so who wants to help me solve a multivariable nonlinear ODE?

[Fenixgoon]

damned homework 🙁 it is a grad class though

we're getting into the basics of plasticity theory and ugh, the equations are 100x worse than elasticity. at least simple elastic bounds are pretty easy to compute. plasticity, while infinitely more interesting, is also infinitely harder 🙁

 

[dullard]

I have no time, but you should at least post the equation for those people who do have the time.

 

[Fenixgoon]

Originally posted by: dullard
I have no time, but you should at least post the equation for those people who do have the time.

S(t+dt) = C*[E(t+dt) - Ep(t)] - {[1.5*Eo*dt/Seq(t+dt)]*(Seq(t+dt)/Sy)^1/m}*C*Sdev(t+dt)

S = stress (2nd order tensor)
C = elastic stiffnes (4th order tensor)
E = total strain (2nd order tensor)
Ep = plastic strain (2nd order tensor)
Eo = reference strain rate (0.001 per sec)
Seq = equivalent stress = sqrt(1.5* SijSij)
Sy = yield stress (200 MPa)
Sdev = deviatoric stress
Eeq = equivalent strain = sqrt(0.66666* EijEij)
Epeq = equivalent plastic strain rate = Eo*(Seq/Sy)^1/m

strain E11 = unknown
strain E22 = 0
strain E33 = -0.001*t
stress S22 = unknown

plastic strain rate = 1.5*(Epeq/Seq)*Sdev

i think that's everything 😛

apparently we end up with 3 equations and 3 unknowns, but they're nonlinear. tomorrow will be fun 🙂