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'¶
- 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'¶
- 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'¶