Continuum mechanics is a powerful framework for describing physical processes by modeling matter as a continuous medium, allowing for the analysis of deformable objects and phenomena that vary in space and time.
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welcome to the first video of a series
of videos on Continuum mechanics in this
first video I will give an overview of
Continuum mechanics or more generally
Continuum physics and explain why
continum mechanics is so powerful for
describing physical processes in our daily
daily
life most of you are probably familiar
with the term mechanics mechanics is a
branch of physics in which the forces
acting on objects and the resulting
motion of these objects are studied in
classical mechanics the objects are
typically assumed to be rigid that is
they may move in Space over time but do
not deform up on acting
forces here you can see an exemplary
animation of some moving particles that
do not change their shape over
time in continum mechanics objects are
not anymore assumed to be rigid but
instead their shape may change over time
as you can see in this exemplary
simulation of a solid that deforms under external
external
forces so does this mean that classical
mechanics is the study of non-deformable
objects and continum mechanics is the
study of deformable objects well yes you
could say that but there is a little bit
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it
any object that is modeled within the
framework of continum mechanics occupies
a certain domain in this
three-dimensional space this domain is
often denoted by Capital Omega if a
point x with its three components being
X1 X2 and X3 lies within the domain we
say that X is an element of Omega if not
we say that X is not element of Omega
points that are right at the border of
the domain get a special treatment we
say that they are element of the
boundary of Omega which is denoted by partial
partial
Omega The crucial Assumption of
Continuum mechanics is that the domain
Omega is filled by a so-called Continuum
but what does this mean it means that at
every Point within the domain the
physical state of mattera can be defined
through a set of variables one example
of such a state variable is the
temperature capital
T because the temperature is defined at
each point in our domain we can define a
function T of X this function which
gives us for any point in the domain the
temperature at this point is called the temperature
