Depending on the settings, nonlinear analysis may require the input of stress/strain curves. When
that is the case, the curve should be entered using the correct definitions for stress and
strain.
The table below summarizes the types of stress and strain to be used as input for the stress/strain curve, depending on the analysis option and the type of material model used.
| Analysis Options |
|---|
| Material Model |
Small Strain,
Small Displacement |
Small Strain,
Large Displacement |
Large Strain,
Large Displacement |
| Non Linear
Elastic |
True Stress,
Engineering Strain |
True Stress,
Engineering Strain |
N/A |
| Elasto - Plastic
von Mises
Plasticity,
Tresca
Plasticity,
Drucker
Prager |
True Stress,
Engineering Strain |
True Stress,
Engineering Strain |
True Stress,
Logarithmic Strain |
| Hyper Elastic:
Mooney-Rivlin,
Ogden
Blatz Ko |
Engineering Stress,
Stretch ratio |
Engineering Stress,
Stretch ratio |
Engineering Stress,
Stretch ratio |
| Super Elastic |
True Stress,
Logarithmic Strain |
True Stress,
Logarithmic Strain |
True Stress,
Logarithmic Strain |
| Viscoelastic |
True Stress,
Engineering Strain |
True Stress,
Engineering Strain |
N/A |
After the analysis completes, the stress output is the Cauchy stress, which is the true stress in the deformed geometry.
The strain output depends on the material model and the choice of small or large strain formulation.
For non-linear elastic models: von Mises Plasticity, Tresca Plasticity,
Drucker Prager, Super Elastic, and Viscoelastic the small strain option produces engineering strains; the large strain option produces logarithmic strains.
|
True Stress and Strain
|
If the deformation of a bar in tension becomes significant, its cross-sectional area will change. The traditional engineering definitions for stress and strain are no longer accurate and new measures, namely true stress and true strain, are introduced. Alternative names for these quantities are Cauchy stress, logarithmic strain, and natural strain. The true stress is  , where a is the final deformed cross-sectional area.
The true strain is  , where l is the final length and L is the initial undeformed length of the bar.
|
|
Engineering Stress and Strain
|
The engineering stress (or nominal stress)  , where A is the initial undeformed cross-sectional area.
The engineering strain (or nominal strain) is  where Δl is the final bar deformation.
|
- Engineering strain is a small strain measure which is invalid once the strain in your model
is no longer "small" (approximately larger than 5%). Logarithmic strain, which is a nonlinear strain
measure that is dependent upon the final length of the model, is used for large strain
simulations.
- For viscoelastic material model, the definition of stress versus strain is replaced by relaxation
function versus time.
- Extrapolation of stress/strain curve after the curve's last data points: for plasticity or nonlinear
elastic material definition the last couple of data points are extrapolated linearly to calculate pairs of data points outside the defined stress/strain curve.
- When you define a stress-strain curve, the first point on the curve should be the yield point of the material. Material properties like elastic modulus, Yield strength, etc will be taken from the stress-strain curve when it is available and not from the material properties table in the Material dialog box. Only the Poisson's ratio (NUXY) will be taken from the table.