Nikhil Madan, M.Sc.

Department of Information and Computational Science (ZIiNO)
Division of Computational Methods in Nonlinear Mechanics (PMOMN)
position: doctoral student
telephone: (+48) 22 826 12 81 ext.: 412
room: 422
e-mail: nmadan

Recent publications
1.Madan N., Rojek J., Nosewicz S., Convergence and stability analysis of the deformable discrete element method, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.6014, pp.1-22, 2019
Abstract:

This work investigates numerical properties of the algorithm of the discrete element method employing deformable circular discs presented in an earlier authors' publication. The new formulation, called the deformable discrete element method (DDEM) enhances the standard discrete element method (DEM) by introducing an additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. An accurate computation of the contact forces would require an iterative solution of the implicit relationship between the contact forces and particle displacements. In order to preserve efficiency of the DEM, the new formulation has been adapted to the explicit time integration. It has been shown that the explicit DDEM algorithm is conditionally stable and there are two restrictions on its stability. Except for the limitation of the time step as in the standard DEM, the stability in the DDEM is governed by the convergence criterion of the iterative solution of the contact forces. The convergence and stability limits have been determined analytically and numerically for selected regular and irregular configurations. It has also been found out that the critical time step in DDEM remains unchanged with respect to standard DEM.

Keywords:

discrete element method; deformable particles; iterative solution; convergence criterion;explicit scheme; stability

Affiliations:
Madan N.-IPPT PAN
Rojek J.-IPPT PAN
Nosewicz S.-IPPT PAN
2.Rojek J., Zubelewicz A., Madan N., Nosewicz S., The discrete element method with deformable particles, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.5767, Vol.114, No.8, pp.828-860, 2018
Abstract:

This work presents a new original formulation of the discrete element method (DEM) with deformable cylindrical particles. Uniform stress and strain fields are assumed to be induced in the particles under the action of contact forces. Particle deformation obtained by strain integration is taken into account in the evaluation of interparticle contact forces. The deformability of a particle yields a nonlocal contact model, it leads to the formation of new contacts, it changes the distribution of contact forces in the particle assembly, and it affects the macroscopic response of the particulate material. A numerical algorithm for the deformable DEM (DDEM) has been developed and implemented in the DEM program DEMPack. The new formulation implies only small modifications of the standard DEM algorithm. The DDEM algorithm has been verified on simple examples of an unconfined uniaxial compression of a rectangular specimen discretized with regularly spaced equal bonded particles and a square specimen represented with an irregular configuration of nonuniform-sized bonded particles. The numerical results have been verified by a comparison with equivalent finite elementmethod results and available analytical solutions. The micro-macro relationships for elastic parameters have been obtained. The results have proved to have enhanced the modeling capabilities of the DDEM with respect to the standard DEM.

Keywords:

average stress, deformable particles, discrete element method, elastic constants, micro-macro relationships, nonlocal contact model

Affiliations:
Rojek J.-IPPT PAN
Zubelewicz A.-University of New Mexico (US)
Madan N.-IPPT PAN
Nosewicz S.-IPPT PAN

Conference papers
1.Rojek J., Zubelewicz A., Madan N., Nosewicz S., New formulation of the discrete element method, CMM 2017, 22nd International Conference on Computer Methods in Mechanics, 2017-09-13/09-16, Lublin (PL), DOI: 10.1063/1.5019043, Vol.1922, pp.030009-1-8, 2018
Abstract:

A new original formulation of the discrete element method based on the soft contact approach is presented in this work. The standard DEM has heen enhanced by the introduction of the additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. Uniform stresses and strains are assumed for each particle. The stresses are calculated from the contact forces. The strains are obtained using an inverse constitutive relationship. The strains allow us to obtain deformed particle shapes. The deformed shapes (ellipses) are taken into account in contact detection and evaluation of the contact forces. A simple example of a uniaxial compression of a rectangular specimen, discreti.zed with equal sized particles is simulated to verify the DDEM algorithm. The numerical example shows that a particle deformation changes the particle interaction and the distribution of forces in the discrete element assembly. A quantitative study of micro-macro elastic properties proves the enhanced capabilities of the DDEM as compared to standard DEM.

Affiliations:
Rojek J.-IPPT PAN
Zubelewicz A.-University of New Mexico (US)
Madan N.-IPPT PAN
Nosewicz S.-IPPT PAN

Conference abstracts
1.Rojek J., Madan N., Nosewicz S., Zubelewicz A., The deformable discrete element method, 6th European Conference on Computational Mechanics (ECCM 6), 7th European Conference on Computational Fluid Dynamics (ECFD 7), 2018-06-11/06-15, Glasgow (GB), pp.1, 2018
Keywords:

Discrete Element Method, Deformable Particles, Nonlocal Contact Model, Poisson's Effect

Affiliations:
Rojek J.-IPPT PAN
Madan N.-IPPT PAN
Nosewicz S.-IPPT PAN
Zubelewicz A.-University of New Mexico (US)
2.Madan N., Rojek J., Zubelewicz A., Nosewicz S., Convergence limit of a deformable discrete element model, SolMech 2018, 41st SOLID MECHANICS CONFERENCE, 2018-08-27/08-31, Warszawa (PL), pp.204-205, 2018
3.Rojek J., Zubelewicz A., Madan N., Nosewicz S., Lumelskyj D., A novel treatment for the deformability of discrete elements, SolMech 2018, 41st SOLID MECHANICS CONFERENCE, 2018-08-27/08-31, Warszawa (PL), pp.202-203, 2018
4.Rojek J., Zubelewicz A., Madan N., Nosewicz S., New formulation of the discrete element method, CMM 2017, 22nd International Conference on Computer Methods in Mechanics, 2017-09-13/09-16, Lublin (PL), pp.MS13-27-MS13-28, 2017
Abstract:

This work presents a new original formulation of the discrete element method based on the soft contact approach. The standard DEM has been enhanced by introduction of the additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. Uniform stresses and strains are assumed for each particle. The stresses are calculated from the contact forces. The strains are obtained using an inverse constitutive relationship. The strains allow us to obtain deformed particle shapes. The deformed shapes (ellipses) are taken into account in contact detection and evaluation of the contact forces. The numerical example shows that a particle deformation changes the particle interaction and the distribution of forces in the discrete element assembly.

Keywords:

discrete element method; deformable particles; soft contact

Affiliations:
Rojek J.-IPPT PAN
Zubelewicz A.-University of New Mexico (US)
Madan N.-IPPT PAN
Nosewicz S.-IPPT PAN