1. 1.033/1.57 Mechanics of Material Systems (Mechanics and Durability of Solids I) Franz-Josef Ulm Lecture: MWF1 // Recitation: F 3:00-4:30 1.033/1.57: Mechanics of Material Systems

2. Part IV: Plasticity and Yield Design 8. Plasticity Models

3. 1.033/1.57: Mechanics of Material Systems Content 1.033/1.57 Part I. Deformation and Strain 1 Description of Finite Deformation 2 Infinitesimal Deformation Part II. Momentum Balance and Stresses 3 Momentum Balance 4 Stress States / Failure Criterion Part III. Elasticity and Elasticity Bounds 5 Thermoelasticity, 6 Variational Methods Part IV. Plasticity and Yield Design 7 1D-Plasticity – An Energy Approach 8 Plasticity Models 9 Limit Analysis and Yield Design

4. 1D 1.033/1.57: Mechanics of Material Systems Stress Strain Plastic Strain Hardening Variable Hardening Force etc

5. 1.033/1.57: Mechanics of Material Systems 1D 3D Extension Stress Strain Plastic Strain Hardening Variable Hardening Force Stress Tensor Strain Plastic Strain Tensor Hardening Variable Hardening Force

6. 1.033/1.57: Mechanics of Material Systems Convexity of Elasticity Domain

7. 1.033/1.57: Mechanics of Material Systems Example: Crystal Structure of Steel Impurity = defects in the crystal structure / network Overcome an Obstacle when? Slippage planes = Direction of permanent deformation how?

8. 1.033/1.57: Mechanics of Material Systems Sliding in a Monocrystal (Kinematics) Elastic Plastic When ?How ?

9. 1.033/1.57: Mechanics of Material Systems Stress Vector on Deviator Plane Orientation of hydrostatic axis

10. 1.033/1.57: Mechanics of Material Systems Von-Mises Plasticity: Yield Criterion Principal Stress SpaceDeviator Plane

11. 1.033/1.57: Mechanics of Material Systems Von-Mises Plasticity: Kinematics Shear Test During Plastic Loading After Unloading

12. 1.033/1.57: Mechanics of Material Systems Drucker-Prager Plasticity: Yield Criterion

13. 1.033/1.57: Mechanics of Material Systems Drucker-Prager Plasticity: Kinematics During Plastic Loading After Unloading Plastic Dilatation

14. 1.033/1.57: Mechanics of Material Systems Drucker-Prager Plasticity: Thermodynamic Restrictions Thermodynamically Admissible Associated Plasticity Non-Associated Plasticity

15. 1.033/1.57: Mechanics of Material Systems Plastic Hardening Models Isotropic HardeningKinematical Hardening

16. 1.033/1.57: Mechanics of Material Systems Cam-Clay Model: Yield Criterion

17. 1.033/1.57: Mechanics of Material Systems Cam-Clay Model: Kinematics