Adhesion¶
Normal Adhesion Potential¶
- ipctk.normal_adhesion_potential(d: float, dhat_p: float, dhat_a: float, a2: float) float ¶
The normal adhesion potential.
- ipctk.normal_adhesion_potential_first_derivative(d: float, dhat_p: float, dhat_a: float, a2: float) float ¶
The first derivative of the normal adhesion potential wrt d.
- ipctk.normal_adhesion_potential_second_derivative(d: float, dhat_p: float, dhat_a: float, a2: float) float ¶
The second derivative of the normal adhesion potential wrt d.
- ipctk.max_normal_adhesion_force_magnitude(dhat_p: float, dhat_a: float, a2: float) float ¶
The maximum normal adhesion force magnitude.
Tangential Adhesion Potential¶
- ipctk.tangential_adhesion_f0(y: float, eps_a: float) float ¶
The tangential adhesion mollifier function.
- ipctk.tangential_adhesion_f1(y: float, eps_a: float) float ¶
The first derivative of the tangential adhesion mollifier function.
- ipctk.tangential_adhesion_f2(y: float, eps_a: float) float ¶
The second derivative of the tangential adhesion mollifier function.
- ipctk.tangential_adhesion_f1_over_x(y: float, eps_a: float) float ¶
The first derivative of the tangential adhesion mollifier function divided by y.
- ipctk.tangential_adhesion_f2_x_minus_f1_over_x3(y: float, eps_a: float) float ¶
The second derivative of the tangential adhesion mollifier function times y minus the first derivative all divided by y cubed.
Smooth \(\mu\)¶
- ipctk.smooth_mu_a0(y: float, mu_s: float, mu_k: float, eps_a: float) float ¶
Compute the value of the ∫ μ(y) a₁(y) dy, where a₁ is the first derivative of the smooth tangential adhesion mollifier.
Note
The a0/a1 are unrelated to the a0/a1 in the normal adhesion.
- ipctk.smooth_mu_a1(y: float, mu_s: float, mu_k: float, eps_a: float) float ¶
Compute the value of the μ(y) a₁(y), where a₁ is the first derivative of the smooth tangential adhesion mollifier.
Note
The a1 is unrelated to the a1 in the normal adhesion.
- ipctk.smooth_mu_a2(y: float, mu_s: float, mu_k: float, eps_a: float) float ¶
Compute the value of d/dy (μ(y) a₁(y)), where a₁ is the first derivative of the smooth tangential adhesion mollifier.
Note
The a1/a2 are unrelated to the a1/a2 in the normal adhesion.
- ipctk.smooth_mu_a1_over_x(y: float, mu_s: float, mu_k: float, eps_a: float) float ¶
Compute the value of the μ(y) a₁(y) / y, where a₁ is the first derivative of the smooth tangential adhesion mollifier.
Notes
The x in the function name refers to the parameter y. The a1 is unrelated to the a1 in the normal adhesion.
- ipctk.smooth_mu_a2_x_minus_mu_a1_over_x3(y: float, mu_s: float, mu_k: float, eps_a: float) float ¶
Compute the value of the [(d/dy μ(y) a₁(y)) ⋅ y - μ(y) a₁(y)] / y³, where a₁ and a₂ are the first and second derivatives of the smooth tangential adhesion mollifier.
Notes
The x in the function name refers to the parameter y. The a1/a2 are unrelated to the a1/a2 in the normal adhesion.