Computational Contact and Impact Mechanics

Laursen, Tod A.

doi:10.1007/978-3-662-04864-1

Cited by 389 publications

(529 citation statements)

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“…It is able to model the geometry of each particle and to capture the mechanical response without the necessity of complex constitutive laws; the global response of a set of particles is a consequence of multiple contact/friction interactions among a large number of particles (micro-mechanics). Multiple simultaneous and long-lasting contacts might be produced generating particle clusters; an appropriate technique to simulate the contact interaction among particles is penalization, see [25]. This technique does not increase the number of unknowns and produces only small particle overlaps, see Fig.…”

Section: Discrete Element Methodsmentioning

confidence: 99%

“…Due to the dissipative character of the drag forces, the equations are solved using the time integration scheme from [24], which offers a stable and physically consistent framework to model dissipation phenomena. Finally, the contact interactions between particles are simulated using the penalization technique from [25]. This paper is centered on the numerical simulation of the ASTM D-422 [26] sedimentation test; in addition and for comparison purposes the less used buoyancy, [27,28], and pipette [29] tests are also studied.…”

Section: Introductionmentioning

confidence: 99%

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Numerical sedimentation particle-size analysis using the Discrete Element Method

Bravo

Pérez-Aparicio

Gómez‐Hernández

2015

Advances in Water Resources

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Sedimentation processes are generally modelled using an equivalent continuum approach based on the coupling of the Navier-Stokes and the advection-dispersion equations; the sediment concentration within an elementary fluid volume is the variable of interest. Continuous advances in computational capabilities have brought up a new type of modelling that simulates the individual motion and contact interactions of grains: the Discrete Element Method (DEM). In this work, DEM interacts with the simulation of flow using the well known one-way-coupling method, a computationally affordable approach for the time-consuming numerical simulation of the ASTM-D422, buoyancy and pipette sedimentation tests. These tests are used in the laboratory to determine the particle-size distribution of fine-grained aggregates. Five samples with different particle-size distributions are modelled by about six million rigid spheres projected on two-dimensions, with diameters ranging from 2.5 × 10 −6 m to 70 × 10 −6 m, forming a water suspension in a sedimentation cylinder. DEM simulates the particle's movement considering laminar flow interactions of hydrostatic thrust, drag and lubrication forces. The simulation provides the temporal/spatial distributions of densities and concentrations of the suspension.The numerical simulation cannot replace the laboratory tests since it needs the final granulometry as initial data; but, as the results show, these simulations can identify the strong and weak points of each method and eventually recommend useful variations and draw conclusions on their validity, aspects very difficult to achieve in the laboratory.

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Section: Discrete Element Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical sedimentation particle-size analysis using the Discrete Element Method

Bravo

Pérez-Aparicio

Gómez‐Hernández

2015

Advances in Water Resources

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“…The discrete action functional S ns d (φ 1d , φ 2d ) is of the form (76). Given the discrete impenetrability condition See Demoures et al [30] for the full discrete equations of motion outside of contact.…”

Section: Numerical Testsmentioning

confidence: 99%

Multisymplectic Variational Integrators for Nonsmooth Lagrangian Continuum Mechanics

Demoures

Gay–Balmaz

Raţiu

2016

Forum of Mathematics, Sigma

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This paper develops the theory of multisymplectic variational integrators for nonsmooth continuum mechanics with constraints. Typical problems are the impact of an elastic body on a rigid plate or the collision of two elastic bodies. The integrators are obtained by combining, at the continuous and discrete levels, the variational multisymplectic formulation of nonsmooth continuum mechanics with the generalized Lagrange multiplier approach for optimization problems with nonsmooth constraints. These integrators verify a spacetime multisymplectic formula that generalizes the symplectic property of time integrators. In addition, they preserve the energy during the impact. In the presence of symmetry, a discrete version of the Noether theorem is verified. All these properties are inherited from the variational character of the integrator. Numerical illustrations are presented.

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“…In Betsch and Hesch [3], this approach has been successfully applied to the node-to-segment (NTS) contact description. The NTS method is currently the prevalent contact formulation in finite element analysis, see the books by Laursen [4] and Wriggers [5].…”

Section: Introductionmentioning

confidence: 99%

A mortar method for energy‐momentum conserving schemes in frictionless dynamic contact problems

Hesch

Betsch

2008

Numerical Meth Engineering

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SUMMARYIn the present work the mortar method is applied to planar large deformation contact problems without friction. In particular, the proposed form of the mortar contact constraints is invariant under translations and rotations. These invariance properties lay the foundation for the design of energy-momentum timestepping schemes for contact-impact problems. The iterative solution procedure is embedded into an active set algorithm. Lagrange multipliers are used to enforce the mortar contact constraints. The solution of generalized saddle point systems is circumvented by applying the discrete null space method. Numerical examples demonstrate the robustness and enhanced numerical stability of the newly developed energymomentum scheme.

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Computational Contact and Impact Mechanics

Cited by 389 publications

References 0 publications

Numerical sedimentation particle-size analysis using the Discrete Element Method

Numerical sedimentation particle-size analysis using the Discrete Element Method

Multisymplectic Variational Integrators for Nonsmooth Lagrangian Continuum Mechanics

A mortar method for energy‐momentum conserving schemes in frictionless dynamic contact problems

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