Courses Detail Information

ME6101J – Continuum Mechanics


Instructors:

Jaehyung “Joshua” Ju

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