Adhesion¶

Normal Adhesion Potential¶

double ipc::normal_adhesion_potential(const double d,
    const double dhat_p, const double dhat_a, const double a2)¶

The normal adhesion potential.

Parameters:¶

const double d¶

distance

const double dhat_p¶

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

const double dhat_a¶

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

const double a2¶

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

Returns:¶

The normal adhesion potential.

double ipc::normal_adhesion_potential_first_derivative(
    const double d, const double dhat_p, const 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 ( \(\hat{d}_p\)) where \(0 < \hat{d}_p < \hat{d}_a\)

const double dhat_a¶

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

const double a2¶

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

Returns:¶

The first derivative of the normal adhesion potential wrt d.

double ipc::normal_adhesion_potential_second_derivative(
    const double d, const double dhat_p, const 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 ( \(\hat{d}_p\)) where \(0 < \hat{d}_p < \hat{d}_a\)

const double dhat_a¶

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

const double a2¶

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

Returns:¶

The second derivative of the normal adhesion potential wrt d.

double ipc::max_normal_adhesion_force_magnitude(
    const double dhat_p, const double dhat_a, const double a2)¶

The maximum normal adhesion force magnitude.

Parameters:¶

const double dhat_p¶

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

const double dhat_a¶

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

const double a2¶

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

Returns:¶

The maximum normal adhesion force magnitude.

Tangential Adhesion Potential¶

double ipc::tangential_adhesion_f0(
    const double y, const 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 y, const 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 y, const 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 y, const 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 y, const 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.