The Cowper-Symonds strength model lets you define the yield strength of isotropic strain hardening, strain rate dependent materials. The yield surface is defined as
where
| A is yield stress at zero plastic strain |
| B is the strain hardening coefficient |
| n is the strain hardening exponent |
| D and q are the strain rate hardening coefficients |
It should be noted that, in the implementation within the
Explicit Dynamics solver, the plastic strain rate (
) used in the Cowper Symonds model has a minimum value of unity to
allow for compatibility with the linear strain rate correction method. The
consequence of this is that for plastic strain rates less than unity, the material
will exhibit a strain rate hardening effect equal to that for a strain rate of
unity.
The plastic flow algorithm used in this model has an option to reduce high frequency oscillations that are sometimes observed in the yield surface under high strain rates. A first order strain rate correction is applied by default. An additional implicit strain rate correction is available that can be used in cases where the first order strain rate correction doesn’t suffice, although at the cost of extra CPU time usage.
Note that the strain rate constants should be input assuming that the units of strain rate are 1/second.
The Cowper-Symonds strength model can be used in all element types and in combination with all equations of state and failure properties.
| Name | Symbol | Units | Notes |
|---|---|---|---|
| Initial Yield Stress | A | Stress | |
| Hardening Constant | B | Stress | |
| Hardening Exponent | n | None | |
| Strain Rate Constant | D | None | Assumed 1/second in all cases |
| Strain Rate Constant | q | None | |
| Strain Rate Correction | - | None | Option List: None 1st Order (Default) Implicit |
Custom results variables available for this model:
| Name | Description | Solids | Shells | Beams |
|---|---|---|---|---|
| EFF_PL_STN | Effective Plastic Strain | Yes | Yes* | Yes* |
| EFF_PL_STN_RATE | Effective Plastic Strain Rate | Yes | Yes* | Yes* |
| SUBL_EPS | Effective sublayer plastic strain | No | Yes | No |
*Resultant value over shell/beam section.