Limit analysis of composite materials with anisotropic microstructures: A homogenization approach

Li, H.X.

doi:10.1016/j.mechmat.2011.06.007

Cited by 20 publications

(13 citation statements)

References 45 publications

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“…Recently, Bleyer et al proposed a novel numerical procedure for homogenization of periodic plates, in which kinematic theorem was combined with the prescribed curvatures, and prescribed moments were employed in the static formulation. However, in this paper, we will present a novel computational homogenization limit analysis based on the kinematic approach described in . On the boundary of the RVE, the external prescribed loading condition considered is macroscopic strains, which are treated as variables.…”

Section: Computational Homogenization For Kinematic Limit Analysismentioning

confidence: 99%

“…For periodic plates, a theoretical study on the overall homogenized Love–Kirchhoff strength domain of a rigid perfectly plastic multi‐layered plate was reported by , and numerical determination of the macroscopic bending strength criterion was presented in . By means of homogenization techniques and kinematic limit analysis in conjunction with non‐linear programming, the plastic limit loads and failure modes of periodic composites governed by ellipsoid yield criteria can be determined . Using the elastic stresses of the periodic microstructure, a static direct method in combination with homogenization was proposed in for two and three‐dimensional limit analysis of periodic metal‐matrix composites.…”

Section: Introductionmentioning

confidence: 99%

“…The objective of the present paper is to develop a novel computational homogenization procedure for kinematic limit analysis of periodic materials. The total velocity fields at microscopic level are approximated by finite elements, instead of the fluctuating (periodic) velocity as in . Consequently, the auxiliary limit analysis problem of microstructure is similar to a limit analysis problem formulated for structures.…”

Section: Introductionmentioning

confidence: 99%

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A computational homogenization approach for limit analysis of heterogeneous materials

Nguyen

Askes

et al. 2017

Int. J. Numer. Meth. Engng

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model together with coupled kinematic and static theorems as well as homogenization theory. Based on finite elements and primal-dual interior point optimization algorithm, the assessment of the macroscopic strength criterion and stability analysis of soils reinforced by stone columns were performed in [9][10][11][12][13]. For periodic plates, a theoretical study on the overall homogenized Love-Kirchhoff strength domain of a rigid perfectly plastic multi-layered plate was reported by [14,15], and numerical determination of the macroscopic bending strength criterion was presented in [16,17]. By means of homogenization techniques and kinematic limit analysis in conjunction with non-linear programming, the plastic limit loads and failure modes of periodic composites governed by ellipsoid yield criteria can be determined [18][19][20][21][22][23]. Using the elastic stresses of the periodic microstructure, a static direct method in combination with homogenization was proposed in [24][25][26][27][28] for two and threedimensional limit analysis of periodic metal-matrix composites. In the method, the strong form of the equilibrium equations was transformed into the so-called weak form and to be satisfied locally in an average sense using approximated virtual displacement fields. Based on linear matching method, limit analysis of reinforced concrete structures has also been studied in [29][30][31][32][33]. Practical multi-scale modeling and homogenization can be found in [34].Direct approaches for limit analysis of structures and materials lead to a problem of constrained optimization involving either linear or nonlinear programming, and hence, the development of efficient optimization algorithms to enable solutions to be obtained is one of the major research directions in the field. From a mathematical point of view, linear programming is very attractive and has been widely applied to limit analysis problems [35][36][37]. Although powerful software based on interior point algorithms is available for the resolution of the resulting optimization problem, a large number of constraints generated in the linearization process would be needed in order to provide accurate solutions, thereby increasing the computational cost. Attempts have been made to solve problems involving exact convex yield functions using nonlinear programming algorithms [38][39][40][41][42][43]. In recent years, thanks to the development of such an efficient primal-dual interior point algorithm, implemented in a commercial optimization software Mosek [44], limit analysis problems have gained increasing attention. In fact, most commonly used yield criteria can be cast in the form of conic or semi-definite constraints, and optimization problems involving such constraints can be solved efficiently by such an algorithm, evidenced by recent works [11-13, 16, 17, 45-50].The objective of the present paper is to develop a novel computational homogenization procedure for kinematic limit analysis of periodic materials. The total velocity fields at microscopic level ar...

