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Continuum Mechanics
Continuum mechanics
Continuum mechanics is a branch of
physics that
deals with solids
and fluids
(i.e., liquids
and gases).
Continuum mechanics makes the assumption that these materials are
continuous:
the fact that matter is made of atoms is ignored. Therefore, physical
quantities, such as space,
time,
energy, and
momentum
can be handled in the
infinitesimal
limit.
Differential equations are thus the mathematical tool of choice for
continuum mechanics. These differential equations are often derived from
fundamental physical laws, such as
conservation of mass or
conservation of momentum.
The physical laws of solids and fluids should not depend on
the
coordinate system of the differential equations. Continuum mechanics thus
uses tensors,
which are mathematical objects that are independent of coordinate system. These
tensors can be expressed in coordinate systems, for computational convenience.
See
tensor analysis for more information.
There are two main branches of continuum mechanics:
-
Elasticity, which deals with the physics of solids.
-
Fluid Mechanics, which deals with the physics of fluids.
The boundary between these two branches is blurry, because
elasticity handles materials with
viscosity.
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