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  • Open Access

    ABSTRACT

    Numerical Modeling of Material Deformation Responses Using Gradient Continuum Theory

    Jurica Sorić*, Boris Jalušić, Tomislav Lesičar, Filip Putar, Zdenko Tonković

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.23, No.1, pp. 1-1, 2021, DOI:10.32604/icces.2021.08043

    Abstract In modeling of material deformation responses, the physical phenomena such as stress singularity problems, strain localization and modeling of size effects cannot be properly captured by means of classical continuum mechanics. Therefore, various regularization techniques have been developed to overcome these problems. In the case of gradient approach the implicit gradient formulations are usually used when dealing with softening. Although the structural responses are mesh objective, they suffer from spurious damage growth. Therefore, a new formulation based on the strain gradient continuum theory, which includes both strain gradients and their stress conjugates, has been proposed.… More >

  • Open Access

    ABSTRACT

    Micro/Nano-Sized Piezoelectric Structures Analyzed by Strain Gradient Theory

    Jan Sladek1, Vladimir Sladek1 and Choon-Lai Tan2

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.22, No.1, pp. 109-111, 2019, DOI:10.32604/icces.2019.05685

    Abstract In recent years, a special attention has been directed to the investigation of the relations between the macroscopic material behaviour and its microstructure. For most of the analyses of composite structures, effective or homogenized material properties are used, instead of taking into account the individual component properties and geometrical arrangements. The effective properties are usually difficult or expensive to measure and in the design stage the composition may vary substantially, making frequent measurements prohibitive. Hence a lot of effort has been devoted into the development of mathematical and numerical models to derive homogenized material properties More >

  • Open Access

    ARTICLE

    BEM Solutions for 2D and 3D Dynamic Problems in Mindlin's Strain Gradient Theory of Elasticity

    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 More >

  • Open Access

    ARTICLE

    Evaluation of the Toupin-Mindlin Theory for Predicting the Size Effects in the Buckling of the Carbon Nanotubes

    Veturia Chiroiu1, Ligia Munteanu1, Pier Paolo Delsanto2

    CMC-Computers, Materials & Continua, Vol.16, No.1, pp. 75-100, 2010, DOI:10.3970/cmc.2010.016.075

    Abstract Conventional continuum theories are unable to capture the observed indentation size effects, due to the lack of intrinsic length scales that represent the measures of nanostructure in the constitutive relations. In order to overcome this deficiency, the Toupin-Mindlin strain gradient theory of nanoindentation is formulated in this paper and the size dependence of the hardness with respect to the depth and the radius of the indenter for multiple walled carbon nanotubes is investigated. Results show a peculiar size influence on the hardness, which is explained via the shear resistance between the neighboring walls during the More >

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