By Colin Thornton
This ebook is dedicated to the Discrete point approach (DEM) approach, a discontinuum modelling method that takes under 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 structures within which the particle-particle interactions are collisional and compact structures of debris with a number of enduring contacts.
The ebook offers an in depth and exact clarification of the theoretical historical past of DEM. touch mechanics theories for elastic, elastic-plastic, adhesive elastic and adhesive elastic-plastic particle-particle interactions are provided. different touch strength versions also are mentioned, together with corrections to a few of those types as defined within the literature, and demanding parts of additional study 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 impression with a wall. this is often mentioned utilizing the output acquired from the touch strength types defined prior, that are in comparison for elastic and inelastic collisions. furthermore, additional perception is supplied for the impression of adhesive debris. the writer then strikes directly to give you the result of chosen DEM purposes to agglomerate affects, fluidised beds and quasi-static deformation, demonstrating that the DEM strategy can be utilized (i) to imitate experiments, (ii) discover parameter sweeps, together with proscribing values, or (iii) establish new, formerly unknown, phenomena on the microscale.
In the DEM purposes the emphasis is on getting to know new details that boosts 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 end up too complex for functional implementation. The publication should be of curiosity to educational and commercial researchers operating in particle technology/process engineering and geomechanics, either experimentalists and theoreticians.
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Additional info for Granular Dynamics, Contact Mechanics and Particle System Simulations: A DEM study
The distribution of the tangential traction at the start of unloading is given by Eq. 19a, b). To obtain the traction distribution during unloading, a negative traction is superimposed of the form Á À 2 Á i 3μFn hÀ 2 2 1=2 2 1=2 qðr Þ ¼ À2 À r À c À r a f or 0 2π a3 Á1=2 3μFn À 2 qðr Þ ¼ À2 f or c r a À r2 3 2π a r c ð3:25aÞ ð3:25bÞ a where c r a defines the annulus of counterslip. The resultant traction distribution is obtained by adding Eqs. 25a, b) to give Á1=2 À Á1=2 À 2 Á1=2 i 3μFn hÀ 2 À 2 c2 À r 2 þ b À r2 a À r2 qð r Þ ¼ À 3 2π a Á À 2 Á i 3μFn hÀ 2 2 1=2 2 1=2 À r À 2 c À r f or b r a qð r Þ ¼ À 2π a3 Á1=2 3μFn À 2 qð r Þ ¼ À f or c r a a À r2 3 2π a f or 0 r b ð3:26aÞ c ð3:26bÞ ð3:26cÞ which is illustrated in Fig.
Until this problem is resolved an alternative and simpler model, which might be appropriate for hard materials, is to assume that no peeling process occurs. In this case, the tangential stiffness is kt ¼ 8G∗ a ð3:89Þ where the contact radius a is obtained from Eq. 75) and the sliding criterion is Ft ¼ μFnH in which FH n is defined by Eq. 76). 4 51 Adhesive, Elastic-Plastic Interactions Two contact mechanics based approaches to the modelling of adhesive, elasticplastic particle interactions have been reported in the literature by Martin (2003) and by Thornton and Ning (1998).
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. This is also illustrated in Fig. 8, which shows the evolution of the normal contact pressure distribution for the impact of an elastic sphere against an elastic-perfectly plastic half-space, obtained from finite element analysis by Wu et al. (2003). Thornton (1997) proposed that the evolution of the contact pressure distribution, described above and illustrated in Fig.