A microscopic nonlinear programming approach to shakedown analysis of cohesive–frictional composites

Li, H.X.

doi:10.1016/j.compositesb.2013.01.018

Cited by 17 publications

(17 citation statements)

References 59 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%

“…The set of macroscopic stresses, which can be carried by the heterogeneous material, characterizes the strength of the homogenized material. In the present study, the kinematic formulation for limit analysis of composite materials will be reformulated in terms of total strain rates (or total velocities), and hence, the resulting formulation is different from those presented in , in which the fluctuation strain rates/velocities are the problem variable fields.…”

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: Computational Homogenization For Kinematic Limit Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A computational homogenization approach for limit analysis of heterogeneous materials

Nguyen

Askes

et al. 2017

Int. J. Numer. Meth. Engng

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“…[42], Schwabe [35], Maier [28], Magoariec et al [27], Zhang et al [45], You et al [44], Chen et al [10,11] solve the problem by a static approach. In contrast, Carvelli [6], Chen and Ponter [9], Li [26], and Barrera [3] deal the problem by the kinematic approach.…”

Section: Introductionmentioning

confidence: 91%

On the Statistical Determination of Yield Strength, Ultimate Strength, and Endurance Limit of a Particle Reinforced Metal Matrix Composite (PRMMC)

Chen

Özden

Bezold

et al. 2015

Direct Methods for Limit and Shakedown Analysis of Structures

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In this paper we present a numerical methodology to determine the load bearing capacity of a random heterogeneous material. It is applied to a particulate reinforced metal matrix composite (PRMMC), WC-30 Wt.% Co, to predict its strength against both monotonic and cyclic loads. In this approach, limit and shakedown analysis based on Melan's static theorem [30] is performed on representative volume element (RVE) models generated from real material microstructure and the obtained results are converted to macroscopic load domains through homogenization. To evaluate microstructure's impact on the overall material strength, the relationship between strength and composite structure is investigated by means of statistics. Meanwhile, several numerical issues, e.g. the impact of RVE's size, mesh density, as well as the discrepancy between 2D and 3D models, are studied.

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Complementarity Problems in Structural Engineering: An Overview

Bolzon

2015

Arch Computat Methods Eng

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This paper summarizes the formulation of structural engineering problems concerned with inelastic phenomena that can be described in complementarity format. This mathematical construct can be transferred to the discretized version of the continuum problem by generalized variables. The evaluation of safety factors against collapse conditions, of primary deemed relevance for a safe and rational design in harmonized European Standards, can be performed in a consistent framework. The main features of these approaches and the relevant computational tools are revised

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A microscopic nonlinear programming approach to shakedown analysis of cohesive–frictional composites

Cited by 17 publications

References 59 publications

A computational homogenization approach for limit analysis of heterogeneous materials

A computational homogenization approach for limit analysis of heterogeneous materials

On the Statistical Determination of Yield Strength, Ultimate Strength, and Endurance Limit of a Particle Reinforced Metal Matrix Composite (PRMMC)

Complementarity Problems in Structural Engineering: An Overview

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