sfepy.terms.termsSurface module¶

class sfepy.terms.termsSurface.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.termsSurface.LinearTractionTerm(name, arg_str, integral, region, **kwargs)[source]¶

Linear traction forces (weak form), 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.

Definition :

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

Call signature:

dw_surface_ltr (material, virtual)

Arguments :	material : $\ull{\sigma}$ virtual : $\ul{v}$

arg_shapes = [{'material': 'S, 1', 'virtual': ('D', None)}, {'material': 'D, 1'}, {'material': '1, 1'}]¶

arg_types = ('material', 'virtual')¶

function()¶

get_fargs(traction, virtual, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

integration = 'surface'¶

name = 'dw_surface_ltr'¶

class sfepy.terms.termsSurface.SDSufaceNormalDotTerm(name, arg_str, integral, region, **kwargs)[source]¶

Sensitivity of scalar traction.

Definition :

$\int_{\Gamma} p \ul{c} \cdot \ul{n} \nabla \cdot \ul{\Vcal}$

Call signature:

d_sd_surface_ndot (material, parameter, parameter_mesh_velocity)

Arguments :	material : $\ul{c}$ parameter : $p$ parameter_mesh_velocity : $\ul{\Vcal}$

arg_shapes = {'parameter_mesh_velocity': 'D', 'material': 'D, 1', 'parameter': 1}¶

arg_types = ('material', 'parameter', 'parameter_mesh_velocity')¶

static function(out, material, val_p, div_mv, sg)[source]¶

get_eval_shape(mat, par, par_mv, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

get_fargs(mat, par, par_mv, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

integration = 'surface'¶

name = 'd_sd_surface_ndot'¶

class sfepy.terms.termsSurface.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.termsSurface.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'¶

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