MEL7220 Continuum Mechanics 

Welcome to the course! Please go through the First Course Handout (FCH) to know more about the rules and regulations.

Lectures:  Tuesday, Thursday and Friday  (11:00AM-11:50AM)    Lecture Room:  

Mathematical Foundations [6 Lectures]: Scalars, vectors, and tensors; index notation; tensor products and contractions; invariants; eigenvalues and eigenvectors of symmetric tensors; change of basis and transformation laws; scalar, vector, and tensor fields; differential operators. 

Kinematics [8 Lectures]: Bodies and configurations; reference and current descriptions; motion, displacement, velocity, and acceleration fields; material and spatial derivatives; deformation gradient; transformation of line, area, and volume elements; polar decomposition; strain measures and linearized kinematics; velocity gradient, rate of deformation, and spin tensor; rigid body motions and objectivity in kinematics.

 Stress Measures and the Concept of Stress [6 Lectures]: Traction vectors and Cauchy’s postulate; existence and interpretation of the Cauchy stress tensor; stress transformation, principal and extremal stresses, and stress invariants; alternative stress measures including the first and second Piola-Kirchhoff stresses; physical interpretation through representative stress states. 

Mechanical Balance Laws and Field Equations [5 Lectures]: Conservation of mass; Reynolds transport theorem; balance of linear and angular momentum; balance of mechanical energy. 

Constitutive Principles and Objectivity [5 Lectures]: Constitutive response functions; material frame indifference and change of observer; objective scalar, vector, and tensor fields; objective stress rates; material symmetry and isotropy; linearization of constitutive laws. 

Nonlinear Elasticity and Hyperelastic Materials [5 Lectures]: Hyperelastic material concept; strain energy density functions; compressible and incompressible responses; classical hyperelastic models including Neo-Hookean, Mooney Rivlin, Ogden, Gent, etc. 

Applications [4 Lectures]: Homogeneous deformation of hyperelastic membranes under uniaxial and biaxial loading, and simple shear; balloon inflation, instabilities of soft materials: snap through instability and morphological instabilities: wrinkles, creases, folds, and ridges.


45%: Major Examination                        25%: Minor Examinations                   30%: Quizzes/Assignments