.
Enter your library card number to sign in. It is important to understand that the relation between these two is very deep and there is no chance that one can grow without another. The objects are not taken in an atom formation.
The motion of a continuum body is a continuous time sequence of displacements. Something universal is easier to understand and in this concept the same rule is applied.
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In this aspect the availability of the continuum mechanics is a bless for the scientists. thermodynamic properties and flow velocity, which describe or characterize features of the material body, are expressed as continuous functions of position and time, i. The term is important to be understood and what the function of it is even more important to be understood. It can be thought as the rate at which the property changes when measured by an observer traveling with that group of particles. [.
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Choose this option to get remote access when outside your institution. In this case the description of motion is made in terms of the spatial coordinates, in which case is called the spatial description or Eulerian description, i.
There is continuity during motion or deformation of a continuum body in the sense that:
It is convenient to identify a reference configuration or initial condition which all subsequent configurations are referenced from. Also,
where
v
{\displaystyle \mathbf {v} }
is a vector field,
S
{\displaystyle {\boldsymbol {S}}}
is a second-order tensor field, and
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i
{\displaystyle \mathbf {E} _{i}}
are the components of an orthonormal basis in the reference configuration.
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The first Piola-Kirchhoff stress tensor is related to the Cauchy stress tensor by
We can alternatively define the nominal stress tensor
N
{\displaystyle {\boldsymbol {N}}}
which is the transpose of the first Piola-Kirchhoff stress tensor such that
Then the balance laws become
The operators in the above equations are defined as such that
where
v
{\displaystyle \mathbf {v} }
is a vector field,
S
{\displaystyle {\boldsymbol {S}}}
is a second-order tensor field, and
i
{\displaystyle \mathbf {e} _{i}}
are the components of an orthonormal basis in the current configuration. .