[CIG-SHORT] plastic deformation

Charles Williams willic3 at gmail.com
Mon Oct 6 13:07:11 PDT 2014 

Hi Birendra,


On 6/10/2014, at 5:43 pm, Birendra jha <bjha7333 at yahoo.com> wrote:

> Hi Charles
> 
> Thank you very much. That is very helpful. 
> 
> Eq.(5.113): Yes, cohesion c should not be there and the missing term is 3*\alpha_f*P^I.

Yes, that is what I have.

> 
> Can you please confirm that derivative of d w.r.t epsilon i.e. Eqs.(5.123), with (5.124), is correct?

I have not reworked this equation, but it should be correct.  If you derive it yourself from equation 111, keep in mind that there is a factor of 2 involved for off-diagonal terms depending on whether you are using the tensor form or the vectorized equivalent of the stress/strain tensors.

> 
> Eq.(5.117): Should P^I be multiplied with R_i as well? Although, this won't change the tangent matrix.

Yes.  I think I left it out because I knew it wouldn’t affect the tangent matrix, but I am making these corrections in the manual.


> 
> I saw a recent paper (A new exact integration method for the Drucker–Prager elastoplastic model with linear isotropic hardening,
> László Szabó and Attila Kossa, Int J Solids Structures, 2012) that looks useful because it has exact expressions for tangent matrix.
> What do you think about these methods?

I haven’t looked at this, but I will try to have a look.  We don’t have that journal here at GNS.

Cheers,
Charles



> 
> Thanks again
> Birendra
> --------------------------------------------
> On Sun, 10/5/14, Charles Williams <willic3 at gmail.com> wrote:
> 
> Subject: Re: [CIG-SHORT] plastic deformation
> To: cig-short at geodynamics.org
> Date: Sunday, October 5, 2014, 4:41 PM
> 
> 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
> 1 Fairway Drive, Avalon
> PO Box
> 30368
> Lower Hutt  5040
> New
> Zealand
> ph (office): 0064-4570-4566
> fax (office): 0064-4570-4600
> C.Williams at gns.cri.nz
> 
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Charles A. Williams
Scientist
GNS Science
1 Fairway Drive, Avalon
PO Box 30368
Lower Hutt  5040
New Zealand
ph (office): 0064-4570-4566
fax (office): 0064-4570-4600
C.Williams at gns.cri.nz

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