Lecture notes
Class notes on Continuum Mechanics
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In this note a brief discussion on Continuum Mechanics is discussed.
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Lecture Notes On Continuum MechanicsFor Post Graduate students
3/4/2021
, INTRODUCTION
Matter
Solid Liquid Gas Plasma
Continuum
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Solid Fluid(Liquid & Gas)
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Viscous Fluid Inviscid Fluid
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Newtonian Fluid Non-Newtonian Fluid
Mechanics is that branch of science which studies the effects of forces on a
physical object.
Continuum Mechanics: It is a branch of mechanics that deal with the
analysis of kinematics and the mechanical behavior of materials modeled as
a continuous mass rather than discrete particles.
Mechanics
___________________________________________________
, Statics Kinematics Dynamics
Study of objects Study of objects Study
of effect of forces
at rest in motion on objects
Continuum Mechanics
_____________________________________________
Mechanics of Solids Mechanics of Fluids
Elasticity Plasticity Newtonian fluids Non-
Newtonian fluids
Fundamental laws of Continuum Mechanics:
Conservation of Mass
Conservation of Linear Momentum
Conservation of Angular Momentum
Conservation of Energy etc.
The mathematical formulations of above conservation laws are known as
field equations.
Q. Why do we need to study Continuum Mechanics?
Answer: The study of motion of solid and fluid particles through a unified
approach constitutes the subject of continuum mechanics. This subject is divided
into three natural parts.
The first part deals with the field equations common to both solid and fluid
mechanics.
, The second part deals with the constitutive equations that are different for
solids and fluids.
The third part deals with different branches of the subject whose governing
equations are obtained by combining the field equations and constitutive
equations.
Q. What is Continuum word?
Answer: Continuum = Continuous Medium = Matter is continuously distributed.
Every physical object is made up of molecules, atoms and even smaller
particles. While studying the external effects on physical objects, the gaps between
the particles may or may not be taken into consideration. The study that takes
account of the existence of gaps is called microscopic study and on the other hand,
the study that ignores the gaps and treats a physical object as a continuous
distribution of matter is called macroscopic study.
The Continuum Hypothesis
The molecules of gas are separated by vacuous regions with linear dimensions
much larger than those of molecules themselves. Even in a liquid, in which the
molecules are nearly as closely packed as the strong short-range repulsive forces
will allow, the mass of the material is concentrated in the nuclei of the atoms
composing a molecule and is very far from being smeared uniformly over the
volume occupied by the liquid. Other properties, such as composition or velocity,
have a violently non-uniform distribution when the fluid is viewed on such a small
scale as to reveal the individual molecules. The mechanism of fluid flow is mainly
concerned with the behavior of matter in large, on a macroscopic scale large
compared with the distance between the molecules and it will not often happen that
the molecular structure of a fluid need be taken into account explicitly. We
suppose that the macroscopic behaviour of fluids is the same as if they were
perfectly continuous in structure. Physical quantities such as the mass, momentum
associated with the matter contained within a small volume will be regarded as
being spread uniformly over the volume.
Configuration of a Continuum
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