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