NormalAdhesionPotential¶

class NormalAdhesionPotential : public ipc::NormalPotential;¶

The normal adhesion potential.

Public Functions¶

NormalAdhesionPotential(const double _dhat_p, const double _dhat_a,
    const double _Y, const double _eps_c);¶

virtual double force_magnitude(const double distance_squared,
    const double dmin,
    const double barrier_stiffness) const override;¶

Compute the force magnitude for a collision.

Parameters:¶

const double distance_squared¶

The squared distance between elements.

const double dmin¶

The minimum distance offset to the barrier.

const double barrier_stiffness¶

The barrier stiffness.

Returns:¶

The force magnitude.

virtual VectorMax12d force_magnitude_gradient(
    const double distance_squared,
    Eigen::ConstRef<VectorMax12d> distance_squared_gradient,
    const double dmin,
    const double barrier_stiffness) const override;¶

Compute the gradient of the force magnitude for a collision.

Parameters:¶

const double distance_squared¶

The squared distance between elements.

Eigen::ConstRef<VectorMax12d> distance_squared_gradient¶

The gradient of the squared distance.

const double dmin¶

The minimum distance offset to the barrier.

const double barrier_stiffness¶

The stiffness of the barrier.

Returns:¶

The gradient of the force.

VectorMax12d gradient(const NormalCollision& collision,
    Eigen::ConstRef<VectorMax12d> positions) const override;¶

Compute the gradient of the potential for a single collision.

Parameters:¶

const NormalCollision &collision¶

The collision.

Eigen::ConstRef<VectorMax12d> positions¶

The collision stencil’s positions.

Returns:¶

The gradient of the potential.

virtual double gradient(
    const double distance_squared, const double dmin = 0) const
    = 0;¶

Compute the gradient of the unmollified distance-based potential for a collision.

Parameters:¶

const double distance_squared¶

The distance (squared) between the two objects.

const double dmin = 0¶

The minimum distance (unsquared) between the two objects.

Returns:¶

The gradient of the unmollified distance-based potential.

MatrixMax12d hessian(const NormalCollision& collision,
    Eigen::ConstRef<VectorMax12d> positions,
    const PSDProjectionMethod project_hessian_to_psd
    = PSDProjectionMethod::NONE) const override;¶

Compute the hessian of the potential for a single collision.

Parameters:¶

const NormalCollision &collision¶

The collision.

Eigen::ConstRef<VectorMax12d> positions¶

The collision stencil’s positions.

const PSDProjectionMethod project_hessian_to_psd = PSDProjectionMethod::NONE¶

Whether to project the hessian to the positive semi-definite cone.

Returns:¶

The hessian of the potential.

virtual double hessian(
    const double distance_squared, const double dmin = 0) const
    = 0;¶

Compute the hessian of the unmollified distance-based potential for a collision.

Parameters:¶

const double distance_squared¶

The distance (squared) between the two objects.

const double dmin = 0¶

The minimum distance (unsquared) between the two objects.

Returns:¶

The hessian of the unmollified distance-based potential.

Public Members¶

double dhat_p;¶

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

double dhat_a;¶

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

double Y;¶

The Young’s modulus ( \(Y\)).

double eps_c;¶

The critical strain ( \(\varepsilon_c\)).

Protected Functions¶

virtual double operator()(const double distance_squared,
    const double dmin = 0) const override;¶

Compute the barrier potential for a collision.

Parameters:¶

const double distance_squared¶

The distance (squared) between the two objects.

const double dmin = 0¶

The minimum distance (unsquared) between the two objects.

Returns:¶

The barrier potential.

virtual double gradient(const double distance_squared,
    const double dmin = 0) const override;

Compute the gradient of the barrier potential for a collision.

Parameters:¶

const double distance_squared¶

The distance (squared) between the two objects.

const double dmin = 0¶

The minimum distance (unsquared) between the two objects.

Returns:¶

The gradient of the barrier potential.

virtual double hessian(const double distance_squared,
    const double dmin = 0) const override;

Compute the hessian of the barrier potential for a collision.

Parameters:¶

const double distance_squared¶

The distance (squared) between the two objects.

const double dmin = 0¶

The minimum distance (unsquared) between the two objects.

Returns:¶

The hessian of the barrier potential.

Private Types¶

using Super = NormalPotential;¶

Private Functions¶

std::array<double, 3> normal_adhesion_potential_args(
    const double dmin) const;¶