sfepy.terms.terms_fibres module¶

class sfepy.terms.terms_fibres.FibresActiveTLTerm(*args, **kwargs)[source]¶

Hyperelastic active fibres term. Effective stress $S_{ij} = A f_{\rm max} \exp{\left\{-(\frac{\epsilon - \varepsilon_{\rm opt}}{s})^2\right\}} d_i d_j$ , where $\epsilon = E_{ij} d_i d_j$ is the Green strain $\ull{E}$ projected to the fibre direction $\ul{d}$ .

Definition:

$\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})$

Call signature:

dw_tl_fib_a

(material_1, material_2, material_3, material_4, material_5, virtual, state)

Arguments:

material_1 : $f_{\rm max}$
material_2 : $\varepsilon_{\rm opt}$
material_3 : $s$
material_4 : $\ul{d}$
material_5 : $A$
virtual : $\ul{v}$
state : $\ul{u}$

arg_shapes = {'material_1': '1, 1', 'material_2': '1, 1', 'material_3': '1, 1', 'material_4': 'D, 1', 'material_5': '1, 1', 'state': 'D', 'virtual': ('D', 'state')}¶

arg_types = ('material_1', 'material_2', 'material_3', 'material_4', 'material_5', 'virtual', 'state')¶

family_data_names = ['green_strain']¶

get_eval_shape(mat1, mat2, mat3, mat4, mat5, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

get_fargs(mat1, mat2, mat3, mat4, mat5, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'dw_tl_fib_a'¶

static stress_function(out, pars, green_strain, fibre_data=None)[source]¶

static tan_mod_function(out, pars, green_strain, fibre_data=None)[source]¶

class sfepy.terms.terms_fibres.FibresExponentialTLTerm(*args, **kwargs)[source]¶

Hyperelastic fibres term with an exponential response. Effective stress $S_{ij} = \max\left(0, \sigma \left[ \exp{\left\{k (\epsilon - \epsilon_0)\right\}} - 1 \right]\right) d_i d_j$ , where $\epsilon = E_{ij} d_i d_j$ is the Green strain $\ull{E}$ projected to the fibre direction $\ul{d}$ .

Definition:

$\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})$

Call signature:

dw_tl_fib_e

(material_1, material_2, material_3, material_4, virtual, state)

Arguments:

material_1 : $\sigma$
material_3 : $k$
material_3 : $\epsilon_{0}$
material_4 : $\ul{d}$
virtual : $\ul{v}$
state : $\ul{u}$

arg_shapes = {'material_1': '1, 1', 'material_2': '1, 1', 'material_3': '1, 1', 'material_4': 'D, 1', 'state': 'D', 'virtual': ('D', 'state')}¶

arg_types = ('material_1', 'material_2', 'material_3', 'material_4', 'virtual', 'state')¶

family_data_names = ['green_strain']¶

get_eval_shape(mat1, mat2, mat3, mat4, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

get_fargs(mat1, mat2, mat3, mat4, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'dw_tl_fib_e'¶

static stress_function(out, pars, green_strain, fibre_data=None)[source]¶

static tan_mod_function(out, pars, green_strain, fibre_data=None)[source]¶

class sfepy.terms.terms_fibres.FibresSoftPlusExponentialTLTerm(*args, **kwargs)[source]¶

Hyperelastic fibres term with an exponential response. Effective stress $S_{ij} = \max\left(0, \sigma \left[ e^{k (\epsilon - \epsilon_0)} - 1 \right]\right) d_i d_j$ , where $\epsilon = E_{ij} d_i d_j$ is the Green strain $\ull{E}$ projected to the fibre direction $\ul{d}$ . The $\max$ is approximated by the softplus function scaled by $\alpha$ , i.e. $\frac{1}{\alpha} \log\left(1 + e^{\alpha x}\right)$ .

Definition:

$\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})$

Call signature:

dw_tl_fib_spe

(opt_material_0, material_1, material_2, material_3, material_4, virtual, state)

Arguments:

material_0 : $\alpha$ (default: 50)
material_1 : $\sigma$
material_3 : $k$
material_3 : $\epsilon_{0}$
material_4 : $\ul{d}$
virtual : $\ul{v}$
state : $\ul{u}$

arg_shapes = [{'material_1': '1, 1', 'material_2': '1, 1', 'material_3': '1, 1', 'material_4': 'D, 1', 'opt_material_0': '.: 1', 'state': 'D', 'virtual': ('D', 'state')}, {'opt_material_0': None}]¶

arg_types = ('opt_material_0', 'material_1', 'material_2', 'material_3', 'material_4', 'virtual', 'state')¶

family_data_names = ['green_strain']¶

get_eval_shape(mat1, mat2, mat3, mat4, mat5, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

get_fargs(mat0, mat1, mat2, mat3, mat4, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'dw_tl_fib_spe'¶

static stress_function(out, pars, green_strain, fibre_data=None)[source]¶

static tan_mod_function(out, pars, green_strain, fibre_data=None)[source]¶

sfepy.terms.terms_fibres.compute_fibre_strain(green_strain, omega)[source]¶: Compute the Green strain projected to the fibre direction.

sfepy.terms.terms_fibres.create_omega(fdir)[source]¶: Create the fibre direction tensor $\omega_{ij} = d_i d_j$ .