Chengya Hua¹, Leihua Yao^1,*, Chenguang Song¹, Qihang Ni¹, Dongfang Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.2, pp. 413-434, 2022, DOI:10.32604/cmes.2022.020260 - 15 June 2022

Abstract A new variational method treating the system as a whole with rigorous mathematical and physical derivation was presented in this paper. Combined with classical and engineering examples, variational energy expressions of slopes were derived. In addition, the calculation programs were written in the FISH language set in FLAC3D (fast Lagrangian analysis of continua in three dimensions) software. Factors of safety (FOSs) of the models were determined by the variational method based on the strength reduction method (SRM) and then compared with other criteria or methods. The result showed that the variational method reflected the process… 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… 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… More >

N.A. Dumont¹, E.Y. Mamani¹

CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.2, pp. 109-150, 2011, DOI:10.3970/cmes.2011.078.109

Abstract A particular implementation of the hybrid boundary element method is presented for the two-dimensional analysis of potential and elasticity problems, which, although general in concept, is suited for fracture mechanics applications. Generalized Westergaard stress functions, as proposed by Tada, Ernst and Paris in 1993, are used as the problem's fundamental solution. The proposed formulation leads to displacement-based concepts that resemble those presented by Crouch and Starfield, although in a variational framework that leads to matrix equations with clear mechanical meanings. Problems of general topology, such as in the case of unbounded and multiply-connected domains, may More >

Michael Yu Wang^1,2, Shiwei Zhou²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.6, pp. 547-566, 2004, DOI:10.3970/cmes.2004.006.547

Abstract In this paper we present a variational method to address the topology optimization problem -- the phase transition method. A phase-field model is employed based on the phase-transition theory in the fields of mechanics and material sciences. The topology optimization is formulated as a continuous problem with the phase-field as design variables within a fixed reference domain. All regions are described in terms of the phase field which makes no distinction between the solid, void and their interface. The Van der Waals-Cahn-Hilliard theory is applied to define the variational topology optimization as a dynamic process… More >

K. Garikipati¹

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.2, pp. 175-184, 2002, DOI:10.3970/cmes.2002.003.175

Abstract The embedding of micromechanical models in the macromechanical formulation of continuum solid mechanics can be treated by a variational multiscale method. A scale separation is introduced on the displacement field into coarse and fine scale components. The fine scale displacement is governed by the desired micromechanical model. Working within the variational framework, the fine scale displacement field is eliminated by expressing it in terms of the coarse scale displacement and the remaining fields in the problem. The resulting macromechanical formulation is posed solely in terms of the coarse scale displacements, but is influenced by the More >