Metals Material Modelling: Plasticity

How is plastic behaviour in metals simulated and used in practical engineering applications?
What are potential difficulties and challenges in modelling plasticity problems using FE software?
What are the potential errors and limitations of the FE plasticity solutions?

This course gives you practical advice with a minimum of theory.

Metals Material Modelling: Plasticity

This eLearning course is aimed at engineers and designers who want to learn about how plastic behaviour in metals is modelled using FE software.

The course will cover plasticity theories that are widely used to analyse practical engineering applications in metals. Mathematical formulations and equations are intentionally kept to a minimum. Emphasis will be placed on how engineering design incorporates these theories and how the FE method models plasticity.

Difficulties encountered by both the FE user and the FE software in modelling plasticity will be highlighted using many examples to demonstrate plastic behaviour and how to assess the accuracy of the FE solutions.

The pre-requisite for this course is a working knowledge of linear finite element theory and applications. No prior knowledge of plasticity theory is required. The course is independent of any FE software code.


Why an e-learning class?

Travel and training budgets are always tight! The e-Learning course has been developed to help you meet your training needs.

If your company has a group of engineers, or specific training requirements across any subjects, please contact us to discuss options.

Course Program

This is a three-week live web-based eLearning course with a total of 6 hours of tuition (presented as a two-hour session per week). Delegates will be provided with copies of all lecture slides including many self-test problems (with worked solutions).

Session 1

Introduction to Plasticity

  • Metals and ductility
  • Elastic stress-strain relationships
  • Elastic-plastic behaviour
  • Laboratory uniaxial tests and stress-strain curves
  • Yield stress and proof stress
  • Modelling Nonlinear Material Behaviour

Review of Plasticity formulations

  • True stress and true strain
  • Deviatoric and hydrostatic Stress
  • Yield criteria
  • Von Mises Yield Surface- A geometric volume
  • Post-yield behaviour and work hardening
  • Plastic flow behaviour
  • Other yield criteria used in FE software
  • Reversed loading and Hysteresis Loop
  • Cyclic Loading, shakedown and Ratchetting

Self-test questions (optional homework)- Questions to reinforce the topics covered in the lectures


Session 2

Computational Modelling of Plasticity

  • Dividing the load into small chunks (increments)
  • Iterations- checking all is well before proceeding to the next increment
  • A simple plasticity algorithm
  • How does the algorithm become more complicated?
  • Is plasticity really time-independent?
  • What is pseudo-time?
  • What happens at very high temperatures?
  • Can plastic collapse (too much plasticity) be modelled?

Solutions to self-test questions (Full solutions highlighting the key aspects)

Plasticity in Engineering design

  • Can plasticity be useful in engineering?
  • Partially controlled plasticity (autofrettage)
  • Residual stresses
  • Shot peening
  • Plasticity around cracks
  • Plasticity in beams and thick cylinders

More Self-test questions (optional homework)


Session 3

Modelling Plasticity Using FE software

  • Is it difficult to model plasticity using FE software?
  • What plasticity data should be input in the FE code?
  • What are the limitations of FE plasticity models?
  • What happens after the material reaches the Ultimate Tensile Stress?
  • What can go wrong in the FE simulation?

Solutions to more self-test questions

FE Plasticity Examples

  • Isotropic hardening example
  • Kinematic hardening example
  • Multiaxial cylinder example
  • Cyclic loading example
  • Rigid punch example

Summary of key points, tips and guidelines


Feedback from former e-Learning students:

"Super! Doesn't get better than this. Good idea to start having e-Learning courses."


"I'm really happy not to pay a big fraction of my annual training budget to airlines and hotels. A BIG plus to e-learning."




PSE Competencies addressed by this training course

IDCompetence Statement
PLASkn1 For a beam under pure bending sketch the developing stress distribution from first yield, to collapse.
PLASkn2 For a simple steel thick cylinder or sphere under internal pressure, state the location of first yield.
PLASkn7Sketch a stress-strain curve for an elastic-perfectly plastic and bi-linear hardening material showing elastic and plastic moduli.
PLASco1Discuss salient features of the inelastic response of metals.
PLASco2 Explain the terms Isotropic Hardening, Kinematic Hardening and Rate Independency.
PLASco3Discuss the role of the Hydrostatic and Deviatoric Stress Components in yield criteria for isotropic, polycrystalline solids.
PLASco7Explain the phenomenon of Shakedown and define the term Shakedown Load.
PLASco8Contrast the terms Ratchetting and Low Cycle Fatigue.
PLASco11Explain how plastic effects in a Finite Element system are commonly handled as a series of incremental iterative linear analyses
PLASco12Explain, in general terms, the function of the Mises Flow Rule or Prandtl-Reuss Equations, used in a finite element solver.
PLASco13 Outline how the cumulative and incremental displacements, total strains, elastic strains, elastic stresses and plastic strains are related in the finite element method
PLASco14 Illustrate typical examples of Local Plastic Deformation and Gross Plastic Deformation.
PLASco16 Explain the significance of a Hysteresis Loop in a load/deflection test.
PLASco23 Describe the Bauschinger Effect.
PLASco27Explain the process of Stress Redistribution.
PLASco28Describe the process and common purpose of Autofrettage.
PLASap4Use FEA to illustrate Shakedown for a range of components/structures and actions.
PLASap5Use FEA to determine the presence of ratchetting for a range of components and actions.
PLASap7Using standard material data, derive a true stress vs true strain curve to be used for nonlinear analysis.
PLASsy2Plan a series of simple benchmarks in support of a more complex plasticity analysis.
PLASsy4Prepare an analysis specification for a nonlinear material analysis, including modelling strategy, highlighting any assumptions relating to geometry, loads, boundary conditions...
PLASev1Select appropriate solution schemes for non-linear material problems.
PLASev4 Assess the significance of simplifying geometry, material models, mass, loads or boundary conditions, on a non linear material analysis.


Metals Material Modelling: Plasticity


Three-Session Online Training Course

2 hours per session
PDH Credits - 6

Attend the live sessions, or view the recordings at your convenience.

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Engineering Board PDH Credits

*It is your individual responsibility to check whether these e-learning courses satisfy the criteria set-out by your state engineering board. NAFEMS does not guarantee that your individual board will accept these courses for PDH credit, but we believe that the courses comply with regulations in most US states (except Florida, North Carolina, Louisiana, and New York, where providors are required to be pre-approved)

Special Note(s):

Telephony surcharges may apply for attendees who are located outside of North America, South America and Europe. These surcharges are related to individuals who join the audio portion of the web-meeting by calling in to the provided toll/toll-free teleconferencing lines. We have made a VoIP option available so anyone attending the class can join using a headset (headphones) connected to the computer. There is no associated surcharge to utilize the VoIP option, and is actually encouraged to ensure NAFEMS is able to keep the e-Learning course fees as low as possible. Please send an email to the e-Learning coordinator (e-learning @ ) to determine if these surcharges may apply to your specific case.

Just as with a live face-to-face training course, each registration only covers one person. If you plan to register a large group (10+), please send an email to e-learning @ in advance for group discounts.

For NAFEMS cancellation and transfer policy, click here.