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Engineering Online
Engineering Online

MAE 730 Modern Plasticity

3 Credit Hours

This course will introduce: (1) Classical theories of plasticity, yielding criterion, flow rules; (2) crystal plasticity finite element and other computational methods for static and dynamic plasticity; and (3) modeling plastic deformation behavior of materials by considering the fundamental mechanisms, such as the motion of dislocations and atoms, underlying it.




Course introduction video

Prerequisites

MAE 314 Solid Mechanics;
MAE 316 Strength of Mechanical Components;
MAE 430 Applied Finite Element Analysis [Optional].

Course Objectives

  1. Students will gain fundamental knowledge on how to describe plastic deformation behavior in engineering materials from theoretical, computational, and applied point of view.
  2. Students will be equipped with skills on using/developing several state-of-art computational methods, such as finite element (FE) method, crystal plasticity finite element (CPFE), and dislocation dynamics (DD) method for modeling the material’s plastic deformation behavior.
  3. Students will demonstrate their capability of deploying these methods to model the plastic deformation behavior in a variety of engineering materials, such as metals, lightweight Mg-/Ti-alloys, steels, semiconductors, biological/biomimetic materials, biopolymers, minerals, and their composites, processed by extrusion, high pressure torsion, additive manufacturing, indentation or mechanical nano-stamping, and among many others. Students will be able to apply the knowledge to be gained from this course in their own research and engineering practices.

Course Outline

1 Basic Engineering Plasticity
1.1 Stress Analysis
1.2 Strain Analysis
1.3 Yield Criteria
1.4 Non-hardening Plasticity
1.5 Elastic-perfect Plasticity

2 Crystal Plasticity
2.1 Resolved Shear Stresses
2.2 Lattice Slip System
2.3 Hardening
2.4 Yield Surface
2.5 Flow Rule

3 Finite Element Simulation of Plastic Deformation in Materials
3.1 Elastic Stiffness Matrix
3.2 Energy Methods
3.3 Elastic-Plastic Stiffness Matrix
3.4 Finite Element Simulations of Plasticity
3.5 Examples

4 Implementation of Plasticity Models into Finite Element Code [Advanced Topics]
4.1 Introduction
4.2 Elasticity Implementation
4.3 Verification of Implementation
4.4 Isotropic Hardening Plasticity Implementation
4.5 Large Deformation Implementation
4.6 Elasto-viscoplasticity Implementation

5 Line Dislocation Dynamics [Advanced Topics]
5.1 Introduction
5.2 Nodal Representation of Dislocation Networks
5.3 Energy and Forces
5.4 Mobility Laws
5.5 Time Integrators
5.6 An Example: Dislocation Multiplication through Frank-Read Sources

Course Requirements

Homework and Mini-Projects40%
Midterm Exam30%
Final Project Presentation20%
Final Project Report10%

Textbook

Basic Engineering Plasticity: An Introduction with Engineering and Manufacturing Applications
Author: D.W.A. Rees. Publisher: Butterworth-Heinemann.

Recommended reading

  1. Introduction to Computational Plasticity
    Author: F. Dunne and N. Petrinic. Publisher: Oxford University Press 2005.
  2. Computer Simulations of Dislocations
    Author: V.V. Bulatov and W. Cai. Publisher: Oxford University Press 2006.

Software Requirements

ANSYS, COMSOL, ABAQUAS, or any other similar finte element analysis software.

Created: 05/16/2025