Convergence and stability analysis of the deformable discrete element method

Madan, Nikhil; Rojek, Jerzy; Nosewicz, Szymon

doi:10.1002/nme.6014

Cited by 10 publications

(11 citation statements)

References 20 publications

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“…The stability is restricted by the critical time step of the explicit time integration and the convergence limit of the iterative solution of an implicit relationship given by Equation (37). It has also been demonstrated in Reference 23 that the critical time step for the DDEM remains unchanged with respect to the SDEM. To establish the convergence criterion of the iterative scheme, the general form of the iterative scheme presented in Equation (37) is transformed into the following recursive relationship for the successive differences between the approximations of the contact forces, cf.…”

Section: Formulation Of the Ddemmentioning

confidence: 93%

“…It has been shown in Reference 23 that the stability of the explicit DDEM solution scheme is conditionally stable. The stability is restricted by the critical time step of the explicit time integration and the convergence limit of the iterative solution of an implicit relationship given by Equation (37).…”

Section: Formulation Of the Ddemmentioning

confidence: 99%

“…To establish the convergence criterion of the iterative scheme, the general form of the iterative scheme presented in Equation (37) is transformed into the following recursive relationship for the successive differences between the approximations of the contact forces, cf. Reference 23:

F_{c}^{(n, k + 1)} - F_{c}^{(n, k)} = B (F_{c}^{(n, k)} - F_{c}^{(n, k - 1)}) .

…”

Section: Formulation Of the Ddemmentioning

confidence: 99%

“…It has also been shown in Reference 22 that the DDEM allows obtaining a broader range of the macroscopic Poisson's ratio in comparison to the SDEM. Numerical properties of the algorithm of the DDEM with circular discs have been investigated thoroughly by Madan et al 23 It has been shown that the explicit DDEM algorithm is conditionally stable. Its stability is restricted by the critical time step, which is the same as in the SDEM, and by the convergence criterion of the iterative solution of the contact forces.…”

Section: Introductionmentioning

confidence: 99%

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3D formulation of the deformable discrete element method

Rojek

Nosewicz

Thoeni

2021

Numerical Meth Engineering

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This work presents a 3D extension of the deformable discrete element method (DDEM) developed previously for 2D problems. The 3D formulation employs spherical particles. The particle deformation is made up of a global and local deformation mode. The global mode is assumed to be produced by uniform stress due to the contact forces. Particle deformability yields a nonlocal contact model, in which one contact between particles is influenced by contacts with other particles. It also leads to the formation of new contacts in the particle assembly. The DDEM affects the behavior of the granular material at the macroscopic level and gives new possibilities in material modeling by the discrete element method (DEM). The new algorithm is verified on a unconfined uniaxial compression test of a cuboid specimen discretized with equal‐size bonded particles aligned in a simple cubic pattern using an analytical solution. Enhanced modeling capabilities are presented by simulating cylindrical specimens discretized with a nonuniform size of bonded particles. The micro–macro relationships for elastic parameters are obtained. It is shown that the DDEM extends the range of the Poisson's ratio achievable with the DEM. Additional simulations are performed to determine the stability limits of the DDEM.

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Section: Formulation Of the Ddemmentioning

confidence: 93%

Section: Formulation Of the Ddemmentioning

confidence: 99%

F_{c}^{(n, k + 1)} - F_{c}^{(n, k)} = B (F_{c}^{(n, k)} - F_{c}^{(n, k - 1)}) .

…”

Section: Formulation Of the Ddemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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3D formulation of the deformable discrete element method

Rojek

Nosewicz

Thoeni

2021

Numerical Meth Engineering

Self Cite

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“…In recent years, there have been different efforts to solve this problem by introducing the deformability of discrete elements. We can mention the work of Brodu et al [12], Rojek et al [13,14], Celigueta et al [15] and others. In these works, the idea of the deformability of an element (that is, changes in its volume and shape during deformation of contacts) is implemented in various forms.…”

Section: Introductionmentioning

confidence: 92%

The development of the formalism of movable cellular automata for modeling the nonlinear mechanical behavior of viscoelastic materials

Shilko¹,

Dudkin²,

Grigoriev³

2019

EPJ Web Conf.

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The paper is devoted to the development of the formalism of the computational method of discrete elements (DEM) for describing the mechanical behavior of consolidated viscoelastic materials. We considered an advanced implementation of DEM, namely, the method of movable cellular automata (MCA). A feature of this implementation of DEM is the use of a generalized many-body formulation of the relations for the forces of element-element interaction. 3D numerical models of viscoelastic material with a spectrum of relaxation times (Kelvin and Maxwell models, the standard model of elastomers, and others) were developed within the formalism of MCA. The correctness of the developed discrete element formalism and its applicability for modeling the processes of deformation and fracture of viscoelastic materials under dynamic loading are shown using the standard model of elastomers as an example. The relevance of the results is determined by the prospects for the further development of DEM and its application to study and predict the mechanical response of viscoelastic materials of various nature under dynamic loading including contact problems.

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Development of optimal L-PBF process parameters using an accelerated discrete element simulation framework

Aarab,

Dorussen,

Poelsma

et al. 2024

Granular Matter

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Laser Powder Bed Fusion (L-PBF) has immense potential for the production of complex, lightweight, and high-performance components. The traditional optimization of process parameters is costly and time-intensive, due to reliance on experimental approaches. Current numerical analyses often model single-line scans, while it is necessary to model multiple fully scanned layers to optimize for bulk material quality. Here, we introduce a novel approach utilizing discrete element simulations with a ray tracing-modeled laser heat source. Our approach significantly reduces the cost and time consumption compared to conventional optimization methods. GPU acceleration enables efficient simulation of multiple layers, resulting in parameters optimized for bulk material. In a case study, parameters were optimized for AlSi10Mg in just 5 days, a process that would have taken over 8 months without GPU acceleration. Experimental validation affirms the quality of the optimized process parameters, achieving an optical density of 99.91%. Graphical Abstract Optimization using the accelerated simulation yielded an optimized parameter set within 5 days. This resulted in a part with an optical density of 99.91%.

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Convergence and stability analysis of the deformable discrete element method

Cited by 10 publications

References 20 publications

3D formulation of the deformable discrete element method

3D formulation of the deformable discrete element method

The development of the formalism of movable cellular automata for modeling the nonlinear mechanical behavior of viscoelastic materials

Development of optimal L-PBF process parameters using an accelerated discrete element simulation framework

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