In this model the materials are treated as elastic solids
parameterized by their Young Modulus E and Poisson ratio . The
stress tensor is calculated uniquely from the strain tensor which is
solved from the Navier Stokes equations [Zie91] together with the
displacement boundary conditions.
In theory of linear elasticity with small displacements the strain
tensor can be defined as
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(5.1) |
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(5.2) |
Assuming a linear material law, the stress tensor can now be
calculated using the equation
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(5.4) |
Introducing the distributed body forces
f (x, y, z) = ![]() ![]() ![]() |
(5.5) |
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(5.6) | ||
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(5.7) | ||
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(5.8) |