi-discrete system of elastodynamics equations: a) the quantification and the suppression of spurious high frequencies; b) the selection of the amount of numerical dissipation for a time-integration method; and c) accurate time integration of low modes. The finite element method used in the paper or other methods can be applied for the space discretization. A new two-stage time-integration procedure consisting of basic computations and the filtering stage is developed. For accurate integration of all frequencies, a time-integration method with zero (or small)… More >

L. Dong¹, S. N. Atluri²

CMC-Computers, Materials & Continua, Vol.24, No.1, pp. 61-104, 2011, DOI:10.3970/cmc.2011.024.061

Abstract A simple procedure to formulate efficient and stable hybrid/mixed finite elements is developed, for applications in macro- as well as micromechanics. In this method, the strain and displacement field are independently assumed. Instead of using two-field variational principles to enforce both equilibrium and compatibility conditions in a variational sense, the independently assumed element strains are related to the strains derived from the independently assumed element displacements, at a finite number of collocation points within the element. The element stiffness matrix is therefore derived, by simply using the principle of minimum potential energy. Taking the four-node… More >

S. Kucukcoban¹, L.F. Kallivokas²

CMES-Computer Modeling in Engineering & Sciences, Vol.64, No.2, pp. 109-146, 2010, DOI:10.3970/cmes.2010.064.109

Abstract We are concerned with elastic wave simulations arising in elastic, semi-infinite, heterogeneous, three-dimensional media with a vertical axis of symmetry through the coordinate origin. Specifically, we discuss the development of a new mixed displacement-stress formulation in PML-truncated axisymmetric media for forward elastic wave simulations. Typically, a perfectly-matched-layer (PML) is used to surround a truncated finite computational domain in order to attenuate outwardly propagating waves without reflections for all non-zero angles-of-incidence and frequencies. To date, standard formulations use split fields, where the displacement components are split into normal and parallel to the PML interface components. In More >

Marcin Maździarz¹

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.1, pp. 1-24, 2010, DOI:10.3970/cmes.2010.066.001

Abstract The paper presents unified approach to 3D isoparametric Lagrange brick, tetra, and prism finite elements. All shape functions, linear, quadratic and cubic, are depicted in one Cartesian orthogonal coordinate system x,y,z regardless of the type of element. This allows one to use a single transformation rule to calculate global derivatives and a second for integration. Proper numerical Gauss quadratures for these isoparametric elements in a unified approach are presented additionally. More >

K.P. Baxevanakis¹, A.E. Giannakopoulos²

CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.2, pp. 181-198, 2010, DOI:10.3970/cmes.2010.060.181

Abstract The present work gives a systematic and rigorous implementation of (edge type) circular Volterra dislocation loops in ordinary axisymmetric finite elements using the thermal analogue and the integral representation of dislocations through stresses. The accuracy of the proposed method is studied in problems where analytical solutions exist. The full fields are given for loop dislocations in isotropic and anisotropic crystals and the Peach-Koehler forces are calculated for loops approaching free surfaces and bimaterial interfaces. The results are expected to be very important in the analysis of plastic yield strength, giving quantitative results regarding the influence More >

A. Frangi¹, M. Pagani¹, U. Perego¹, R. Borsari²

CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.3, pp. 205-224, 2010, DOI:10.3970/cmes.2010.057.205

Abstract This paper is concerned with the finite element simulation of a thin membrane cutting by a sharp blade. Smeared crack finite element approaches appear to be unsuitable for this purpose, since very small elements would be required to conform to the sharp edge of the cutter. Furthermore, when the membrane material is very ductile, classical interface cohesive elements, where the cohesive forces are transmitted in the direction of the crack opening displacement, cannot correctly reproduce situations where the blade crosses the process zone. A simplified approach, based on the new concept of "directional" cohesive elements,… More >

Dongwoo Sohn¹, Jae Hyuk Lim², Young-Sam Cho³, Seyoung Im¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.10, No.2, pp. 53-54, 2009, DOI:10.3970/icces.2009.010.053

Abstract A novel multiscale finite element (FE) scheme is proposed for a simulation of crack propagation in the heterogeneous media including randomly distributed microstructures, such as voids, rigid fibers. A fine scale mesh is employed to capture the singularity of the crack tip and the effect of microstructures at the vicinity of crack tip. On the other hand, a region far from the crack tip is composed of coarse scale mesh, wherein the effect of the microstructures is averaged through the homogenization theory. An interface between the fine scale mesh and the coarse scale mesh is More >