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> I wanted to say that I was actually doing a numerical integration > with trapezoidal rule instead of using analytical method. > Yes, this was clear to me. > > > 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. > Jan, I think there is some misunderstanding here. Or maybe you are not updated with the way we calculate plastic dissipation. We do it _incrementally_. See the code in plasticDissipation() and see also attached files I sent to Bruno a while ago which explain more analytically the concept. The elastic part can be always computed in a once analytically since anyway the friction force cannot overcome the maximum value. Therefore what we compute in elasticEnergy is only elastic part, both for shear and normal direction. > > > > 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. > Sure, see above. > > 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? It is clear and, in fact, it is also what we are doing. That is why I am struggling because it should give the expected result, total energy constant. I will try again.. > > > 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<https://launchpad.net/%7Eyade-users> > Post to : yade-users@xxxxxxxxxxxxxxxxxxx > Unsubscribe : https://launchpad.net/~yade-users<https://launchpad.net/%7Eyade-users> > More help : https://help.launchpad.net/ListHelp >
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Energy_1.pdf
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Energy_2.pdf
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