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Mechanics of Material Systems: Dynamics, Stress Analysis, and Plasticity in Engineering

This course delves into the fundamental concepts of Mechanics of Material Systems, focusing on deformation, strain, momentum balance, and stress states. With detailed examination of elasticity, variability in thermomechanical properties, and concepts of plasticity, students will learn to apply these principles in engineering design and analysis. Emphasis is placed on critical failure criteria and advanced techniques like Mohr's circles for stress analysis. Practical applications, including triaxial tests and circular foundations, will be covered, ensuring a robust understanding of material behavior under various loading conditions.

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Mechanics of Material Systems: Dynamics, Stress Analysis, and Plasticity in Engineering

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  1. 1.033/1.57 • Mechanics of Material Systems • (Mechanics and Durability of Solids I) Franz-Josef Ulm Lecture: MWF1 // Recitation: F3:00-4:30 1.033/1.57 Mechanics of Material Systems

  2. Part II: Momentum Balance, Stresses and Stress States 4. Stress States / Failure Criteria 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 Approac • 8 Plasticity Models • 9 Limit Analysis and Yield Design 1.033/1.57 Mechanics of Material Systems

  4. Stress Vector and Stress Components Stress components on a material surface oriented in the principal stress direction n = uI Stress components on a material surface oriented by unit normal n 1.033/1.57 Mechanics of Material Systems

  5. Stress Vector in the Principal Stress Space • (Illustration of Stress Invariants) • = Orientation of hydrostatic axis • T(−u3) • 1.033/1.57 Mechanics of Material Systems

  6. Stress Vector in the Mohr Plane 1.033/1.57 Mechanics of Material Systems

  7. Mohr Circles and The Mohr Circle The Mohr Circle 1.033/1.57 Mechanics of Material Systems

  8. Selected Stress States: Hydrostatic Pressure σ = −p1 Material Plane Mohr Stress Plane 1.033/1.57 Mechanics of Material Systems

  9. Selected Stress States: Uniaxial Tension • σ = σI ez⊗ez • Material Plane Mohr Stress Plane • 1.033/1.57 Mechanics of Material Systems

  10. Selected Stress States: Pure Shear • σ = τ (ex⊗ey+ ey⊗ex) • Material Plane Mohr Stress Plane • 1.033/1.57 Mechanics of Material Systems

  11. Selected Stress States: Plane Stress • T(n=ez) = σ ⋅ez = 0 • Material Plane Mohr Stress Plane • 1.033/1.57 Mechanics of Material Systems

  12. Tension Cut-Off Shear Direct Tension −τmax 1.033/1.57 Mechanics of Material Systems

  13. Tresca Criterion

  14. Tresca Criterion: Application 1.033/1.57 Mechanics of Material Systems

  15. Mohr- Coulomb 1.033/1.57 Mechanics of Material Systems

  16. Mohr- Coulomb Direct Tension Shear Uniaxial Compression 1.033/1.57 Mechanics of Material Systems

  17. Training Set: Excavation Set 1.033/1.57 Mechanics of Material Systems

  18. Max. Excavation Depth of Tresca Material 1.033/1.57 Mechanics of Material Systems

  19. Homework Set #2 • Part I: Triaxial Test Part II: Circular Foundation

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