Appendix A.15 - User Material Constants #17-18: Strain Rate Strengthening Parameters

(Abaqus/Explicit only, does not apply to Abaqus/Standard)

In addition to the material degradation time period (user material constant 11), there are two additional constants that are specific to analyses run in Abaqus/Explicit that use Helius PFA materials.

Matrix Strain Rate Strengthening Parameter (ζ_m)- User Material Constant #17

This constant is used to determine the strengthening of the matrix material due to the rate of strain change. In other words, the matrix strength is increased as the strain rate increases. This parameter scales the strengthening in the following manner:

where the static strength, S₀, is assumed to be the strength at the strain rate, = 0.001 s^-1. The default value for is 0.1. Given the potential for variation in the chosen failure criteria for the fiber and matrix, the scaling is performed on the failure index rather than the strength as such:

Note, this assumes a failure criterion with all quadratic terms. If a failure criterion is chosen that uses linear terms or a combination of linear and quadratic terms, the above equation is still used and may yield an unexpected result. This includes the following criteria:

• Max Stress
• Max Strain
• Tsai-Wu
• Christensen
• Puck

Fiber Strain Rate Strengthening Parameter (ζ_f) - User Material Constant #18

This constant is used to determine the strengthening of the fiber material due to the rate of strain change. This value is used in exactly the same manner as the matrix strain rate strengthening parameter. The default value for is zero (no strengthening occurs by default).