Microscopic limit analysis of cohesive-frictional composites with non-associated plastic flow

Li, H.X.

doi:10.1016/j.euromechsol.2012.07.005

Cited by 8 publications

(7 citation statements)

References 58 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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“…Besides, using the similar approach, a quasi-lower bound formulation for periodic composite and heterogeneous materials using the nonlinear programming was presented in [10]. In contrast, the kinematic formulations in combination with nonlinear algorithms can be found in [11][12][13][14][15]. In those works, both of isotropic and anisotropic materials obeying the von Mises or elliptic yield criterion were considered.…”

Section: Introductionmentioning

confidence: 99%

Limit analysis of microstructures based on homogenization theory and the element-free Galerkin method

2020

Vietnam J. Mech.

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This paper presents a novel numerical formulation of computational homogenization analysis of materials at limit state. The fluctuating displacement field are approximated using the Element-Free Galerkin (EFG) meshless method. The estimated yield surface of materials can be determined by handling the multiscale (macro-micro) transition. Taking advantage of high-order EFG shape function and the second-order cone programming, the resulting optimization problem can be solved rapidly with the great accuracy. Several benchmark examples will be investigated to demonstrate the computational efficiency of proposed method.

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Thrust in a symmetric masonry arch with frictional joints on spreading supports

Trentadue,

De Tommasi,

Marasciuolo

et al. 2023

Acta Mech

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The effect of a supports settlement in a symmetric masonry arch is studied by modeling the arch as a system of rigid plastic blocks with frictional sliding. It is shown that in a collapse state due to a horizontal settlement the thrust attains its minimum statically admissible value, so extending to the case of frictional sliding a well-known result of standard limit analysis, which considers collapse states only due to the opening of joints. The case of both vertical and horizontal settlements is also analyzed. It is demonstrated that the collapse thrust in case of horizontal settlement is a lower bound for the collapse thrust in case of generic settlement. Extensive numerical analyses illustrate the above results.

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Microscopic limit analysis of cohesive-frictional composites with non-associated plastic flow

Cited by 8 publications

References 58 publications

A computational homogenization approach for limit analysis of heterogeneous materials

A computational homogenization approach for limit analysis of heterogeneous materials

Limit analysis of microstructures based on homogenization theory and the element-free Galerkin method

Thrust in a symmetric masonry arch with frictional joints on spreading supports

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