Accurate modelling of the elastic behavior of a continuum with the Discrete Element Method

Celigueta, Miguel Ángel; Latorre, Salvador; Arrufat, Ferrán; Oñate, Eugenio

doi:10.1007/s00466-017-1453-9

Cited by 39 publications

(34 citation statements)

References 19 publications

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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: 91%

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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Section: Introductionmentioning

confidence: 91%

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 main difficulty in DEM consists in deriving a correct set of forces between elements to discretize the continuous equations (in the present case, dynamic elastoplasticity). DEM originally used sphere packing to discretize the domain 5 and were forced to fit parameters in order to obtain relevant values for the Young modulus E or the Poisson ratio

ν

6,7 . Moreover, simulating a material with a Poisson ratio

ν

larger than 0.3 met with difficulties 8 .…”

Section: Introductionmentioning

confidence: 99%

A variational discrete element method for quasistatic and dynamic elastoplasticity

Marazzato

Ern

Monasse

2020

Numerical Meth Engineering

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Summary We propose a new discrete element method supporting general polyhedral meshes. The method can be understood as a lowest‐order discontinuous Galerkin method parametrized by the continuous mechanical parameters (Young's modulus and Poisson's ratio). We consider quasistatic and dynamic elastoplasticity, and in the latter situation, a pseudoenergy conserving time‐integration method is employed. The computational cost of the time‐stepping method is moderate since it is explicit and used with a naturally diagonal mass matrix. Numerical examples are presented to illustrate the robustness and versatility of the method for quasistatic and dynamic elastoplastic evolutions.

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“…Among these models, challenging problems often concern the ability of DEM to reproduce complex fracture phenomena such as coupled mode fracture, internal friction, compressive hardening or fracture softening. Indeed, such DEM models are not able to model easily simple elastic behaviour (19,20) defined by only two physical (apparent) parameters : a Young's modulus and a Poisson's ratio. The number of local parameters to manage is high regarding the few number of apparent parameters.…”

Section: Introduction Motivation Of Studymentioning

confidence: 99%

A novel DEM approach for modeling brittle elastic media based on distinct lattice spring model

Debenath

Girardot

Hubert

2019

Computer Methods in Applied Mechanics and Engineering

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The Discrete Element Method (DEM), also known as Distinct Element Method (DEM), is extensively used to study divided media such as granular materials. When brittle failure occurs in continuum such as concrete or ceramics, the considered media can be viewed as divided. In such cases, DEM offers an interesting way to study and simulate complex fracture phenomena such as crack branching, crack extension, crack deviation under coupled mode or crack lip closure with friction. The fundamental difficulty with DEM is the inability of the method to deal directly with the constitutive equations of continuum mechanics. DEM uses forcedisplacement interaction laws between particles instead of stress-strain relationships. Generally, this difficulty is bypassed by using inverse methods, also known as calibration processes, able to translate macroscopic stress-strain relationships into local force-displacement interaction laws compatible within DEM frameworks. However, this calibration process may be fastidious and really hard to manage. The presented work proposes to improve the Distinct Lattice Spring Model in order to deal with non-regular domains, by using Voronoi cells, which allows to completely fill the volume space of discrete domains. With this approach, the rotational effects must be included in the contact formulation, which enables the management of large rigid body rotations. This work also introduces a simple

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Accurate modelling of the elastic behavior of a continuum with the Discrete Element Method

Cited by 39 publications

References 19 publications

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

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

A variational discrete element method for quasistatic and dynamic elastoplasticity

A novel DEM approach for modeling brittle elastic media based on distinct lattice spring model

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