M. Steffen¹, P.C. Wallstedt², J.E. Guilkey^2,3, R.M. Kirby¹, M. Berzins¹

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.2, pp. 107-128, 2008, DOI:10.3970/cmes.2008.031.107

Abstract The Material Point Method (MPM) has shown itself to be a powerful tool in the simulation of large deformation problems, especially those involving complex geometries and contact where typical finite element type methods frequently fail. While these large complex problems lead to some impressive simulations and solutions, there has been a lack of basic analysis characterizing the errors present in the method, even on the simplest of problems. The large number of choices one has when implementing the method, such as the choice of basis functions and boundary treatments, further complicates this error analysis.\newline In More >

J.N. Johnson¹, J.M. Owen²

CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.3, pp. 165-188, 2007, DOI:10.3970/cmes.2007.022.165

Abstract In this paper, we propose a Meshless Local Petrov-Galerkin method for studying the diffusion of a magnetic field within a non-magnetic (μ = μ₀) conducting medium with non-homogeneous and anisotropic electrical resistivity. We derive a local weak form for the magnetic diffusion equation and discuss the effects of different trial/test functions and nodal spacings on its solution. We then demonstrate that the method produces convergent results for several relevant one-dimensional test problems for which solutions are known. This method has the potential to be combined with other mesh-free methods such as Smoothed Particle Hydrodynamics (SPH) to More >

A. Sellier¹

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.2, pp. 105-132, 2007, DOI:10.3970/cmes.2007.021.105

Abstract We examine the low-Reynolds-number migration of a conducting and arbitrarily-shaped solid particle freely immersed in a metal liquid of different conductivity when subject to uniform ambient electric and magnetic fields. The boundary formulation established elsewhere for an insulating particle is extended and the incurred particle's rigid-body motion is then obtained by determinating a very few surface quantities on the particle's surface. The behavior of either oblate or prolate conducting spheroids is analytically investigated and the poposed procedure for the challenging case of other non-trivial geometries is implemented and benchmarked against those solutions. The numerical implementation More >

A. J. C. Crespo¹, M. Gómez-Gesteira¹, R. A. Dalrymple²

CMC-Computers, Materials & Continua, Vol.5, No.3, pp. 173-184, 2007, DOI:10.3970/cmc.2007.005.173

Abstract Smoothed Particle Hydrodynamics is a purely Lagrangian method that can be applied to a wide variety of fields. The foundation and properties of the so called dynamic boundary particles (DBPs) are described in this paper. These boundary particles share the same equations of continuity and state as the moving particles placed inside the domain, although their positions and velocities remain unaltered in time or are externally prescribed. Theoretical and numerical calculations were carried out to study the collision between a moving particle and a boundary particle. The boundaries were observed to behave in an elastic More >

V.G. Kozlov^1,2, A.A. Ivanova³, P. Evesque¹

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.3, pp. 203-210, 2006, DOI:10.3970/fdmp.2006.002.203

Abstract Sedimentation of granular matter in a vertical channel filled with a viscous liquid and subject to longitudinal translational vibration is studied, starting froma compact suspension. A new vibrational effect is foundexperimentally and described theoretically; it is the formation of blocks (with a relatively high density) of sedimenting granular matter with stable lower and upper horizontal demarcations and a sharp density discontinuity. Owing to this phenomenon the sedimentation velocity of such granular matter is reduced. A new theoreticalmodel based on viscous vibrational particle interactionin the limit of concentrated suspensions is elaborated, assuming particle-particle attraction in direction More >

R. Vignjevic¹, T. De Vuyst², J. C. Campbell¹

CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.1, pp. 35-48, 2006, DOI:10.3970/cmes.2006.013.035

Abstract An approach to the treatment of contact problems involving frictionless sliding and separation under large deformations in meshless methods is proposed. The method is specially suited for non-structured spatial discretisation. The contact conditions are imposed using a contact potential for particles in contact. Inter-penetration is checked as a part of the neighbourhood search. In the case of conventional SPH contact conditions are enforced on the boundary layer 2h thick while in the case of the normalized SPH contact conditions are enforced for the particles lying on the contact surface. The implementation of the penalty based More >