Books on Computational Plasticity

[antonio]

Dear FEAP users and developers:

first at all, my more sincere congratulations because the idea of creating a user forum for FEAP. Although I am novice in using FEAP (a code which I have a sincere intention to learn...), I have long experience in implementing finite element methods both in academia and industry. This post is my first contribution to this community and it is a pleasure for me to suggest two books on computational plasticity, both written by world authorities on the subject, and which have been rather useful for my understanding of general principles and algorithms and the implementation of material models:

Inelastic Analysis of Solids and Structures
M. Kojic, K. J. Bathe
Springer (2005)

Computational Methods for Plasticity. Theory and Applications
E. A. de Souza Neto, D. Peric, D. R. J. Owen
Wiley (2008)

The former is notable for exposing the Governing Parameter Method. This method developed by both authors, basically consists of reducing the resolution of the governing equations to solving a equation of a single variable. This function is often monotone decreasing), with a resolution very robust. This methodology is very different from the traditional method discussed in other texts where are used Newton methods with several variables whose convergence is very difficult (almost miraculous!!!). Interestingly, incremental approaches (rate formulations) are not described.

The later is of a much more general approach. In particular, apart from addressing the incremental and hyperelastic formulations in plasticity, also addresses element formulations especially useful for incompressibility: mixed formulations and F-bar formulations (first time in a textbook). Worth noting the description of algorithms in principal values, which they apply to various geomaterial models. These authors were pioneers in applying this methodology in a effective way for multisurface plasticity.

In short, both books are superb...

I am convinced them will be very useful for everyone interested in the implementation of constitutive models in FEAP.


Antonio
Madrid, Spain

PD: sorry my English faults.

[Prof. R.L. Taylor]

Dear Antonio,

Thank you for your comments.  In the past we have used the methods presented in the books:

Computational Inelasticiy
J.C. Simo and T.J.R. Hughes
Springer, 1998

and

J.C. Simo
Topics on the numerical analysis and simulation of plasticity
Handbook of Numerical Analysis
Elsevier, 1999

Usually, the Newton scheme involves only a scalar in the iteration process - but not always.
The addition of the two newer books should be a nice complement to these older works.

FEAP does use a method that is equivalent to F-bar (it is a mixed approach, but the mixed variables are eliminated at the element level in an efficient manner).  The approach is documented in the FE book:

O.C. Zienkiewicz and R.L. Taylor},
The Finite Element Method for Solid and Structural Mechanics},6th ed
Elsevier, Oxford, 2005

[antonio]

Dear Professor Taylor, thanks for your kind words.

Of course, Simo...

Anyone who loves Computational Mechanics should always keep in mind the name of Juan Carlos Simo. Berkeley and Stanford were very fortunate, and I know they are also very proud, to have had such a brillant, creative (and passionate) mechanician between them. Be long until there is someone like him.

His figure is unforgettable...

[kstn]

I would praise on the book by de Souza Neto. The companion Fortran code is amazing, which helps reader to double check his code as needed. The numerical examples are clear and convincing.