sfepy.terms.terms_surface module

class sfepy.terms.terms_surface.ContactPlaneTerm(*args, **kwargs)[source]

Small deformation elastic contact plane term with penetration penalty.

The plane is given by an anchor point \ul{A} and a normal \ul{n}. The contact occurs in points that orthogonally project onto the plane into a polygon given by orthogonal projections of boundary points \{\ul{B}_i\}, i = 1, \dots, N_B on the plane. In such points, a penetration distance d(\ul{u}) = (\ul{X} + \ul{u} -
\ul{A}, \ul{n}) is computed, and a force f(d(\ul{u})) \ul{n} is applied. The force depends on the non-negative parameters k (stiffness) and f_0 (force at zero penetration):

  • If f_0 = 0:

    f(d) = 0 \mbox{ for } d \leq 0 \;, \\
f(d) = k d \mbox{ for } d > 0 \;.

  • If f_0 > 0:

    f(d) = 0 \mbox{ for } d \leq -\frac{2 r_0}{k} \;, \\
f(d) = \frac{k^2}{4 r_0} d^2 + k d + r_0
\mbox{ for } -\frac{2 r_0}{k} < d \leq 0 \;, \\
f(d) = k d + f_0 \mbox{ for } d > 0 \;.

    In this case the dependence f(d) is smooth, and a (small) force is applied even for (small) negative penetrations: -\frac{2
r_0}{k} < d \leq 0.

Definition:

\int_{\Gamma} \ul{v} \cdot f(d(\ul{u})) \ul{n}

Call signature:
dw_contact_plane (material_f, material_n, material_a, material_b, virtual, state)
Arguments:
  • material_f : [k, f_0]
  • material_n : \ul{n} (special)
  • material_a : \ul{A} (special)
  • material_b : \{\ul{B}_i\}, i = 1, \dots, N_B (special)
  • virtual : \ul{v}
  • state : \ul{u}
arg_shapes = {‘material_n’: ‘.: D’, ‘material_a’: ‘.: D’, ‘material_b’: ‘.: N, D’, ‘material_f’: ‘1, 2’, ‘state’: ‘D’, ‘virtual’: (‘D’, ‘state’)}
arg_types = (‘material_f’, ‘material_n’, ‘material_a’, ‘material_b’, ‘virtual’, ‘state’)
static function(out, force, normal, geo, fmode)[source]
geometries = [‘3_4’, ‘3_8’]
get_fargs(force_pars, normal, anchor, bounds, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
integration = ‘surface’
name = ‘dw_contact_plane’
static smooth_f(d, k, f0, a, eps, diff)[source]
class sfepy.terms.terms_surface.ContactSphereTerm(*args, **kwargs)[source]

Small deformation elastic contact sphere term with penetration penalty.

The sphere is given by a centre point \ul{C} and a radius R. The contact occurs in points that are closer to \ul{C} than R. In such points, a penetration distance d(\ul{u}) =
R - ||\ul{X} + \ul{u} - \ul{C}|| is computed, and a force f(d(\ul{u})) \ul{n}(\ul{u}) is applied, where \ul{n}(\ul{u})
= (\ul{X} + \ul{u} - \ul{C}) / ||\ul{X} + \ul{u} - \ul{C}||. The force depends on the non-negative parameters k (stiffness) and f_0 (force at zero penetration):

  • If f_0 = 0:

    f(d) = 0 \mbox{ for } d \leq 0 \;, \\
f(d) = k d \mbox{ for } d > 0 \;.

  • If f_0 > 0:

    f(d) = 0 \mbox{ for } d \leq -\frac{2 r_0}{k} \;, \\
f(d) = \frac{k^2}{4 r_0} d^2 + k d + r_0
\mbox{ for } -\frac{2 r_0}{k} < d \leq 0 \;, \\
f(d) = k d + f_0 \mbox{ for } d > 0 \;.

    In this case the dependence f(d) is smooth, and a (small) force is applied even for (small) negative penetrations: -\frac{2
r_0}{k} < d \leq 0.

