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# Please suggest self study book for continuum plasticity theory

Fri, 2015-12-25 10:25 - AP

Hello, I am new to theory of plasicity and need to learn it by myself. Please suggest a good book for self study for continuum plasticity theory. I am specially interested in metal plasticity theories, in analytical and numerical aspects.

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## Plasticity Theory

For a general, quick introduction to plasticity I would suggest reading a book chapter called "Elements of Phenomenological Plasticity" written by Brannon. It's freely available on her website: http://www.mech.utah.edu/~brannon/pubs/7-2007BrannonPlasticityBookChapte...

However, this suggestion is made with the assumption that you already have a foundation in mechanics (stress, strain, elasticity, etc). Most books that touch on anything plasticity-related, usually have a short primer on basic plasticity in the beginning.

Read through that one and let me know what you think and I might be able to suggest something else based on your review.

## Plasticity Theory

Thanks for your reply. The link was helpful. Do you have any further suggestion for a more comprehensive book? As I am not expert in plasticity, I cannot tell what this text was lacking, etc. But I would be looking for a more comprehensive reference on the similar lines of this text (I, a beginner in plasticity, would use that as a self study means)

What I would prefer is a more mathematical book. I am from pure mathematics background and feel that the present text lacks in mathematical treatment. Of couse, this was a single chapter which cannot cover everything. Let me give you an example. When the author talks about differentiating the yield functional with respect to stress functional, I expect that the author should mention what forms the basis vector for the vector space, dual vector space. I saw applications in differential geometry, but the underlying concepts are not generalized. The theory pretty much seems to adhere to Cartesian 3D coordinates. I don't know whether this is the standard way in plasticity, as I do not much about it. If you know, please suggest such mathematically oriented book.

## Dear AP,

I know of only one book on the theory of metal plasticity that was written from a purely mathematical perspective: Temam's "Mathematical problems in plasticity". However, this book deals mostly with the "existentialist" part of the topic.

The book by Simo and Hughes (Computational Inelasticity) is the starting point for understanding the numerical approach (to solving actual problems). Another good book dedicating significant portions to the topic is "Nonlinear Finite Element Methods for Continua and Structures" by Belytschko, Liu and Moran.

Regarding the "analytical" aspect, the book by Hill (Mathematical Theory of Plasticity) is the standard. However, it should be pointed out that, due to the complexity and nonlinearity of the constitutive relations, analytical solutions in plasticity are rare and only for very particular and highly idealized cases.

Good luck !

## Plasticity Theory

Dear AP

I highly recommend the "Plasticity for structural engineers" by Chen and Han. Two other books on plasticity theory and continuum mechanics that i also recommend are:

1. Continuum Mechanics and Plasticity by Han-Chin Wu

2. Continuum Theory of Plasticity by Akhtar S. Khan, Sujian Huang

You can also download the "Plasticity theory" by J. Lubliner from the belowl link.

http://www.ewp.rpi.edu/hartford/~ernesto/F2008/MEF2/Z-Links/Papers/Lubliner.pdf

Regards

Kumar

## Good books on plasticity

I found these books helpful for me.

Simo and Hughes book deals with computational aspects. If you have regorous mathematics background then you may find this book good. Bathe and Kojic book discuss numerical and continuum aspects of plasticity. Dixit's book discusses a lot of priliminary information and plasticity, damage mechanics, etc. Reader may find Khan and Huang's book a good reference.

## Plasticity Modeling & Computation

I would also recommend Plasticity Modeling & Computation by R.I. Borja. It's concise and includes all the essential elements.

## Mechanics of Materials and Interfaces: The Disturbed State Conce

here is one

http://www.amazon.com/Mechanics-Materials-Interfaces-Disturbed-Concept/d...

## Plasticity

The following book is also a very good reference on plasticity:

S. Nemat-Nasser, Plasticity - A Treatise on Finite Deformation of Heterogeous Inelastic Materials, Cambridge Press, 2009

Mohsen