# A reference request for computational plasticity

My background is in applied mathematics and I'm trying to learn plasticity. I have successfully understood the theory and finite element implementation of: linear elasticity, hyperelasticity (Neo-Hookean etc.), elastic contact problems (penalty and Lagrange multiplier-type methods). Recently I have been studying plasticity and so far having a very painful experience.

I have tried reading the following books:

• Simo, Hughes. Computational inelasticity.
• Wriggers. Nonlinear finite elements.
• Han, Reddy. Plasticity.

I'm looking for a reference where one starts with the simplest possible setup, say perfect plasticity, and goes through all the steps from the equations to the Newton's linear systems, and only after that starts increasing complexity. Does anyone know good beginner references for plasticity modeling?

• Try Belytschko, Liu, Moran, "Nonlinear finite elements ...". The basics are explained well in that book. For the theory it's always good to start with Hill's "The Mathematical theory of plasticity". But keep in mind that plasticity can be a mine field that we don't really understand, even though there are > 10k papers on the subject. – Biswajit Banerjee Jul 27 '18 at 20:57
• @BiswajitBanerjee, would you like to add your comment as an answer … or if you prefer, you can start a community post. – nicoguaro Jul 27 '18 at 21:15
• @nicoguaro: This question deserves a more detailed answer that I'm able to write up at the moment. Also, I haven't read any of the newer texts on the subject, so there may be better options. Please start a community post and I'll add to that. – Biswajit Banerjee Jul 28 '18 at 1:21

As mentioned by Biswajit Banerjee, the following reference explains well the basics, although I have not checked this "new" version.

• Belytschko, Ted, et al. Nonlinear finite elements for continua and structures. John wiley & sons, 2013.

I asked a colleague who has worked in computational plasticity and suggested the following reference.

• E.A. de Souza Neto, D. Perić and D.R.J. Owen. Computational Methods for Plasticity: Theory and application.

It presents the following topics:

• Linear algebra
• Finite elements from a virtual works perspective
• Theory of plasticity
• Finite Elements in plasticity, centering in return mapping algorithm. It explains the basic models: Tresca, von Mises, Drucker-Prager and Mohr-Coulomb.