1. Mechanics of Material Systems (Mechanics and Durability of Solids I)
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
9. Limit Analysis and Yield Design
1.033/1.57: Mechanics of Material Systems

3. 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
1.033/1.57: Mechanics of Material Systems

4. Excavation Pit Plastic Collapse:
1.033/1.57: Mechanics of Material Systems

5. Generalized Divergence Theorem
Zone 2
Zone 1
1.033/1.57: Mechanics of Material Systems

6. Exercise: Hollow Sphere
1.033/1.57: Mechanics of Material Systems

7. Constructing the Domain of Safe Loads
Lower Limit Theorem:
Constructing the Domain of Safe Loads
from the “Inside”
1.033/1.57: Mechanics of Material Systems

8. Excavation Pit: Lower Bound
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9. Construction from “Outside”
Upper Limit Theorem
Construction from “Outside”
“Outside”
Load Bearing Envelope
1.033/1.57: Mechanics of Material Systems

10. Excavation Pit: … from “Outside”
1.033/1.57: Mechanics of Material Systems

11. Excavation Pit: Tension Cut-Off
Tresca Criterion + Tension
Cut-Off in the Mohr Plane
Failure Mechanisms
1.033/1.57: Mechanics of Material Systems

12. Excavation Pit:… from “Outside”
unsafe
1.033/1.57: Mechanics of Material Systems

13. Lower and Upper Bound of
Structural Elements
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14. Plastic Hinge
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15. 1.033/1.57: Mechanics of Material Systems

16. Improved Lower Bound for ‘Bulk’ Collapse
‘Reuss-Strength’ Bound
Angle α [Degree]
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17. Effect of Debonding Strength Interface Criterion
Shear
Strength
Interface
Criterion
Angle α [Degree]
1.033/1.57: Mechanics of Material Systems

18. Effect of Delamination Interface Strength Criterion
Tension Cut-Off
Strength Interface
Criterion
Angle α [Degree]
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19. Section Strength of Combined Bending and Axial Force
1.033/1.57: Mechanics of Material Systems