sfepy.terms.terms_membrane module¶

class sfepy.terms.terms_membrane.TLMembraneTerm(*args, **kwargs)[source]¶

Mooney-Rivlin membrane with plain stress assumption.

The membrane has a uniform initial thickness $h_0$ and obeys a hyperelastic material law with strain energy by Mooney-Rivlin: $\Psi = a_1 (I_1 - 3) + a_2 (I_2 - 3)$ .

Call signature:

dw_tl_membrane

(material_a1, material_a2, material_h0, virtual, state)

Arguments:

material_a1 : $a_1$
material_a2 : $a_2$
material_h0 : $h_0$
virtual : $\ul{v}$
state : $\ul{u}$

arg_shapes = {'material_a1': '1, 1', 'material_a2': '1, 1', 'material_h0': '1, 1', 'state': 'D', 'virtual': ('D', 'state')}¶

arg_types = ('material_a1', 'material_a2', 'material_h0', 'virtual', 'state')¶

static eval_function(out, a1, a2, h0, mtx_c, c33, mtx_b, mtx_t, geo, term_mode, fmode)[source]¶

static function(out, fun, *args)[source]¶

Notes

fun is either weak_function or eval_function according to evaluation mode.

geometries = ['3_4', '3_8']¶

get_eval_shape(a1, a2, h0, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

get_fargs(a1, a2, h0, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

integration = 'facet'¶

name = 'dw_tl_membrane'¶

static weak_function(out, a1, a2, h0, mtx_c, c33, mtx_b, mtx_t, bfg, geo, fmode)[source]¶

sfepy.terms.terms_membrane.eval_membrane_mooney_rivlin(a1, a2, mtx_c, c33, mode)[source]¶

Evaluate stress or tangent stiffness of the Mooney-Rivlin membrane.

[1] Baoguo Wu, Xingwen Du and Huifeng Tan: A three-dimensional FE nonlinear analysis of membranes, Computers & Structures 59 (1996), no. 4, 601–605.