By Colin Thornton
This e-book is dedicated to the Discrete aspect strategy (DEM) method, a discontinuum modelling technique that takes into consideration the truth that granular fabrics are composed of discrete debris which engage with one another on the microscale point. This numerical simulation process can be utilized either for dispersed platforms within which the particle-particle interactions are collisional and compact structures of debris with a number of enduring contacts.
The ebook presents an intensive and designated clarification of the theoretical history of DEM. touch mechanics theories for elastic, elastic-plastic, adhesive elastic and adhesive elastic-plastic particle-particle interactions are awarded. different touch strength types also are mentioned, together with corrections to a couple of those versions as defined within the literature, and significant components of additional learn are pointed out.
A key factor in DEM simulations is whether a code can reliably simulate the easiest of structures, particularly the only particle indirect effect with a wall. this is often mentioned utilizing the output got from the touch strength types defined past, that are in comparison for elastic and inelastic collisions. moreover, additional perception is supplied for the impression of adhesive debris. the writer then strikes directly to give you the result of chosen DEM functions to agglomerate affects, fluidised beds and quasi-static deformation, demonstrating that the DEM method can be utilized (i) to imitate experiments, (ii) discover parameter sweeps, together with proscribing values, or (iii) determine new, formerly unknown, phenomena on the microscale.
In the DEM functions the emphasis is on gaining knowledge of new details that reinforces our rational realizing of particle platforms, that may be extra major than constructing a brand new continuum version that encompasses all microstructural features, which might probably turn out too advanced for useful implementation. The e-book should be of curiosity to educational and business researchers operating in particle technology/process engineering and geomechanics, either experimentalists and theoreticians.
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Extra resources for Granular Dynamics, Contact Mechanics and Particle System Simulations: A DEM study
85) becomes zero. Hence, ÂÀ Á Ã1=2 Ftc ¼ 4 Fn Fnc þ F2nc G* =E* ð3:86Þ It was argued by Savkoor and Briggs (1977) that when Ft ¼ Ftc the contact area would collapse to the Hertzian value. However, at Ft ¼ Ftc Eq. 85) reduces to a3 ¼ 3R* ðFn þ 2Fnc Þ 4E* ð3:87Þ and it was suggested by Thornton (1991) that, following peeling the micro-slip model of Mindlin and Deresiewicz (1953) could apply, see Sect. 2, by replacing Fn by ðFn þ 2Fn Þ and using Eq. 87) to define the contact radius. It then follows that the sliding condition becomes Ft ¼ μðFn þ 2Fnc Þ ð3:88Þ However, although experimental evidence of peeling has been provided for rubber (Savkoor and Briggs 1977) results obtained by Homola et al.
Tc ¼ πRmin πRmin ¼ vR λ rﬃﬃﬃﬃ ρ G ð2:16Þ where Rmin is the minimum particle radius, ρ is the particle density, G is the particle shear modulus, vR is the Rayleigh wave speed and λ can be obtained from À 2 À λ2 Á4 À Á ¼ 16 1 À λ2 1 À λ2 ! 1 À 2ν 2ð 1 À ν Þ ð2:17Þ which can be approximated by λ ¼ 0:8766 þ 0:1631ν ð2:18Þ where ν is the Poisson’s ratio of the particle. 4 Damping Unlike most other DEM codes, the Birmingham code does not include a dashpot force as part of the contact force. There are, however, dashpots that are used to dissipate a small amount of energy due to elastic wave propagation through a solid particle.
Further compression results in a spreading of the plastic deformation zone below the surface and a slight modification of the shape of the contact pressure distribution as the maximum contact pressure increases further. 4 times the yield stress, the plastic deformation zone in the substrate reaches the contact surface at the perimeter of the contact area. Beyond this point, further compression results in a significant change in the form of the pressure distribution. Over an increasing central portion of the contact area the contact pressure becomes almost constant with only a slight increase in the pressure at the centre of the contact area.
Granular Dynamics, Contact Mechanics and Particle System Simulations: A DEM study by Colin Thornton