The Ogden strain energy density function, defined as:
where: λi are the principal stretches, αi, μi are material constants, and N is the number of terms in the function, is considered one of the most successful functions in describing the large deformation range of rubber-like materials.
The penalty function used in the formulation of the Ogden model takes the form of the one used in Mooney-Rivlin model. The strain energy function actually used is a modified type of the Ogden function:
where J is the ratio of the deformed volume to the undeformed volume, N is the number of terms in the function, G(J) = J2-1, and
where ν is the Poisson ratio.
Three-term (modified Ogden) models are widely used. Up to four-term models (N=4) are available in the program.
Besides the material constants mentioned above, Poisson ratio is also required. For most cases, satisfactory results can be obtained by assigning Poisson's ratio from 0.49 to 0.499. Further, increasing the Poisson's ratio will not have significant effect on the numerical results unless considerable volumetric strain is involved.
When the Poisson's ratio is extremely close to 0.5, it may cause solution termination due to negative diagonal terms in the stiffness matrix or lack of convergence.
The material properties for the Ogden model are input through the
Material dialog box. The required quantities are:
- First through Fourth Power material coefficients (αi)
- First through Fourth material constants (μi) (depending on the number of constants).
- Poisson's ratio