Contact force calculation

In the Globals subsection, the contact models for particle-to-particle and particle-to-geometry interactions are defined (see C in Figure 7.15). EDEM has a number of built-in contact models such as Hertz-Mindlin no-slip model (i.e., Hertz model is used for normal contact force calculations [see Section 7.1.4.1.2] and Mindlin no-slip model is used for tangential contact force calculations [Section 7.1.4.1.4]), linear-spring model (see Section 7.1.4.1.1), and JKR adhesive model (see Section 7.1.4.2.1). 

The paper discusses the application of dynamic indentation method and apparatus for the evaluation of viscoelastic properties of polymeric materials. The three-element model of viscoelastic material has been used to calculate the rigidity and the viscosity. Using a measurements of the indentation as a function of a current velocity change on impact with the material under test, the contact force and the displacement diagrams as a function of time are plotted. Experimental results of the testing of polyvinyl chloride cable coating by dynamic indentation method and data of the static tensile test are presented. 

Fig. 4. Schematic of the JKR treatment of contact mechanics calculations. The point (, a, P) corresponds to the actual state under the action of interfacial forces and applied load P. P is the equivalent Hertzian load corresponding to contact radius a between the two surfaces, ( o, P) and (S], a, P ) are the Hertzian contact points. The net stored elastic energy and displacement S are calculated as the difference of steps 1 and 2.

The methodology discussed previously can be applied to the study of colloidal suspensions where a number of different molecular forces and hydrodynamic effects come into play to determine the dynamics. As an illustration, we briefly describe one example of an MPC simulation of a colloidal suspension of claylike particles where comparisons between simulation and experiment have been made [42, 60]. Experiments were carried out on a suspension of AI2O3 particles. For this system electrostatic repulsive and van der Waals attractive forces are important, as are lubrication and contact forces. All of these forces were included in the simulations. A mapping of the MPC simulation parameters onto the space and time scales of the real system is given in Hecht et al. [42], The calculations were carried out with an imposed shear field. 

The calculation of the contact force between two particles is actually quite involved. A detailed model for accurately computing contact forces involves complicated contact mechanics (Johnson, 1985), the implementation of which is extremely cumbersome. Many simplified models have therefore been proposed, which use an approximate formulation of the interparticle contact force. The simplest one was originally proposed by Cundall and Strack (1979), where a linear-spring and dashpot model is employed to calculate the contact forces (see Fig. 11 and 12). In this model, the normal component of the contact force between two particles a and b can be calculated by... 

Therefore, for Hertzian contact, using Eq. (2.75) and Eq. (2.76), the maximum radius of contact rc, the maximum approaching distance a, and the corresponding maximum pressure can be calculated on the basis of the contact force, the elastic material properties of the spheres, and the radii of the spheres. 

In the general case of an assembly with a very large number of disks the calculation cycle is as follows the F, = kAn, is applied at each contact point of any disk and the vectorial sum of the contact forces is calculated to yield the net force acting on the disk. However, for an... 

The Discreet-Element Method for an Assembly of Two-dimensional Disks Example 4.2 serves as a simple illustration of the DEM cycling through a force-displacement constitutive response, F, = kAuj and the law of motion, which relates the F, with Xt and, thus, particle motions. In the general case of an assembly with a very large number of disks the calculation cycle is as follows the F, = kAn, is applied at each contact point of any disk and the vectorial sum of the contact forces is calculated to yield the net force acting on the disk. For such an assembly there are both normal and tangential... 

In the pendular state, bonding is localized at the points of particle contact and calculated values of the cohesive force between two particles may be substituted directly for H into eqn. (4) to yield the tensile strength of the assembly. For two particles in contact, H is given by [8,10] ... 

When the gap width between two particles becomes very small, numerical calculations involved in both the bispherical coordinate method and the boundary collocation technique are computationally intensive because the number of terms in the series required to be retained to achieve a desired accuracy increases tremendously. To solve this near-contact motion more effectively and accurately, Loewenberg and Davis [43] developed a lubrication solution for the electrophoretic motion of two spherical particles in near contact along their line of centers with the assumption of infinitely thin ion cloud. The axisymmetric motion of the two particles in near contact can be approximated as the pairwise motion of the spheres in point contact plus a deviation stemming from their relative motion caused by the contact force. The lubrication results agree very well with those obtained from the collocation method. It is shown that near contact electrophoretic interparticle... 

The method is based on Wilhelmy s plate technique for measuring DCAs. The technique involves the measurement of force as a plate is (automatically) immersed into and then emersed from a liquid at a constant rate. The forces (weight) can be plotted as a function of the immersion depth, and, from this, contact angles calculated (Figure 1.29a,b). 

Figure 4.9 Capillary force calculation between two contacting spherical particles having identical radius of Rs. If a liquid completely wets the surfaces of the particles (9 = 0°), then the liquid will condense into the gap around the contact zone, (—r) is the first radius of curvature, and the second radius of curvature is R2 = z by definition, where the distance, z, is as shown in the figure.

Let US consider two spherical emulsion drops approaching each other, which interact through the van der Waals attractive surface force. Sooner or later interfacial deformation will occur in the zone of drop-drop contact. The calculations (138) show that, if the drop radius a is greater than 80 jm, the drop interfaces bend inwards (under the action of the hydrodynamic pressure) and a dimple is formed in the contact zone soon the dimple transforms into an almost plane-parallel film (Fig. 2D). In contrast, if the drop radius... 

Crystals were grown on glass substrates by evaporating a dilute sodium chloride solution. The tip of the AFM was scanned across the surface to locate the crystals and to measure their size from the flat square top surface. The crystals were cubes up to 50 nm in size. Then, the contact force was raised to a high level and the tip was used to break the crystals from the surface. Humidity was found to be very important and was controlled to high precision in the microscope. Once the probe touched a crystal, the lateral force rose to a critical value, then fell as the cube sheared across the surface. The fracture stresses were calculated from the peak force and the crystal interface area, and plotted as a function of crystal size in Fig. 13.11(a). Two striking observations were drawn from this curve in the first place, the stress was much larger than expected for a soft material like NaCI,... 

The new modified value of the contact force vector may now be used in the calculation of the closed-chain joint accelerations as follows ... 

For a more exact evaluation of adhesive force, calculations must be based not on the particle cross-sectional area, but rather on the number of contacts between the particles and the surface. Then the specific force of adhesion of a layer of particles F[ can be expressed by the equation [29] ... 

After holding a dust-covered surface in an atmosphere saturated with carbon tetrachloride vapor for 24 h, 95% of all particles in the 100-120-/xm size range are retained when a detaching force of 1.53 dyn is applied. The capillary forces calculated from Eqs. (IV.38) and (IV.39) when carbon tetrachloride vapor condenses in the contact zone are equal to 1.81 dyn. Apparently, thin layers of nonpolar liquids do not have any disjoining effect. Hence, we do not observe any reduction of the adhesive force due to the action of the liquid interlayer in the contact zone. This confirms the vahdity of Eq. (IV.46) for use in estimating the disjoining effect. 

There are a number of computational models used to investigate granular media. Event-driven or hard-sphere algorithms are based on the calculation of changes from distinct collisions between single grains that are often approximated by spheres, ellipsoids, or polyhedral.MD of soft-particle models are another common way to simulate granular materials. In this approach, the repulsive contact force in normal direction is typically proportional to the particle... 

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