This note explains the following topics: Vectors, Tensors, Tensor
properties, Vector and tensor fields, Configurations, Motion, The Lagrangian
description of motion, Stretch and strain tensors, The polar decomposition,
Velocity gradients, and rates of deformation, Balance of mass, Reynolds
transport theorem, Linear and angular momentum, Models of viscous fluids,
Material symmetry, Classical continuum mechanics, The heat transport equation,
The free energy functional, Phase separation-non convex free energy, The Cahn-Hilliard
Topic of continuum mechanics
deals with the basics equations of motion that governs the mechanics of both
solid and fluid objects in nature. Topics covered includes: Set, notation,
Functions, Vectors, Matrices, Tensors, Kinematics, Stress measures and stress
rates, Balance law, Balance laws.
This note will create a much
more stable basis for continued work or study in the field of mechanics of
continua, be they solid or fluid. Topics covered includes: Vectors and second
order tensors, Change of coordinates, Higher order tensors, Derivatives,
Analysis of small deformations, Kinematics, The dynamic equations of continuum
mechanics, Elastic materials, Isotropic linearly elastic solids, Compatibility
and Plane elasticity, Variational principles, Newtonian fluids and Elastic
This note explains the following topics: Tensor
calculus, Tensor algebra, Tensor analysis, Kinematics, Rates of kinematic
quantities, Gradients of kinematic quantities, Balance equations, Concept of
mass flux, Concept of stress, Balance of mass, Balance of linear momentum,
Balance of angular momentum, Balance of energy, Constitutive equations, Linear
These notes provide an introduction to the mechanics of elastic
solids for beginning graduate students. They may be downloaded without charge.
Topics covered includes: Kinematics: Deformation, Kinematics: Motion, Mechanical
Balance Laws and Field Equations, Thermodynamic Balance Laws and Field
Equations, Singular Surfaces and Jump Conditions, Constitutive Principles,
Elastic Materials, Linearized Elasticity, Compressible Fluids, Liquid Crystals.
This textbook develops the subject of continuum mechanics from the
point of view of an applied physicist with interests in geophysics and
astrophysics. Topics covered includes: The Notion of Stress, Budgets, Fluxes,
and the Equations of Motion, Kinematics in Continuum Mechanics, Elastic Bodies,
Waves in an Elastic Medium, Statics of Elastic Media, Newtonian Fluids, Creeping
Flow and High Reynolds Number Flow.
This book covers the following topics: Geometry Of Deformation,
Kinematics, Measures Of Stress, Fundamental Balance Laws, Moving Spatial Frame,
Constitutive Equations, Entropy Principle, Classical Linear Elasticity, Small
Motions in A Medium with a finite Pre-stress.
This note covers the following topics: Concepts of stress, strain and
elasticity, Beams, columns, plates, shells, Elasticity, general theory, Waves,
Stress concentrations and fracture, Linear and Angular Momentum Principles,
Geometry of Deformation, Stress-Strain Relations, Equations of linear
elasticity, mechanical theory, Some elementary two-dimensional solutions and
Equations of finite deformation.
This textbook is intended to introduce engineering graduate students to
the essentials of modern Continuum Mechanics.It covers the following topics: One-Dimensional Continuum Mechanics, Kinematics of Motion, Equations of Balance,
Models of Material Behavior and Materials with Internal State Variables.
This book covers the following topics: What is deformation, The
deformation gradient, Homogenous deformations, Constructing the deformation
gradient using dyads, Polar decomposition, Strain , Example: non-rotational
deformations and Axisymmetric deformations.