CIV E 664: Introduction to Solid Mechanics

CIV E 664

Course Contents

• Vectors and tensors

   - Vector algebra

       - Vector calculus

       - Review of indicial and tensor notation

• Strain and deformation

      - Description of motion

      - Deformation analysis

      - Strain measures

      - Infinitesimal strain tensor

      - Compatibility equations

• Stress

      - Cauchy stress tensor

      - Stress transformation

      - Other stress measures

      - Equilibrium equations

• Linear elastic stress-strain relationship, Hooke’s law

• Plane strain and plane stress analysis

     - The governing differential equations

     - Equations in cylindrical coordinates

•  Elasticity theory

     - Potential functions

     - Analytical solutions to linear elastic boundary value problems

• Governing equations

     - Conservation of Mass

     - Conservation of Momenta

     - Conservation of Energy

• Constitutive equations

     - Hyperbolic elastic model

     - Flow rule and plastic potential

     - Associated versus non-associated plasticity

     - Perfectly plastic models

         Tresca criterion

         Von Mises criterion

         Drucker-Prager criterion

         Mohr-Coulomb criterion

         General equations for perfectly plastic models

         Model calibration

         Discussion of the perfectly-plastic model

    - Concept of isotropic strain hardening/softening

         The hardening parameter

         The hardening modulus

          Hardening/softening model calibration

          Discussion of the hardening/softening model

    - Shear band formation

    - Critical state based models

         Cam-clay model

         Modified Cam-clay model