Mechanical Behavior of Materials

Mechanical Behavior of Materials is the study of how materials deform and fracture under the influence of applied forces or loads. This field investigates the relationship between stress (force per unit area) and strain (deformation) to characterize fundamental properties like strength, stiffness, ductility, toughness, and fatigue resistance. By understanding how a material's internal structure—from its atomic arrangement to its macroscopic features—governs these properties, engineers can predict performance, prevent failure, and select or design materials for safe and reliable applications in everything from aerospace structures to biomedical implants.

1. Introduction to Mechanical Behavior
   1. Scope and Importance
      1. Applications in Engineering Design
      2. Safety and Reliability Considerations
      3. Material Selection Criteria
   2. Concepts of Stress and Strain
      1. Definitions of Stress and Strain
      2. Engineering Stress and Strain
         1. Nominal Stress
         2. Nominal Strain
         3. Assumptions and Limitations
      3. True Stress and Strain
         1. Instantaneous Area and Length
         2. Conversion between Engineering and True Values
      4. State of Stress at a Point
         1. Stress Components
            1. Normal Stress Components
            2. Shear Stress Components
         2. Stress Tensor
            1. Matrix Representation
            2. Symmetry of the Stress Tensor
         3. Principal Stresses
            1. Determination of Principal Directions
            2. Maximum Normal Stress
            3. Minimum Normal Stress
         4. Maximum Shear Stress
            1. Planes of Maximum Shear
            2. Mohr's Circle Interpretation
      5. State of Strain at a Point
         1. Strain Components
            1. Normal Strain Components
            2. Shear Strain Components
         2. Strain Tensor
            1. Matrix Representation
            2. Symmetry of the Strain Tensor
         3. Principal Strains
            1. Determination of Principal Directions
            2. Maximum Strain
            3. Minimum Strain
   3. Stress and Strain Transformations
      1. Transformation Equations
         1. 2D Stress Transformation
         2. 3D Stress Transformation
      2. Mohr's Circle for Stress
         1. Construction for 2D Stress
         2. Construction for 3D Stress
         3. Interpretation of Results
      3. Mohr's Circle for Strain
         1. Construction and Use
         2. Physical Meaning