Miroslav Repka^1,*, Jan Sladek¹, Vladimir Sladek¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.23, No.1, pp. 10-10, 2021, DOI:10.32604/icces.2021.08308

Abstract The flexoelectric effect is investigated in quantum dot (QD) nano-sized structures. The lattice mismatch between QD and matrix results in non-uniform strains and presence of the strain gradients in the structure. The strain gradients induces the change of the polarization in QD structure as a consequence of the flexoelectric effect. When the dimensions of the QDs are of the same order of magnitude as the material length scale, gradient elasticity theory should be used to account for the size dependent of such nano-sized QDs. In this work the flexoelectric theory is applied for 3D analysis of QDs with the functionally… More >

Ney Augusto Dumont

The International Conference on Computational & Experimental Engineering and Sciences, Vol.23, No.1, pp. 2-2, 2021, DOI:10.32604/icces.2021.08187

Abstract The mathematical modeling of microdevices, in which structure and microstructure have approximately the same scale of magnitude, as well as of macrostructures of markedly granular or crystal nature (microcomposites), demands a nonlocal approach for strains and stresses. The present proposition is based on a simplified strain gradient theory laid down by Aifantis, which has also been applied mainly by Beskos and collaborators in the context of the boundary element method. This paper is an extension of a presentation made during the ICCES 2014 Conference in Crete, Greece, now relying on machine-precision evaluation of all singular and hypersingular integrals required in… More >

L. Teneketzis Tenek¹, E.C. Aifantis^1,2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.6, pp. 731-741, 2002, DOI:10.3970/cmes.2002.003.731

Abstract A two-dimensional finite element implementation of a special form of gradient elasticity is developed and a connection between classical and the proposed gradient elasticity theory is established. A higher-order constitutive equation is adopted which involves a gradient term of a special form; the higher-order term is precisely the second gradient of the lower-order term. A weak form of the equilibrium equations, based on the principle of virtual work, is formulated for the classical problem. The problem in hand, is solved by means of the finite element method in two steps. First, the displacement field of classical elasticity is computed. Then,… More >

N.A. Dumont, D. Huaman

The International Conference on Computational & Experimental Engineering and Sciences, Vol.19, No.4, pp. 111-112, 2011, DOI:10.3970/icces.2011.019.111

Abstract This paper proposes a hybrid finite element formulation of the strain gradient elasticity that provides a natural conceptual framework to properly deal with the interelement compatibility of normal displacement gradients and the equilibrium of non-classical boundary forces. It is based on developments firstly proposed by Mindlin and further elaborated by Aifantis. Consistency is assessed - in the full manuscript version - by means of several generalized patch tests. More >

N.A. Dumont ¹, D. Huamán¹

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.6, pp. 387-419, 2014, DOI:10.3970/cmes.2014.101.387

Abstract The present paper starts with Mindlin’s theory of the strain gradient elasticity, based on three additional constants for homogeneous materials (besides the Lamé’s constants), to arrive at a proposition made by Aifantis with just one additional parameter. Aifantis’characteristic material length g², as it multiplies the Laplacian of the Cauchy stresses, may be seen as a penalty parameter to enforce interelement displacement gradient compatibility also in the case of a material in which the microstructure peculiarities are in principle not too relevant, but where high stress gradients occur. It is shown that the hybrid finite element formulation – as proposed by… More >

E.J. Sellountos¹, S.V. Tsinopoulos², D. Polyzos³

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.2, pp. 145-170, 2012, DOI:10.3970/cmes.2012.086.145

Abstract A Local Boundary Integral Equation (LBIE) method for solving two dimensional problems in gradient elastic materials is presented. The analysis is performed in the context of simple gradient elasticity, the simplest possible case of Mindlin's Form II gradient elastic theory. For simplicity, only smooth boundaries are considered. The gradient elastic fundamental solution and the corresponding boundary integral equation for displacements are used for the derivation of the LBIE representation of the problem. Nodal points are spread over the analyzed domain and the moving least squares (MLS) scheme for the approximation of the interior and boundary variables is employed. Since in… More >

S.V. Tsinopoulos¹, D. Polyzos², D.E. Beskos^3,4

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.2, pp. 113-144, 2012, DOI:10.3970/cmes.2012.086.113

Abstract This paper reviews the theory and the numerical implementation of the direct boundary element method (BEM) as applied to static and dynamic problems of strain gradient elastic solids and structures under two- and three- dimensional conditions. A brief review of the linear strain gradient elastic theory of Mindlin and its simplifications, especially the theory with just one constant (internal length) in addition to the two classical elastic moduli, is provided. The importance of this theory in successfully modeling microstructural effects on the structural response under both static and dynamic conditions is clearly described. The boundary element formulation of static and… More >

A. Papacharalampopoulos², G. F. Karlis², A. Charalambopoulos³, D. Polyzos⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.1, pp. 45-74, 2010, DOI:10.3970/cmes.2010.058.045

Abstract A Boundary Element Method (BEM) for solving two (2D) and three dimensional (3D) dynamic problems in materials with microstructural effects is presented. The analysis is performed in the frequency domain and in the context of Mindlin's Form II gradient elastic theory. The fundamental solution of the differential equation of motion is explicitly derived for both 2D and 3D problems. The integral representation of the problem, consisting of two boundary integral equations, one for displacements and the other for its normal derivative is exploited for the proposed BEM formulation. The global boundary of the analyzed domain is discretized into quadratic line… More >

G.F. Karlis¹, S.V. Tsinopoulos², D. Polyzos³, D.E. Beskos⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.3, pp. 189-208, 2008, DOI:10.3970/cmes.2008.026.189

Abstract A boundary element method, suitable for solving two and three dimensional gradient elastic fracture mechanics problems under static loading, is presented. A simple gradient elastic theory (a simplied version of Mindlin's Form-II general theory of gradient elasticity) is employed and the static gradient elastic fundamental solution is used to construct the boundary integral representation of the problem with the aid of a reciprocal integral identity. In addition to a boundary integral representation for the displacement, a boundary integral representation for its normal derivative is also necessary for the complete formulation of a well-posed problem. Surface quadratic line and quadrilateral boundary… More >