From: Nachiket Gokhale <gokhalen@bu...>  20051226 18:57:32

On Thu, 20051222 at 09:58 0800, li pan wrote: > Hi Nachiket, > Hey Nachiket, > I implemented the algorithm of K.J.Bathe from his book > << Finite element method >>, chapter 6, 1990. The > algorithm is called Total Lagrange Formulation. I > haven't calculated material tangent > modulus. Because I only need stiffness matrix and > second Piolar stress tensor. There must be something > wrong in my implemented algorithm. I have to check it. > Or you could give me some advice. I'm trying to > implement an algorithm for large deformation, which > fill the condition of Viscoelasticity. Hi Pan, As I understand the Total Lagrange formulation, the equations of elasticity (or for that matter viscoelasticity) are solved in the reference configuration. To solve them, one needs to linearize them, since they are nonlinear equations. This linearization requires the calculation of the material tangent modulus. Nachiket. > > best > > pan > >  Nachiket Gokhale <gokhalen@...> wrote: > > > On Wed, 20051221 at 12:38 0600, Roy Stogner > > wrote: > > > On Wed, 21 Dec 2005, li pan wrote: > > > > > > > I used Newton iteration to solve a nonlinear > > elastic > > > > problem. This method is embedded in a Newmark > > implicit > > > > time integration. At the first several timestep > > the > > > > Newton iteration convergenced very well (10 > > steps). > > > > > > Did you see quadratic convergence? > > > > I agree with everything that Roy said. > > > > If it is not too much trouble, could you post the > > constitutive relations > > that you are using?. That is, (strain energy > > function (W), the second > > PiolaKirchhoff tensor (S), and the material tangent > > modulus (C_{IJKL}). > > I ask this just to make sure that you are assembling > > the right > > consistent tangent matrix. > > > > Nachiket. > > > > > > > > > > > > > > > The first thing you ought to check > > > if Newton's method is behaving oddly is whether > > you get quadratic > > > convergence as you approach the root  if not, > > then (assuming your > > > linear solves are accurate enough) your Jacobian > > (i.e. your system > > > matrix, not the geometric Jacobians) is probably > > inconsistent with > > > your residual function. If that happens, your > > iteration can still > > > converge, but the region of convergence may be > > smaller. > > > > > > Other possible problems: > > > > > > You may be starting from a bad initial guess. > > This has happened to me > > > before, when I left junk in a solution vector. > > Depending on whether > > > you're solving for the next timestep's solution or > > for the > > > delta_solution, a relatively safe initial guess > > might be the previous > > > timestep's solution or zero. > > > > > > The nonlinearities in your problem may be so bad > > that the region of > > > covnergence is too small for you to hit with your > > initial guess. In > > > that case you'll want to use a slower but safer > > method (successive > > > approximation, perhaps, or continuation) to get > > close to the root > > > followed by Newton to eliminate the last of your > > error. > > > > > > > The error could be numerical calculation of > > inversing matrix, > > > > because I used simple Gauss elimination. I will > > apply the method of > > > > Petsc. > > > > > > We've had some problems before with LASPACK not > > converging, but Gauss > > > elimination isn't one of them  I often switch to > > complete LU > > > factorization as a preconditioner when I'm trying > > to make sure that > > > the linear solver isn't causing me problems. > > Gauss is bad because > > > it's slow, not because it's inaccurate. > > >  > > > Roy Stogner > > > > > > > > > > > >  > > > This SF.net email is sponsored by: Splunk Inc. Do > > you grep through log files > > > for problems? Stop! Download the new AJAX search > > engine that makes > > > searching your log files as easy as surfing the > > web. DOWNLOAD SPLUNK! > > > > > > http://ads.osdn.com/?ad_id=7637&alloc_id=16865&op=click > > > _______________________________________________ > > > Libmeshusers mailing list > > > Libmeshusers@... > > > > > > https://lists.sourceforge.net/lists/listinfo/libmeshusers > >  > > > > > > > > > > >  > > This SF.net email is sponsored by: Splunk Inc. Do > > you grep through log files > > for problems? Stop! Download the new AJAX search > > engine that makes > > searching your log files as easy as surfing the > > web. DOWNLOAD SPLUNK! > > > http://ads.osdn.com/?ad_id=7637&alloc_id=16865&op=click > > _______________________________________________ > > Libmeshusers mailing list > > Libmeshusers@... > > > https://lists.sourceforge.net/lists/listinfo/libmeshusers > > > > > __________________________________________________ > Do You Yahoo!? > Tired of spam? Yahoo! Mail has the best spam protection around > http://mail.yahoo.com > > >  > This SF.net email is sponsored by: Splunk Inc. Do you grep through log files > for problems? Stop! Download the new AJAX search engine that makes > searching your log files as easy as surfing the web. DOWNLOAD SPLUNK! > http://ads.osdn.com/?ad_id=7637&alloc_id=16865&op=click > _______________________________________________ > Libmeshusers mailing list > Libmeshusers@... > https://lists.sourceforge.net/lists/listinfo/libmeshusers  Nachiket Gokhale, Ph.D. Candidate (Mechanical Engg), Department of Aerospace and Mechanical Engineering Boston University, Boston, MA. Cell: 6173720637 email: gokhalen@... 