Combining the modified discrete element method with the virtual element method for fracturing of porous media

Nilsen, Halvor Møll; Larsen, I.; Raynaud, Xavier

doi:10.1007/s10596-017-9668-6

Cited by 4 publications

(8 citation statements)

References 35 publications

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“…Note that the principle of action and reaction is encoded in the fact that ι c − ,F + ι c + ,F = 0 for all F = ∂c − ∩ ∂c + ∈ F i . Finally, putting everything together, we infer that the the first equation in (19) becomes…”

Section: Interpretation As a Discrete Element Methodsmentioning

confidence: 98%

“…In this section we rewrite the first equation in (19) as a particle method by introducing the dofs of the discrete displacement u h (t) ∈ V hD attached to the mesh cells and to the boundary vertices lying on the Neumann boundary, which we write U DEM := (U p (t)) p∈P with P := C ∪ Z ∂ N and…”

Section: Interpretation As a Discrete Element Methodsmentioning

confidence: 99%

“…Note that the plasticity relations in (19) are enforced cellwise, i.e., a mesh cell c ∈ C is either in the elastic state or in the plastic state depending on the value of ϕ(Σ c (u h ), p c ).…”

Section: Discrete Problemmentioning

confidence: 99%

“…Note also the possibility to use DEM only in a limited zone, where crack occurs for instance, in order to mitigate these issues. For example, a modified DEM (MDEM) has been coupled with a consistent virtual element method (VEM) for elasticity to discretize fracturing porous media [19].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A variational discrete element method for quasi-static and dynamic elasto-plasticity

Marazzato,

Ern,

Monasse

2019

Preprint

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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 quasi-static and dynamic elasto-plasticity, and in the latter situation, a pseudo-energy conserving time-integration method is employed. The computational cost of the timestepping 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 quasi-static and dynamic elasto-plastic evolutions.

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Section: Interpretation As a Discrete Element Methodsmentioning

confidence: 98%

Section: Interpretation As a Discrete Element Methodsmentioning

confidence: 99%

Section: Discrete Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A variational discrete element method for quasi-static and dynamic elasto-plasticity

Marazzato,

Ern,

Monasse

2019

Preprint

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show abstract

“…Note also the possibility to use DEM only in a limited zone, where crack occurs, for instance, in order to mitigate these issues. For example, a modified DEM has been coupled with a virtual element method for elasticity to discretize fracturing porous media 9 …”

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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Virtual elements for sound propagation in complex poroelastic media

2021

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We develop a novel Virtual Element Method (VEM) to resolve the mixed Biot displacement pressure formulation governing wave propagation in porous media. Within this setting, the weak form of the governing equations is discretized using implicitly defined canonical basis functions and the resulting integral forms are computed using appropriate polynomial projections. The projection operator accounting for the solid, fluid, and coupling phases of the problem are presented. Different boundary, interface and excitation conditions are accounted for. The convergence behaviour, accuracy, and efficiency of the method is examined through a set of illustrative examples. A node insertion strategy is proposed to resolve non-conforming interfaces that naturally arise in multilayered systems. Finally the power of the VEM is exploited to examine the acoustic response of composite materials with periodic and non-periodic inclusions of complex geometries.

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Combining the modified discrete element method with the virtual element method for fracturing of porous media

Cited by 4 publications

References 35 publications

A variational discrete element method for quasi-static and dynamic elasto-plasticity

A variational discrete element method for quasi-static and dynamic elasto-plasticity

A variational discrete element method for quasistatic and dynamic elastoplasticity

Virtual elements for sound propagation in complex poroelastic media

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