Continuum mechanics

Welcome to this learning project about continuum mechanics!

Introduction edit

Topic of continuum mechanics deals with the basics equations of motion that governs the mechanics of both solid and fluid objects in nature.

Project metadata edit

  Educational level: this is a tertiary (university) resource.
  Subject classification: this is an engineering resource.

Content summary edit

This is an introductory course on the continuum mechanics of materials. Small deformation theory is generalized for finite deformation scenarios and applied for both solid and fluids.

Goals edit

This learning project aims to.

  • provide the mathematical foundations of continuum mechanics
  • expose students to extension of small deformation theory into the finite deformation regime in solids and fluids

Contents edit

Syllabus and Learning Materials

Syllabus and Learning Materials edit

Assignments, tests and quizzes

Assignments edit

Syllabus and Learning Materials edit

  1. Mathematical Preliminaries
    1. Set notation
    2. Functions
    3. Vectors
    4. Matrices
    5. Tensors
      1. Useful tensor algebra identities
      2. Useful relations between tensors and vectors
      3. Curl of the gradient of a vector
      4. Relations between surface and volume integrals
      5. Leibniz formula in one dimension
      6. Leibniz formula in three dimensions
    6. Partial differential equations
    7. Variational calculus
  2. Kinematics
    1. Motion, displacement, velocity, acceleration
    2. Strains and deformations
    3. Polar decomposition
    4. Spectral decompositions of kinematic quantities
    5. Volume change and area change
    6. Time derivatives and rate quantities
    7. Objectivity of kinematic quantities
  3. Stress measures and stress rates
    1. Stress measures
    2. Deviatoric and volumetric stress
    3. Objective stress rates
  4. Balance laws
    1. Governing equations and thermodynamics
    2. Balance of mass
    3. Balance of linear momentum
    4. Balance of angular momentum
    5. Balance of energy
    6. Clausius-Duhem inequality
  5. Constitutive relations
    1. Thermoelasticity
      1. Relation between Cauchy stress and Green strain
      2. Maxwell relations for thermoelasticity
      3. Balance of energy
      4. Clausius-Duhem inequality
      5. Specific heat relations
    2. Nonlinear Elasticity
    3. Plasticity
    4. Viscoplasticity
    5. Viscoelasticity.

Tests and Quizzes edit

Textbooks and References edit

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