[CIG-SHORT] plastic deformation
Charles Williams
willic3 at gmail.com
Mon Dec 1 12:40:41 PST 2014
Hi Birendra,
I’m glad to hear you’re implementing the Cam Clay model. Unfortunately, I have no idea on the best reference to use. I have a number of plasticity papers on my computer. After a quick glance, I see a paper by Hashiguchi and Mase (Int. J. Plasticity, 2007) that appears to describe an extension of the Cam Clay model. That might be worth a look.
In answer to your questions:
1. Yes, the best place to start is by altering the existing DruckerPrager3D files. The elasticConsts are the consistent tangent. Also, is the formulation an additive decomposition into elastic and plastic strain?
2. This is hard to answer without knowing the formulation. I think it should work fine.
3. See initial comments above. Also, there are formulations described for existing codes (e.g., DIANA, Robert Taylor’s code, and probably others).
We have not experimented much with the nonlinear solution for plasticity. Matt may be able to help us with this if we come up with some good test problems.
Cheers,
Charles
p.s. If you’re interested in including your model in the PyLith distribution, that would also be great. In that case, we would need to put in a new section in the manual and create some unit tests.
> On 2/12/2014, at 5:58 am, Birendra jha <bjha7333 at yahoo.com> wrote:
>
> Hello Charles
>
> I am implementing the Modified Cam Clay model into Pylith following the paper: Cam-Clay plasticity, Part I Implicit Integration of elasto-plastic constitutive relations, Borja and Lee, CMAME, 1990
>
> 1. Can I start by copying the DruckerPrager3D files and modify the yield function (yieldFunction), calculation of plastic strain, and calculation of consistent tangent (elasticConsts)? The relevant functions are _calcStressElastoplastic, _calcElasticConstsElastoplastic, _updateStateVarsElastoplastic.
>
> 2. Is this a good idea to implement the rate-dependent plasticity (e.g. camclay) using the pylith formulation? I mean, solve for the consistency parameter separately (in an inner Newton loop for cam clay), and for displacement or total strain in the outer Newton loop? The consistency parameter for this non-associative camclay model is the volumetric plastic strain itself.
>
> 3. Can you recommend another source for the Modified Cam Clay implementation? I already found couple of typos in the above paper.
>
> As I am debugging poor convergence of the nonlinear solver, I want to get your expert opinion regarding this.
>
> Thanks and best regards
> Birendra
>
>
> --------------------------------------------
> On Mon, 10/6/14, Charles Williams <willic3 at gmail.com> wrote:
>
> Subject: Re: [CIG-SHORT] plastic deformation
> To: "Birendra jha" <bjha7333 at yahoo.com>
> Date: Monday, October 6, 2014, 5:15 PM
>
> Thanks, Birendra. This
> looks interesting, and it may be worth putting into PyLith
> at some point.
>
> Cheers,
> Charles
>
>
> On 7/10/2014, at 10:06 am, Birendra jha <bjha7333 at yahoo.com>
> wrote:
>
>> I have attached
> the paper.
>>
>>
>>
> --------------------------------------------
>> On Mon, 10/6/14, Charles Williams <willic3 at gmail.com>
> wrote:
>>
>> Subject:
> Re: [CIG-SHORT] plastic deformation
>> To:
> cig-short at geodynamics.org
>> Date: Monday, October 6, 2014, 3:07 PM
>>
>> 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
>>>>>
>>>>>
>>>>>
>>>>>
>>>>
>
>>>
>>
> _______________________________________________
>>>>> CIG-SHORT mailing list
>>>>> CIG-SHORT at geodynamics.org
>>>>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>>>>>
>>>>
>
>>>>
>>>
>>
> _______________________________________________
>>>> CIG-SHORT mailing list
>>>> CIG-SHORT at geodynamics.org
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>>>>
>>>>
>>>
>>
> _______________________________________________
>>>> CIG-SHORT mailing list
>>>> CIG-SHORT at geodynamics.org
>>>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>>>
>>> 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
>>>
>>
>>>
>>
> _______________________________________________
>>> CIG-SHORT mailing list
>>> CIG-SHORT at geodynamics.org
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>>>
>>>
>>
> _______________________________________________
>>> CIG-SHORT mailing list
>>> CIG-SHORT at geodynamics.org
>>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>>
>> 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
>>
>>
> _______________________________________________
>> CIG-SHORT mailing list
>> CIG-SHORT at geodynamics.org
>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short<Szabo_druckerprager_IJSS2012.pdf>
>
> 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
>
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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