chiara modenese said: (by the date of Sun, 4 Jul 2010 17:27:04 +0000) > Hi Janek, thanks for your anwer. > > W=∫k*x*dx = k*x²/2 > > Wᵢ = (Fᵢ+Fᵢ₋₁)*Δxᵢ⁄2 > > > Not sure to understand the point.
I wanted to say that I was actually doing a numerical integration with trapezoidal rule instead of using analytical method. > Using trapezoidal rule, hence working out > the net work done by the spring in an incremental way, or either taking the > value of the integral should give you the same result. This might be not true for slipping - we are entering plastic behaviour regime. See below. > Perhaps the mistake is in the computation of the plastic dissipation. But I > have not found out why :( I will try again, maybe this time I'll help you? Let me rewrite this line from elasticEnergy(): energy += 0.5*(phys->normalForce.squaredNorm()/phys->kn + phys->shearForce.squaredNorm()/phys->ks); into something more readable: E += (Fn²⁄kn + Fs²⁄ks)⁄2 The normal part Wn =∑ (Fnᵢ+Fnᵢ₋₁)*(xᵢ-xᵢ₋₁)⁄2 should be rather equivalent to En+=(Fn²⁄kn)⁄2 But slipping might be actually different in those two approaches: Ws =∑ (Fsᵢ+Fsᵢ₋₁)*(sᵢ-sᵢ₋₁)⁄2 and this: Es+=(Fs²⁄ks)⁄2 That is because the slip distance is implicitly calculated in formula (Fs²⁄ks)⁄2, because after all: Fs²⁄ks = (ks*s)²/ks = ks*s² and I'm afraid that maybe s≠∑(sᵢ-sᵢ₋₁) , because sᵢ is supposed to follow the slipping path (or slip "trace") on the surface of a sphere, while s is calculated from current value Fs. To say in other words, I think that when spheres start to slip on each other and Fs stays constant, the increment of s which stays inside constant Fs differs from the path increment on the sphere's surface slipping path sᵢ-sᵢ₋₁. I'm not sure if I worded myself clearly.... I hope that you can understand what I mean? IIRC Vaclav was calculating somewhere the total accumulated _geometrical_ path of one sphere on another sphere. best regards -- Janek Kozicki http://janek.kozicki.pl/ | _______________________________________________ Mailing list: https://launchpad.net/~yade-users Post to : yade-users@lists.launchpad.net Unsubscribe : https://launchpad.net/~yade-users More help : https://help.launchpad.net/ListHelp
