Adhesion

Normal Adhesion Potential

double ipc::normal_adhesion_potential(const double d,
    
const double dhat_pconst double dhat_aconst double a2);

The normal adhesion potential.

Parameters:
const double d

distance

const double dhat_p

distance of largest adhesion force ( d^p) where 0<d^p<d^a

const double dhat_a

adhesion activation distance ( d^a)

const double a2

adjustable parameter relating to the maximum derivative of a ( a2)

Returns:

The normal adhesion potential.

double ipc::normal_adhesion_potential_first_derivative(
    
const double dconst double dhat_pconst double dhat_a,
    
const double a2);

The first derivative of the normal adhesion potential wrt d.

Parameters:
const double d

distance

const double dhat_p

distance of largest adhesion force ( d^p) where 0<d^p<d^a

const double dhat_a

adhesion activation distance ( d^a)

const double a2

adjustable parameter relating to the maximum derivative of a ( a2)

Returns:

The first derivative of the normal adhesion potential wrt d.

double ipc::normal_adhesion_potential_second_derivative(
    
const double dconst double dhat_pconst double dhat_a,
    
const double a2);

The second derivative of the normal adhesion potential wrt d.

Parameters:
const double d

distance

const double dhat_p

distance of largest adhesion force ( d^p) where 0<d^p<d^a

const double dhat_a

adhesion activation distance ( d^a)

const double a2

adjustable parameter relating to the maximum derivative of a ( a2)

Returns:

The second derivative of the normal adhesion potential wrt d.

double ipc::max_normal_adhesion_force_magnitude(
    
const double dhat_pconst double dhat_aconst double a2);

The maximum normal adhesion force magnitude.

Parameters:
const double dhat_p

distance of largest adhesion force ( d^p) where 0<d^p<d^a

const double dhat_a

adhesion activation distance ( d^a)

const double a2

adjustable parameter relating to the maximum derivative of a ( a2)

Returns:

The maximum normal adhesion force magnitude.

Tangential Adhesion Potential

double ipc::tangential_adhesion_f0(
    
const double yconst double eps_a);

The tangential adhesion mollifier function.

Parameters:
const double y

The tangential relative speed.

const double eps_a

Velocity threshold below which static adhesion force is applied.

Returns:

The tangential adhesion mollifier function at y.

double ipc::tangential_adhesion_f1(
    
const double yconst double eps_a);

The first derivative of the tangential adhesion mollifier function.

Parameters:
const double y

The tangential relative speed.

const double eps_a

Velocity threshold below which static adhesion force is applied.

Returns:

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

double ipc::tangential_adhesion_f2(
    
const double yconst double eps_a);

The second derivative of the tangential adhesion mollifier function.

Parameters:
const double y

The tangential relative speed.

const double eps_a

Velocity threshold below which static adhesion force is applied.

Returns:

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

double ipc::tangential_adhesion_f1_over_x(
    
const double yconst double eps_a);

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

Parameters:
const double y

The tangential relative speed.

const double eps_a

Velocity threshold below which static adhesion force is applied.

Returns:

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

double ipc::tangential_adhesion_f2_x_minus_f1_over_x3(
    
const double yconst double eps_a);

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

Parameters:
const double y

The tangential relative speed.

const double eps_a

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.