Granular contact dynamics using mathematical programming methods

Krabbenhøft, K.; Lyamin, A. V.; Huang, Jinsong; Silva, M. Vicente da

doi:10.1016/j.compgeo.2012.02.006

Cited by 70 publications

(66 citation statements)

References 52 publications

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“…The dynamic model is formulated following the approach proposed in [6,7] for granular materials, though now detailed for two-dimensional assemblages of rectangular blocks.…”

Section: The Rigid Block Dynamic Modelmentioning

confidence: 99%

“…Under the assumption of associative flow rule for displacement increments, the equilibrium equations (2), kinematic conditions (6-7) and sliding friction conditions (8) are equivalent to the following force-based problem [6][7][8][9]:…”

Section: Formulation Of the Qp Problem And Implementationmentioning

confidence: 99%

“…In this perspective, starting from previous studies in the field of granular materials [6,7], a non-smooth contact dynamic formulation for the analysis of masonry structures has been recently developed [8,9] and herein applied to a numerical case study taken from the literature [10] to show potentialities of the adopted modelling approach.…”

Section: Introductionmentioning

confidence: 99%

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Non-Smooth Contact Dynamics of Planar Masonry Structures Using Mathematical Programming

Portioli¹,

Cascini²,

Landolfo³

2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…The dynamic model is formulated following the approach proposed in [6,7] for granular materials, though now detailed for two-dimensional assemblages of rectangular blocks.…”

Section: The Rigid Block Dynamic Modelmentioning

confidence: 99%

Section: Formulation Of the Qp Problem And Implementationmentioning

confidence: 99%

See 1 more Smart Citation

Non-Smooth Contact Dynamics of Planar Masonry Structures Using Mathematical Programming

Portioli¹,

Cascini²,

Landolfo³

2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…Disadvantages are that the uniqueness of the solutions at each time step is not guaranteed and that the computational effort scales super linearly with the number of particles. Krabbenhoft et al [8] extended the method with an infinite "time step" to perform quasi-static simulations.…”

Section: Introductionmentioning

confidence: 99%

“…In the non-smooth contact dynamics [7][8][9][10] method, all particles are modeled as perfectly rigid and the interactions are modeled by means of a Signorini condition. Either two particles are not in contact and thus also have no forces associated with them, or they are in contact and the forces associated with the contact are determined from the fact that the two particles cannot overlap.…”

Section: Introductionmentioning

confidence: 99%

Simulating granular materials by energy minimization

Krijgsman

Luding

2016

Comp. Part. Mech.

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Discrete element methods are extremely helpful in understanding the complex behaviors of granular media, as they give valuable insight into all internal variables of the system. In this paper, a novel discrete element method for performing simulations of granular media is presented, based on the minimization of the potential energy in the system. Contrary to most discrete element methods (i.e., soft-particle method, event-driven method, and non-smooth contact dynamics), the system does not evolve by (approximately) integrating Newtons equations of motion in time, but rather by searching for mechanical equilibrium solutions for the positions of all particles in the system, which is mathematically equivalent to locally minimizing the potential energy. The new method allows for the rapid creation of jammed initial conditions (to be used for further studies) and for the simulation of quasi-static deformation problems. The major advantage of the new method is that it allows for truly static deformations. The system does not evolve with time, but rather with the externally applied strain or load, so that there is no kinetic energy in the system, in contrast to other quasistatic methods. The performance of the algorithm for both types of applications of the method is tested. Therefore we look at the required number of iterations, for the system to converge to a stable solution. For each single iteration, the required computational effort scales linearly with the number of particles. During the process of creating initial conditions, the required number of iterations for two-dimensional systems scales with the square root of the number of particles in the system. The required number of iterations increases for systems closer to the jamming packing fraction. For a quasistatic pure shear deformation simulation, the results of the new method are validated by regular soft-particle dynamics simulations. The energy minimization algorithm is able to capture the evolution of the isotropic and deviatoric stress and fabric of the system. Both methods converge in the limit of quasi-static deformations, but show interestingly different results otherwise. For a shear amplitude of 4 %, as little as 100 sampling points seems to be a good compromise between accuracy and computational time needed.

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A variational rigid‐block modeling approach to nonlinear elastic and kinematic analysis of failure mechanisms in historic masonry structures subjected to lateral loads

Portioli

Godio

Calderini

et al. 2021

Earthq Engng Struct Dyn

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Displacement-based methods contained in recent standards for seismic safety assessment require the determination of the full nonlinear pushover curve for local failure mechanisms in historic masonry structures. This curve should reflect both the initial elastic behavior and the rigid body behavior after the activation of rocking. In this work, a rigid block model is proposed for the displacement-based seismic assessment of local collapse mechanisms of these structures. Masonry is modeled as an assemblage of two-dimensional rigid blocks in contact through frictional interfaces. Two types of contact models are formulated to capture, respectively, the pre and postpeak branches of the pushover curve: a unilateral elastic contact model, capturing the initial nonlinear behavior up to the force capacity of the structure, corresponding to the activation of the collapse mechanism, and a rigid contact model with finite friction and compressive strength, which describes the rigid-body rocking behavior up to the attainment of the displacement capacity of the structure. Tension-only elements are also implemented to model strengthening interventions with tie-rods. The contact problems associated with the elastic and rigid contact models are formulated using mathematical programming. For both models, a sequential solution procedure is implemented to capture the variation of the load multiplier with the increasing deformation of the structure (P-Δ effect). The accuracy of the modeling approach in reproducing the pushover curve of masonry panels subjected to horizontal seismic loads is evaluated on selected case studies. The solution is first tested against hand calculations, existing analytical models, and distinct element simulations. Then, comparisons against experimental tests follow. As a final application, the failure mechanism and pushover curve of a triumphal masonry arch are predicted by the model and its seismic assessment is performed according to codified force-and displacement-based methods, demonstrating the adequacy of the proposed tool for practice.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Granular contact dynamics using mathematical programming methods

Cited by 70 publications

References 52 publications

Non-Smooth Contact Dynamics of Planar Masonry Structures Using Mathematical Programming

Non-Smooth Contact Dynamics of Planar Masonry Structures Using Mathematical Programming

Simulating granular materials by energy minimization

A variational rigid‐block modeling approach to nonlinear elastic and kinematic analysis of failure mechanisms in historic masonry structures subjected to lateral loads

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