Courses Detail Information
ME6101J – Continuum Mechanics
Instructors:
Credits: 3
Pre-requisites: Solid mechanics
Description:
Continuum mechanics is a branch of solid mechanics that analyzes the kinematics and the mechanical behavior of materials modeled as continuous matter rather than discrete particles. Continuum mechanics covers fundamental physics – conservation of mass, momentum, and energy where differential equations are derived to describe the behavior of a continuous matter. Continuum mechanics deals with physical properties independent of any particular coordinate system in which they are observed. These physical properties are then represented by tensors, which are mathematical objects with the required property independent of a coordinate system. These tensors can be expressed in coordinate systems for computational convenience.
Course Topics:
Overview of continuum mechanics, the definition of a vector
Vector algebra 1 – scalar and vector products, triple product
Vector algebra 2 – index notation
Transformation law, theory of matrices
Vector calculus in the cartesian coordinate
Vector calculus in the cylindrical and spherical coordinates
Integral theorems, Tensor-– Dyads, Nonion form of a dyad
Transformation of components of a dyad, Tensor calculus
Kinematics (1): Deformation and configuration, Deformation gradient tensor, various types of deformations
Makeup class for 11/8, Kinematics (2): Green-Lagrangian strain tensor, Analysis of deformation
Kinematics (3): Principal values and principal planes of strains, Rate of deformation, and vorticity tensors
Kinematics (4): Compatibility and Polar Decomposition
Stress (1): Cauchy stress tensor and Cauchy’s formula
Stress (2): Principal stresses, First- and second Piola Kirchhoff stress tensors
Balance law (1): Conservation of mass
Balance law (2): Conservation of momentum
Balance law (3): Conservation of energy
Constitutive equations (1): General principles, Cauchy elastic materials, hyperelastic materials
Constitutive equations (2): Hookean solids, Materials symmetry
Constitutive equations (3): Orthotropic and isotropic materials
Constitutive equations (4): Fluids and heat transfer
Linearized elasticity – Governing equations, Linearized elasticity – strain, stress, strain energy