GaPFlow.topography.ElasticDeformation

class GaPFlow.topography.ElasticDeformation(E: float, v: float, alpha_underrelax: float, grid: dict, n_images: int)

Bases: object

Thin wrapper around the FFTElasticHalfSpace classes from ContactMechanics.

Selects the appropriate Half-Space class based on the periodicity of the problem.

__init__(E: float, v: float, alpha_underrelax: float, grid: dict, n_images: int) → None

Constructor

Parameters:

• E (float) – Young’s modulus.

• v (float) – Poisson’s ratio.

• alpha_underrelax (float) – Underrelaxation factor.

• grid (dict) – Parameters controlling spatial discretization.

• n_images (int) – Number of periodic images for semi-periodic grids.

Methods

__init__(E, v, alpha_underrelax, grid, n_images)	Constructor
get_G_real()	For analysis and illustration purposes.
get_G_real_slices()	For analysis and illustration purposes.
get_deformation(p)	Calculation of the elastic deformation due to given pressure field p.
get_deformation_underrelax(p)	Updates elastic deformation using underrelaxation

get_G_real() → ndarray[tuple[Any, ...], dtype[floating]]

For analysis and illustration purposes. Returns the ‘ordered’ G_real numpy array with centered zero frequency component.

Returns:

G_real_ordered – Green’s function array in real space.

Return type:

ndarray

get_G_real_slices() → Tuple[ndarray[tuple[Any, ...], dtype[floating]], ndarray[tuple[Any, ...], dtype[floating]]]

For analysis and illustration purposes. Returns two middle slices of the G_real array, in x- and y-direction

Returns:

• x_slice (ndarray of shape (M,)) – middle slice of G_real in x-direction

• y_slice (ndarray of shape (N,)) – middle slice of G_real in y-direction

get_deformation(p: ndarray[tuple[Any, ...], dtype[floating]]) → ndarray[tuple[Any, ...], dtype[floating]]

Calculation of the elastic deformation due to given pressure field p. Convention: positive displacement for positive pressure.

Parameters:

p (ndarray) – Pressure array [Pa]

Returns:

disp – Array of resulting displacements [m].

Return type:

ndarray

get_deformation_underrelax(p: ndarray[tuple[Any, ...], dtype[floating]]) → ndarray[tuple[Any, ...], dtype[floating]]

Updates elastic deformation using underrelaxation

Parameters:

p (ndarray of shape (M, N)) – Pressure field.

Returns:

u_relaxed – Updated, underrelaxed deformation field.

Return type:

ndarray of shape (M, N)