ESyS-Particle

meaning of poissonsRatio in FrictionPrms

Asked by Robert Sarracino

I would like to clarify the meaning of the parameter poissonsRatio in FrictionPrms. As I understand it once a bond is broken lateral, or sliding, motion between two particles is governed only by the two friction parameters. The two elastic parameters, youngsModulus and poissionsRatio would, then, determine only radial interaction -- ie, the repulsive force two particles would experience as a function of their distance of overlap.

Because of poissonsRatio this repulsive force should, then, be a function not only of the distance of overlap, but of the 'confining' (lateral) forces on the two particles. for instance, if two overlapping particles had no confining forces on them the repulsive force between them would be

Fx = E*A*(del l) / L, where (del l) is the amount of overlap.

If, however, the confining forces were the same in all directions -- ie, the particles were subject to a 'pressure' due to neighboring particles or confining walls -- the repulsive force between them would be

Fx = E*A*(del l) / (1-2*nu)*L

if the confining forces were in between, the repulsive force would be

Fx = E*A*(del l) / L + nu*A*(sigmay + sigmaz), where sigmay and sigmaz are respectively the stresses on the particles along the y and z axes.

Is this correct?

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Dion Weatherley (d-weatherley) said : 		#1

Hi Robert,

Frictional interactions in ESyS-Particle are implemented in the usual manner for DEM models: when two unbonded particles are in contact, they experience both elastic repulsion and resistance to shear motion. Notionally this involves two linear elastic springs, one for elastic repulsion:
Fn = E.A (del I) / L
and one for shear motion:
Fs = G A (del s) / L
where G = E / (2(1+nu)) and (del s) is the incremental tangential motion between the two particles since the contact was established.

The "frictional" aspect of the interaction is implemented as a cap on the maximum amplitude of the elastic shear force (Fs). Specifically, if Fs > mu.Fn, one sets Fs = mu.Fn and slip between the two particles ensues. If the elastic shear force Fs < mu.Fn then the contact is purely elastic and no slip between the two particles occurs. Thus, both the "stick" and "slip" phases of frictional contacts is captured.

It should now be obvious that poissonsRatio (in combination with youngsModulus) determines the shear stiffness (G.A/L) for frictional interactions.

Cheers,

Dion

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Robert Sarracino (robert-sarracino) said : 		#2

Thanks, Dion.