[CIG-SHORT] plastic deformation

[Charles Williams]

Hi Birendra,

Probably the best reference for the Drucker-Prager stuff is the finite element book by Bathe (Finite Element Procedures, 1995).  Also, much of the solution method for Drucker-Prager elastoplastic materials is analogous to the procedure for power-law viscoelastic materials.

1.  Equation 5.104 is just isolating the elastic deformation component, so that the stress can be computed by operating on the elastic strain. We divide this into deviatoric and volumetric components, which makes things easier.

2.  What we mean here is taking the scalar inner product (defined at the beginning of section 5.3.1).

3.  The cohesion appears to be a typo (I actually think it is left over from an older derivation).  In going through this, however, I believe I discovered a missing factor of 3 * P^I in this equation.  I will need to double-check this and see if this is correct.  If you have derived this equation separately, I would appreciate confirmation.

4.  Are you referring to the split into elastic and plastic parts?  The additive decomposition is frequently used, although I have also seen a multiplicative decomposition (see the book referred to above).

Cheers,
Charles


On 5/10/2014, at 1:20 pm, Birendra jha <bjha7333 at yahoo.com> wrote:

> Hi developers/users,
> 
> I am trying to understand Sec 5.4.2.1 Drucker-Prager Elastoplastic With No Hardening (Perfectly Plastic). Can you please point me to a paper/document which describes this formulation? For example,
> 
> 1. What is the basis of Eq.(5.104), first equality? Can we write this for general loading?
> 
> 2. What is the meaning of "taking the scalar product of both sides", above Eq.(5.109). I can derive lambda by multiplying Eq.(5.100) on both sides by df/dsigma : C^E. But this lamda does not quite look like (5.109) because of (5.104). also, I would like to understand d in Eq(5.110).
> 
> 3. I am not able to derive the term in the bracket in Eq.(113). How does cohesion enter here?
> 
> 4. Eq.(5.117): what is the basis of this split? Is it always valid?
> 
> I'd just like to understand the formulation.
> 
> Thanks for any help
> Birendra
> 
> --------------------------------------------
> On Thu, 10/2/14, Brad Aagaard <baagaard at usgs.gov> wrote:
> 
> Subject: Re: [CIG-SHORT] plastic deformation
> To: cig-short at geodynamics.org
> Date: Thursday, October 2, 2014, 10:50 AM
> 
> Birendra,
> 
> It would help to know what you
> have tried to resolve this problem? Have 
> you checked the scales used in the
> nondimensionalization? Have you 
> verified
> convergence for the same problem with a linear elastic 
> material? Does a linear elastic material
> converge in one nonlinear solve 
> iteration?
> What else have you tried?
> 
> Regards,
> Brad
> 
> 
> On 10/2/14, 6:39 AM,
> Birendra jha wrote:
>> Hi
>> 
>> I am trying to run a
> plastic deformation case with the DruckerPrager3D material.
> The nonlinear solver does not converge. Attached are my
> files, which run.
>> 
>> 
> It's a very small setup: 10x1x1 column, loaded at one
> end with a cyclic load that leads to compression and tension
> in the column in a sinusoidal manner.
>> I
> want to compare the plastic strain output with my analytical
> solution.
>> 
>> Can
> someone please take a look and help me with the convergence
> issue?
>> 
>> Thanks
>> Birendra
>> 
>> 
>> 
>> 
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Charles A. Williams
Scientist
GNS Science
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