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Section: Computational Homogenization For Kinematic Limit Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A computational homogenization approach for limit analysis of heterogeneous materials

Nguyen

Askes

et al. 2017

Int. J. Numer. Meth. Engng

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“…Following Li et al , , a number of important yield criteria for isotropic, anisotropic or pressure‐dependent materials can be expressed in the general form:

F (bold-italic σ) = {bold-italic σ}^{T} boldP bold-italic σ + {bold-italic σ}^{T} boldq - 1 = 0

where F ( σ ) defines a yield function in terms of the stresses and strength parameters and P and q denote, respectively, a coefficient matrix and a vector, which are related to the strength properties.…”

Section: Kinematic Theorem Of Limit Analysismentioning

confidence: 99%

A 3D upper bound limit analysis using radial point interpolation meshless method and second‐order cone programming

Xue

Sloan

2016

Numerical Meth Engineering

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SUMMARYThis paper presents a 3D formulation for quasi-kinematic limit analysis, which is based on a radial point interpolation meshless method and numerical optimization. The velocity field is interpolated using radial point interpolation shape functions, and the resulting optimization problem is cast as a standard secondorder cone programming problem. Because the essential boundary conditions can be only guaranteed at the position of the nodes when using radial point interpolation, the results obtained with the proposed approach are not rigorous upper bound solutions. This paper aims to improve the computing efficiency of 3D upper bound limit analysis and large problems, with tens of thousands of nodes, can be solved efficiently. Five numerical examples are given to confirm the effectiveness of the proposed approach with the von Mises yield criterion: an internally pressurized cylinder; a cantilever beam; a double-notched tensile specimen; and strip, square and rectangular footings.

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“…Some authors have evaluated analytically or numerically the macroscopic strength criterion of lime-column reinforced soils (purely cohesive soil reinforced by purely cohesive solumns) by using both kinematic and static approaches of the yield design theory [27][28][29][30]. The stability analysis has been performed in such a case for different configurations of structures (embankment resting upon a reinforced soil [31] or ultimate bearing capacity of reinforced foundation under inclined loads [32]).…”

Section: The Yield Design Homogenization Approachmentioning

confidence: 99%

Stability analysis of homogenized stone column reinforced foundations using a numerical yield design approach

Gueguin

Hassen²,

Buhan³

2015

Computers and Geotechnics

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This paper deals with the ultimate bearing capacity of soft clayey soils, reinforced by stone columns, analyzed in the framework of the yield design theory. Since such geotechnical structures are almost impossible to analyze directly due to the strong heterogeneity of the reinforced soil, an alternative homogenization approach is advocated here. First, numerical lower and upper bound estimates for the macroscopic strength criterion of the stone column reinforced soil are approximated in a rigorous way with convex ellipsoidal sets, which makes the approximated criteria much easier to handle than the initial ones. Then, both static and kinematic approaches are carried out numerically on the homogenized problem using the above approximated macroscopic strength domains in an adapted finite element method. The whole numerical procedure is applied on one classical geotechnical problem: the ultimate bearing capacity of stone column reinforced foundations. The strength capacity of the structure is rigorously framed and the efficiency of the proposed numerical method is highlighted in terms of accuracy and calculation time.

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Limit analysis of composite materials with anisotropic microstructures: A homogenization approach

Cited by 20 publications

References 45 publications

A computational homogenization approach for limit analysis of heterogeneous materials

A computational homogenization approach for limit analysis of heterogeneous materials

A 3D upper bound limit analysis using radial point interpolation meshless method and second‐order cone programming

Stability analysis of homogenized stone column reinforced foundations using a numerical yield design approach

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