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
= = ^{ . } = L^{ . } | (5.1) |
(x, y, z) = | (5.2) |
Assuming a linear material law, the stress tensor can now be
calculated using the equation
= ^{ . } | (5.4) |
Introducing the distributed body forces
f (x, y, z) = | (5.5) |
+ + = | (5.6) | ||
+ + = | (5.7) | ||
+ + = | (5.8) |