Definition:

\int_{\Gamma} \ul{v} \cdot f(d(\ul{u})) \ul{n}(\ul{u})

Call signature:
dw_contact_sphere (material_f, material_c, material_r, virtual, state)
Arguments:
  • material_f : [k, f_0]
  • material_c : \ul{C} (special)
  • material_r : R (special)
  • virtual : \ul{v}
  • state : \ul{u}
arg_shapes = {‘material_r’: ‘.: 1’, ‘material_c’: ‘.: D’, ‘virtual’: (‘D’, ‘state’), ‘material_f’: ‘1, 2’, ‘state’: ‘D’}
arg_types = (‘material_f’, ‘material_c’, ‘material_r’, ‘virtual’, ‘state’)
static function(out, force, normals, fd, geo, fmode)[source]
geometries = [‘3_4’, ‘3_8’]
get_fargs(force_pars, centre, radius, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
integration = ‘surface’
name = ‘dw_contact_sphere’
class sfepy.terms.terms_surface.LinearTractionTerm(name, arg_str, integral, region, **kwargs)[source]

Linear traction forces, where, depending on dimension of ‘material’ argument, \ull{\sigma} \cdot \ul{n} is \bar{p} \ull{I} \cdot \ul{n} for a given scalar pressure, \ul{f} for a traction vector, and itself for a stress tensor.

The material parameter can have one of the following shapes: 1 or (1, 1), (D, 1), (S, 1). The symmetric tensor storage is used in the last case: in 3D S = 6 and the indices ordered as [11, 22, 33, 12, 13, 23], in 2D S = 3 and the indices ordered as [11, 22, 12].

Definition:

\int_{\Gamma} \ul{v} \cdot \ull{\sigma} \cdot \ul{n},
\int_{\Gamma} \ul{v} \cdot \ul{n},

Call signature:
dw_surface_ltr (opt_material, virtual)
(opt_material, parameter)
Arguments:
  • material : \ull{\sigma}
  • virtual : \ul{v}
arg_shapes = [{‘opt_material’: ‘S, 1’, ‘parameter’: ‘D’, ‘virtual’: (‘D’, None)}, {‘opt_material’: ‘D, 1’}, {‘opt_material’: ‘1, 1’}, {‘opt_material’: None}]
arg_types = ((‘opt_material’, ‘virtual’), (‘opt_material’, ‘parameter’))
static d_fun(out, traction, val, sg)[source]
get_eval_shape(traction, virtual, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
get_fargs(traction, virtual, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
integration = ‘surface’
modes = (‘weak’, ‘eval’)
name = ‘dw_surface_ltr’
set_arg_types()[source]
class sfepy.terms.terms_surface.SDSufaceIntegrateTerm(name, arg_str, integral, region, **kwargs)[source]

Sensitivity of scalar traction.

Definition:

\int_{\Gamma} p \nabla \cdot \ul{\Vcal}

Call signature:
d_sd_surface_integrate (parameter, parameter_mesh_velocity)
Arguments:
  • parameter : p
  • parameter_mesh_velocity : \ul{\Vcal}
arg_shapes = {‘parameter_mesh_velocity’: ‘D’, ‘parameter’: 1}
arg_types = (‘parameter’, ‘parameter_mesh_velocity’)
static function(out, val_p, div_v, sg)[source]
get_eval_shape(par, par_v, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
get_fargs(par, par_v, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
integration = ‘surface’
name = ‘d_sd_surface_integrate’
class sfepy.terms.terms_surface.SufaceNormalDotTerm(name, arg_str, integral, region, **kwargs)[source]

“Scalar traction” term, (weak form).

Definition:

\int_{\Gamma} q \ul{c} \cdot \ul{n}

Call signature:
dw_surface_ndot (material, virtual)
(material, parameter)
Arguments:
  • material : \ul{c}
  • virtual : q
arg_shapes = {‘material’: ‘D, 1’, ‘parameter’: 1, ‘virtual’: (1, None)}
arg_types = ((‘material’, ‘virtual’), (‘material’, ‘parameter’))
static d_fun(out, material, val, sg)[source]
static dw_fun(out, material, bf, sg)[source]
get_eval_shape(mat, virtual, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
get_fargs(mat, virtual, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
integration = ‘surface’
modes = (‘weak’, ‘eval’)
name = ‘dw_surface_ndot’
set_arg_types()[source]
class sfepy.terms.terms_surface.SurfaceJumpTerm(name, arg_str, integral, region, **kwargs)[source]

Interface jump condition.

Definition:

\int_{\Gamma} c\, q (p_1 - p_2)

Call signature:
dw_jump (opt_material, virtual, state_1, state_2)
Arguments:
  • material : c
  • virtual : q
  • state_1 : p_1
  • state_2 : p_2
arg_shapes = [{‘state_1’: 1, ‘opt_material’: ‘1, 1’, ‘state_2’: 1, ‘virtual’: (1, None)}, {‘opt_material’: None}]
arg_types = (‘opt_material’, ‘virtual’, ‘state_1’, ‘state_2’)
static function(out, jump, mul, bf1, bf2, sg, fmode)[source]
get_fargs(coef, virtual, state1, state2, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
integration = ‘surface’
name = ‘dw_jump’