Drucker Prager plasticity model

[carlygao]

Hi,

I am using FEAP v85. There is "plastic drucker sig_t sig_c" option in the manual. However, I didn't find the description of Dracker Prager model in the theory manual. Does Drucker-Prager plasticity model work in FEAP85? In small deformation or finite deformation? Thanks.

Carly

[Prof. R.L. Taylor]

The model is available only in finite strain:  It uses the module: ./elements/material/finite/plasfd.f

You should check if it works though as it is not often used by others.  The problem will be for cases leading to stresses outside the vertex of the cone.

[carlygao]

Prof. Taylor,

Thanks. Is there any plasticity model in FEAP85 can capture the pressure-dependent yielding based on small deformation? My material has different strengths under compression and tension. I want to figure out which plasticity model is good to use in FEAP85.

If I have to implement Drucker-Prager model based on small deformation via user subroutines, is there any good reference book? The Feap manual provides very good reference materials for the J2 plasticity, but I didn't find a good reference for implementing Drucker-Prager model.

Thanks.

Carly

[Prof. R.L. Taylor]

The main references used for plasticity are:

author    = {J.C. Simo and T.J.R. Hughes},
title     = {Computational Inelasticity},
series    = {Interdisciplinary Applied Mathematics},
volume    = {7},
publisher = {Springer-Verlag},
address   = {Berlin},
year      = 1998 }

and

author    = {J.C. Simo},
title     = {Topics on the numerical analysis and simulation of plasticity},
booktitle = {Handbook of Numerical Analysis},
volume    = {III},
editor    = {P.G. Ciarlet and J.L. Lions},
publisher = {Elsevier Science Publisher B.V.},
year      = {1999},
pages     = {183--499} }

The vertex is a main point to consider, possibly by using multiple surfaces.

[carlygao]

Prof. Taylor,

I have a question about how to choose the plasticity model based on the small deformation or the finite deformation. I attached a picture in this message from Melro (Micromechanical analysis of polymer composites reinforced by unidirectional fibres: Part I – Constitutive modelling, 2013). It seems the plasticity model proposed in this paper (belongs to the Drucker-Prager family) is based on the small deformation assumption. However, the stain in the picture is very large, around 30%, and the numerical results match the testing data very well.

1. In FEAP, J2 plasticity is based on the small deformation. Can I use to simulate the large deformation for the steel components, like 30% strain?

2. The Drucker-Prager in FEAP is based on the finite deformation, but can I use it for a small deformation case? I thought the it is easier to implement the numerical model based on the small deformation than the one based on the large deformation. The Drucker-Prager in FEAP is based on the finite deformation, not based on the small deformation. Is there any special reason for this? Does this mean the Drucker-Prager model is more applicable to the large deformation in reality?

Thanks.

Carly

[FEAP_Admin]

1) FEAP will not limit the strains that you apply to a model.  You just have to be careful as to if the results are meaningful.  If there are finite rotations, in particular, you can run into trouble.

2) A finite strain model can always be run with small strain values.  It will just be more expensive than running a small strain model.

[carlygao]

Prof. Taylor,

I attached a simple case to figure out how to use the Drucker-Prager plasticity model in finite deformation. the p value will be changed to be positive or negative for tension or compression load.

If the material block is set as follows, the plasfd.f for the Drucker-Prager model will be called. I want to know whether there is a simple way to verify whether the tension or compression stress is smaller than 350e6 (tension) or 420e6 (compression) specified in the input file. I can't verify this in "plot,stres,1". If I print out all stressed, it seems the sigma_11 value for the first step is very close to sigma_t or sigma_c specified in the input file. Thanks.
 

mate,1
  solid
    elastic isotropic 200e9 0.3
    plastic drucker  350e6 420e6
    plastic hardening  0.0 0.0
    finite

The model is available only in finite strain:  It uses the module: ./elements/material/finite/plasfd.f

You should check if it works though as it is not often used by others.  The problem will be for cases leading to stresses outside the vertex of the cone.

[Prof. S. Govindjee]

plot,pstr,5 will plot tr(sigma)/3 for you.

[Prof. R.L. Taylor]

You may want to plot max min principal stresses see PLOT PSTREss page in manual