Tangential stiffness in Hertz-Mindlin?

[seijieng]

Hello, I am trying to understand how tangential stiffness (K_tau) is calculated for Type C rolling in Eqn (2-33) in the Rocky 2025 R1 technical manual when Hertz and Mindlin-Deresiewicz are chosen.

In the linear spring Coulomb limit model, a tangential stiffness ratio is user-defined for Eqn (2-19) to calculate tangential stiffness. For Hertz, it seems that the ratio remains at the default of 1 in Rocky's SDK. Is that true?

Looking at the SDK in "...Rocky\Modules\sdk\include\rocky20\device\device_contact_model_functions.hpp" for the function calculate_tangential_stiffness(), kn is calculated so that it corresponds to K_H,hat in Eqn (2-13). Then the tangential stiffness is calculated as follows:

kt = 1.5 * (mat_interaction->kt_kn) * kn;

 

Is the factor of 1.5 from taking the derivative of the Hertzian force to get dF/ds = 3/2 * K_H,hat * sqrt(s_n) ?

[Lucas Hoenicke]

Hello.

As stated in equation 2-19, the Tangential Stiffness is defined as the product of Loading Normal Stiffness and Tangential Stiffness Ratio.