Q) Bilinear CZM for use with contact elements is introduced at ANSYS 11.0 (TB,CZM,,,,CBDD/CBDE). What does the C5 "artificial damping" parameter mean, and how to does it work?
A) Equation 4-361 of the ANSYS 11.0 Theory Reference shows the usage of artificial damping. Note that a minus sign is missing from the 11.0 documentation.
Using the alternate notation of P=Tn (normal traction), Equation 4-361 is the following:
P = P_final + (P_initial - P_final)*exp(t/eta)
where P is the contact pressure (normal traction) for Mode I case, t is the time interval, and eta is the C5 artificial damping parameter. P_final represents the final traction at the end of the load step (e.g., 0 for 100% damage) and P_initial is the initial traction at the beginning of the load step. A similar implementation is used for the tangential term.
ANSYS does not know what P_final may be, so Equation 4-361 is not used as-is but implemented through use of a numerically discretized approximation; the developer noted that the actual implementation is not published.
What artificial damping essentially does is to augment the bilinear traction-separation CZM curve with an exponential form. The exponential form makes the bilinear 'tip' a little more blunt, which helps in convergence since the stiffness doesn't suddenly change (going from positive to negative slope). While this form is not meant to replicate the exponential CZM model used with 20x interface elements (TB,CZM,,,,EXPO), it provides a similar effect in that the bilinear CZM curve is discontinuous whereas having a 'smoother' tip (via the 'eta' parameter) aids in convergence.
Since it is implemented through numerical discretization, the actual result is sensitive not only to the 'eta' value (which should be a small value) but also sensitive to timestep size and mesh size.
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Q) Bilinear CZM for use with contact elements is introduced at ANSYS 11.0 (TB,CZM,,,,CBDD/CBDE). What does the C5 "artificial damping" parameter mean, and how to does it work? A) Equation 4-361 of the ANSYS 11.0 Theory Reference shows the usage of artificial damping. Note that a minus sign is missing from the 11.0 documentation. Using the alternate notation of P=Tn (normal traction), Equation 4-361 is the following: P = P_final + (P_initial - P_final)*exp(t/eta) where P is the contact pressure (normal traction) for Mode I case, t is the time interval, and eta is the C5 artificial damping parameter. P_final represents the final traction at the end of the load step (e.g., 0 for 100% damage) and P_initial is the initial traction at the beginning of the load step. A similar implementation is used for the tangential term. ANSYS does not know what P_final may be, so Equation 4-361 is not used as-is but implemented through use of a numerically discretized approximation; the developer noted that the actual implementation is not published. What artificial damping essentially does is to augment the bilinear traction-separation CZM curve with an exponential form. The exponential form makes the bilinear 'tip' a little more blunt, which helps in convergence since the stiffness doesn't suddenly change (going from positive to negative slope). While this form is not meant to replicate the exponential CZM model used with 20x interface elements (TB,CZM,,,,EXPO), it provides a similar effect in that the bilinear CZM curve is discontinuous whereas having a 'smoother' tip (via the 'eta' parameter) aids in convergence. Since it is implemented through numerical discretization, the actual result is sensitive not only to the 'eta' value (which should be a small value) but also sensitive to timestep size and mesh size. |
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