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Principle of virtual work in case of a large plastic deformation
Fri, 2009-03-13 12:49 - swsyoon
Hi, all
I have a question about FE formulation for a finite plastic deformation.
I'm a new on the ABAQUS, but how the ABAQUS deals with the plastic deformation
to solve the FE eqation? I think the software use the principle of virtual work and
I'm wondering how the software modify the virtual work term to take the plastic deformation into account (because of dissipation energy)
(Obviously, the formulation must be different with elastic model)
I appreciate your reply.
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ranababuPrinciple of
ranababu
Principle of virtual displacement is applicable irrespective of whether the system is elastic or plastic.This is not the case with principle of minimum potential energy which is for linear elastic systems only.
Princple of virtual displacement results in the P=KD equation. In case of plastic or any other analysis, K is afunction of D ( Aa part of K actually) and the solution proceeds ( for an example using Newton Raphson or other methods) where Plasicity properties ( essentially 3 factors are needed in palstic analysis: yield criterion, flow rule and hardening) come into action.In a simple way it is explained in the book by Cook, Malkus and PLesha.
ABAQUS or any other FE software will have diferent material models for plasticity like elastic-perfectly plastis etc and also different bhardening rules like isotropic, kinematic etc.
Hope I could provide some help.
Regards
ranababu Principle of
Thank you, ranababu
I found in some literatures that some people use principle of virtual power instead of principle of virtual work for a large deformation of polymer. (F=FeFp)
I understand that all of them comes from balance law, but I don't know why people use different form of principle. And I'm wondering how the equation (P=KD) is derived
if the deformation gradient tensor can be decomposed into elastic part and plastic part.
Let me try to search more. Thanks.