[CIG-SHORT] plastic deformation

[Birendra jha]

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.

Can you please confirm that derivative of d w.r.t epsilon i.e. Eqs.(5.123), with (5.124), is correct?
 
Eq.(5.117): Should P^I be multiplied with R_i as well? Although, this won't change the tangent matrix.

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?

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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 >
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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
 
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