Adhesion¶

Normal Adhesion Potential¶

ipctk.normal_adhesion_potential(d: float, dhat_p: float, dhat_a: float, a2: float) → float¶

The normal adhesion potential.

Parameters:¶

d: float¶

distance

dhat_p: float¶

distance of largest adhesion force (\(\hat{d}_p\)) where \(0 < \hat{d}_p < \hat{d}_a\)

dhat_a: float¶

adhesion activation distance (\(\hat{d}_a\))

a2: float¶

adjustable parameter relating to the maximum derivative of a (\(a_2\))

Returns:¶

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.

Parameters:¶

d: float¶

distance

dhat_p: float¶

distance of largest adhesion force (\(\hat{d}_p\)) where \(0 < \hat{d}_p < \hat{d}_a\)

dhat_a: float¶

adhesion activation distance (\(\hat{d}_a\))

a2: float¶

adjustable parameter relating to the maximum derivative of a (\(a_2\))

Returns:¶

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.

Parameters:¶

d: float¶

distance

dhat_p: float¶

distance of largest adhesion force (\(\hat{d}_p\)) where \(0 < \hat{d}_p < \hat{d}_a\)

dhat_a: float¶

adhesion activation distance (\(\hat{d}_a\))

a2: float¶

adjustable parameter relating to the maximum derivative of a (\(a_2\))

Returns:¶

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.

Parameters:¶

dhat_p: float¶

distance of largest adhesion force (\(\hat{d}_p\)) where \(0 < \hat{d}_p < \hat{d}_a\)

dhat_a: float¶

adhesion activation distance (\(\hat{d}_a\))

a2: float¶

adjustable parameter relating to the maximum derivative of a (\(a_2\))

Returns:¶

The maximum normal adhesion force magnitude.

Tangential Adhesion Potential¶

ipctk.tangential_adhesion_f0(y: float, eps_a: float) → float¶

The tangential adhesion mollifier function.

Parameters:¶

y: float¶

The tangential relative speed.

eps_a: float¶

Velocity threshold below which static adhesion force is applied.

Returns:¶

The tangential adhesion mollifier function at y.

ipctk.tangential_adhesion_f1(y: float, eps_a: float) → float¶

The first derivative of the tangential adhesion mollifier function.

Parameters:¶

y: float¶

The tangential relative speed.

eps_a: float¶

Velocity threshold below which static adhesion force is applied.

Returns:¶

The first derivative of the tangential adhesion mollifier function at y.

ipctk.tangential_adhesion_f2(y: float, eps_a: float) → float¶

The second derivative of the tangential adhesion mollifier function.

Parameters:¶

y: float¶

The tangential relative speed.

eps_a: float¶

Velocity threshold below which static adhesion force is applied.

Returns:¶

The second derivative of the tangential adhesion mollifier function at y.

ipctk.tangential_adhesion_f1_over_x(y: float, eps_a: float) → float¶

The first derivative of the tangential adhesion mollifier function divided by y.

Parameters:¶

y: float¶

The tangential relative speed.

eps_a: float¶

Velocity threshold below which static adhesion force is applied.

Returns:¶

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.

Parameters:¶

y: float¶

The tangential relative speed.

eps_a: float¶

Velocity threshold below which static adhesion force is applied.

Returns:¶

The second derivative of the tangential adhesion mollifier function times y minus the first derivative all divided by y cubed.