In nonlinear analyses, the consistency of analysis types, material models, and physical models is important to generate accurate results.
Consistency Between Material Models and Physical Models
- Linear elastic material models (constant material properties) are only valid for structures of small strains.
- Nonlinear elastic, plastic, or elastic-plastic material models obtained from experimental tests with small strain conditions are only valid for structures of small strains.
Consistency Between Material Models and Analysis Types
- For the Total Lagrangian formulation, the processor expresses the material model in terms of the second Piola-Kirchhoff stress and Green-Lagrange tensors.
- For the Updated Lagrangian formulation, the processor expresses the material model in terms of Cauchy stress and Almansi strain tensors.
- For problems in the small strain range (large displacement, large rotation), both items 1 and 2 are valid and give practically the same results for the same material properties. However, for large strain problems, use the following:
- For Total Lagrangian formulation -- the constitutive model derived from the second Piola-Kirchhoff stress and the Green-Lagrange strain experimental curves.
- For Updated Lagrangian formulation -- the constitutive model derived from the Cauchy stress and the Almansi strain experimental curves.
- For elastic-plastic or viscoelastic-viscoplastic (creep) materials in small strain ranges (may involve large displacement and/or large rotation) where the constitutive relations are expressed in terms of engineering stresses and strains or their rates, the Total Lagrangian formulation is more effective.
- For large strain elastic-plastic materials, the processor uses the Updated Lagrangian formulation where the constitutive relations are expressed in terms of Jaumann stress rate and velocity strain tensors. The material model must be obtained or derived from experiments that give the true stress-strain relations (curves). One example of such experiments is using a true stress-logarithmic strain relation to represent the response of material under an uniaxial load.
Fine Mesh Versus Coarse Mesh
In normal situations, a finer mesh leads to more accurate results. However, when the deformation is expected to be large, especially if it is compression, a fine mesh is more susceptible to element distortion, and this distortion can lead to convergence difficulties. In this situation, a coarser mesh in the area of largest deformation can be a solution.