The familiarity of this situation empowers us to understand a little of the continuum-discrete dichotomy underlying continuum best site in general. A wide and diverse network of senior engineers to provide professional-level reviewing of engineering work.
The previous PDE is one equation with two unknowns, so another equation is needed to form a well-posed problem.
An additional area of continuum mechanics comprises elastomeric foams, which exhibit a curious hyperbolic stress-strain relationship.
In the Lagrangian description, the material derivative of
P
i
j
{\displaystyle P_{ij\ldots }}
is simply the partial derivative with respect to time, and the position vector
X
Web Site
{\displaystyle \mathbf {X} }
is held constant as it does not change with time. 8full citation needed9pageneeded12full citation needed
Materials that exhibit body couples and couple stresses in addition to moments produced exclusively by forces are called polar materials.
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One description for motion is made in terms of the material or referential coordinates, called material description or Lagrangian description.
Space separates molecules that make up solids, liquids, and gases. look at here now start modelling define that:
x
{\displaystyle x}
measures distance (in km) along the highway;
{\displaystyle t}
is time (in minutes);
(
x
,
t
)
{\displaystyle \rho (x,t)}
is the density of cars on the highway (in cars/km in the lane); and
u
(
x
,
t
)
{\displaystyle u(x,t)}
is the flow velocity (average velocity) of those cars ‘at’ position
x
{\displaystyle x}
. .