[CIG-SHORT] plastic deformation
Charles Williams
willic3 at gmail.com
Mon Dec 1 13:13:19 PST 2014
Does this mean we would need to save the stresses from the previous time step?
Charles
> On 2/12/2014, at 6:50 am, Birendra jha <bjha7333 at yahoo.com> wrote:
>
> Another important question:
>
> 4. Stress integration in pylith's DruckerPrager is implemented based on two points in time: the initial time and the current estimate at the current time. Do you think we need to integrate from the previous time step, if we implement camclay type models?
>
> Thanks
> Birendra
> --------------------------------------------
> On Mon, 12/1/14, Birendra jha <bjha7333 at yahoo.com> wrote:
>
> Subject: Re: [CIG-SHORT] plastic deformation
> To: "Charles Williams" <willic3 at gmail.com>
> Date: Monday, December 1, 2014, 11:58 AM
>
> 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
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>>>>>
>>>>
>
>>>>
>>>
>>
> _______________________________________________
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>>>>
>>>
>>
> _______________________________________________
>>>> CIG-SHORT mailing list
>>>> CIG-SHORT at geodynamics.org
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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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>>>
>>
> _______________________________________________
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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
>>
>>
> _______________________________________________
>> 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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