Content
Pepole
CV
(Department) Biomedical Engineering (Division)
(Level and Major)
(Level and Major)
Course Title Continuum Mechanics
Number of Credits 3 Prerequisite
Course Topics:
- Scalars, Vectors, Cartesian Tensors and Tensor Algebra
- Summation Convention, Indicial Notation
- Matrices, Determinants, Principal Values and Principal Directions
- Transformations of Cartesian Tensors
- Second-Order Tensors, Isotropic Tensors
- The Caley-Hamilton Theorem
- The Polar Decomposition Theorem
- Integral Theorems of Gauss and Stokes
- Surface Traction, Cauchy Stress Principle
- The Stress Tensor, Eqs. of Equilibrium, Tensor Symmetry
- Stress Transformation Laws, Principal Stresses, Principal Stress Directions
- Deviator and Spherical Stress States, Octahedral Shear Stress
- Particles, Configurations, Deformation, and Motion
- Material and Spatial Coordinates
- Lagrangian and Eulerian Descriptions
- The Displacement Field
- The Material Derivative
- Deformation Gradients, Finite Strain Tensors
- Infinitesimal Deformation Theory
- Stretch Ratios, Rotation Tensor, Stretch Tensors
- Velocity Gradient, Rate of Deformation, Vorticity
- Material Derivative of Line Elements, Areas, Volumes
- The material time derivative of a volume integral
- Conservation of Mass, Linear Momentum, Angular Momentum, Energy
- Constitutive Equations and Ideal Materials
- Material Symmetry
- Linear Elasticity
- Newtonian Viscous Fluids
- Constitutive Equations and Ideal Materials
- Deformation of a surface element
- Decomposition of a deformation
- Principal stretches and principal axes of Deformation
- Strain invariants and Alternative stress measures
- The theory of finite elastic deformations
- A Strain Energy Theory for Nonlinear Elasticity
- Specific Forms of the Strain Energy
- Viscoelastic Constitutive Equations in Linear Differential Operator Form
- One-Dimensional Theory, Mechanical Models
- Creep and Relaxation, Superposition Principle, Hereditary Integrals
- Harmonic Loadings, Complex Modulus, and Complex Compliance
Reading Resources:
Evaluation:
30% Final Exam
60% Midterm Exam
10% Homework
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