Source code for sfepy.terms.terms_hyperelastic_tl

from __future__ import absolute_import
import numpy as nm

from sfepy.base.base import assert_, Struct
from sfepy.terms.terms import terms
from sfepy.terms.terms_hyperelastic_base import\
    HyperElasticBase, HyperElasticFamilyData

[docs]class HyperElasticTLFamilyData(HyperElasticFamilyData): """ Family data for TL formulation. """ family_function = staticmethod(terms.dq_finite_strain_tl) cache_name = 'tl_common' data_names = ('mtx_f', 'det_f', 'sym_c', 'tr_c', 'in2_c', 'sym_inv_c', 'green_strain')
[docs]class HyperElasticTLBase(HyperElasticBase): """ Base class for all hyperelastic terms in TL formulation family. The subclasses should have the following static method attributes: - `stress_function()` (the stress) - `tan_mod_function()` (the tangent modulus) The common (family) data are cached in the evaluate cache of state variable. """ weak_function = staticmethod(terms.dw_he_rtm) hyperelastic_mode = 0 get_family_data = HyperElasticTLFamilyData()
[docs]class NeoHookeanTLTerm(HyperElasticTLBase): r""" Hyperelastic neo-Hookean term. Effective stress :math:`S_{ij} = \mu J^{-\frac{2}{3}}(\delta_{ij} - \frac{1}{3}C_{kk}C_{ij}^{-1})`. :Definition: .. math:: \int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v}) :Arguments: - material : :math:`\mu` - virtual : :math:`\ul{v}` - state : :math:`\ul{u}` """ name = 'dw_tl_he_neohook' family_data_names = ['det_f', 'tr_c', 'sym_inv_c'] stress_function = staticmethod(terms.dq_tl_he_stress_neohook) tan_mod_function = staticmethod(terms.dq_tl_he_tan_mod_neohook)
[docs]class MooneyRivlinTLTerm(HyperElasticTLBase): r""" Hyperelastic Mooney-Rivlin term. Effective stress :math:`S_{ij} = \kappa J^{-\frac{4}{3}} (C_{kk} \delta_{ij} - C_{ij} - \frac{2}{3 } I_2 C_{ij}^{-1})`. :Definition: .. math:: \int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v}) :Arguments: - material : :math:`\kappa` - virtual : :math:`\ul{v}` - state : :math:`\ul{u}` """ name = 'dw_tl_he_mooney_rivlin' family_data_names = ['det_f', 'tr_c', 'sym_inv_c', 'sym_c', 'in2_c'] stress_function = staticmethod(terms.dq_tl_he_stress_mooney_rivlin) tan_mod_function = staticmethod(terms.dq_tl_he_tan_mod_mooney_rivlin)
[docs]class BulkPenaltyTLTerm(HyperElasticTLBase): r""" Hyperelastic bulk penalty term. Stress :math:`S_{ij} = K(J-1)\; J C_{ij}^{-1}`. :Definition: .. math:: \int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v}) :Arguments: - material : :math:`K` - virtual : :math:`\ul{v}` - state : :math:`\ul{u}` """ name = 'dw_tl_bulk_penalty' family_data_names = ['det_f', 'sym_inv_c'] stress_function = staticmethod(terms.dq_tl_he_stress_bulk) tan_mod_function = staticmethod(terms.dq_tl_he_tan_mod_bulk)
[docs]class BulkActiveTLTerm(HyperElasticTLBase): r""" Hyperelastic bulk active term. Stress :math:`S_{ij} = A J C_{ij}^{-1}`, where :math:`A` is the activation in :math:`[0, F_{\rm max}]`. :Definition: .. math:: \int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v}) :Arguments: - material : :math:`A` - virtual : :math:`\ul{v}` - state : :math:`\ul{u}` """ name = 'dw_tl_bulk_active' family_data_names = ['det_f', 'sym_inv_c'] stress_function = staticmethod(terms.dq_tl_he_stress_bulk_active) tan_mod_function = staticmethod(terms.dq_tl_he_tan_mod_bulk_active)
[docs]class BulkPressureTLTerm(HyperElasticTLBase): r""" Hyperelastic bulk pressure term. Stress :math:`S_{ij} = -p J C_{ij}^{-1}`. :Definition: .. math:: \int_{\Omega} S_{ij}(p) \delta E_{ij}(\ul{u};\ul{v}) :Arguments: - virtual : :math:`\ul{v}` - state : :math:`\ul{u}` - state_p : :math:`p` """ name = 'dw_tl_bulk_pressure' arg_types = ('virtual', 'state', 'state_p') arg_shapes = {'virtual' : ('D', 'state'), 'state' : 'D', 'state_p' : 1} family_data_names = ['det_f', 'sym_inv_c'] weak_function = staticmethod(terms.dw_he_rtm) weak_dp_function = staticmethod(terms.dw_tl_volume) stress_function = staticmethod(terms.dq_tl_stress_bulk_pressure) tan_mod_u_function = staticmethod(terms.dq_tl_tan_mod_bulk_pressure_u)
[docs] def compute_data(self, family_data, mode, **kwargs): det_f, sym_inv_c = family_data.det_f, family_data.sym_inv_c p_qp = family_data.p_qp if mode == 0: out = nm.empty_like(sym_inv_c) fun = self.stress_function elif mode == 1: shape = list(sym_inv_c.shape) shape[-1] = shape[-2] out = nm.empty(shape, dtype=nm.float64) fun = self.tan_mod_u_function else: raise ValueError('bad mode! (%d)' % mode) fun(out, p_qp, det_f, sym_inv_c) return out
[docs] def get_fargs(self, virtual, state, state_p, mode=None, term_mode=None, diff_var=None, **kwargs): vgv, _ = self.get_mapping(state) name = state.name fd = self.get_family_data(state, self.region, self.integral, self.geometry_types[name], self.arg_steps[name], self.arg_derivatives[name]) fd.p_qp = self.get(state_p, 'val') if mode == 'weak': if diff_var != state_p.name: if diff_var is None: stress = self.compute_data(fd, 0, **kwargs) self.stress_cache = stress tan_mod = nm.array([0], ndmin=4, dtype=nm.float64) fmode = 0 else: stress = self.stress_cache if stress is None: stress = self.compute_data(fd, 0, **kwargs) tan_mod = self.compute_data(fd, 1, **kwargs) fmode = 1 fargs = (self.weak_function, stress, tan_mod, fd.mtx_f, fd.det_f, vgv, fmode, 0) else: vgs, _ = self.get_mapping(state_p) fargs = (self.weak_dp_function, fd.mtx_f, fd.sym_inv_c, fd.det_f, vgs, vgv, 1, -1) return fargs elif mode == 'el_avg': if term_mode == 'strain': out_qp = fd.green_strain elif term_mode == 'stress': out_qp = self.compute_data(fd, 0, **kwargs) else: raise ValueError('unsupported term mode in %s! (%s)' % (self.name, term_mode)) return self.integrate, out_qp, vgv, 1 else: raise ValueError('unsupported evaluation mode in %s! (%s)' % (self.name, mode))
[docs] def get_eval_shape(self, virtual, state, state_p, mode=None, term_mode=None, diff_var=None, **kwargs): n_el, n_qp, dim, n_en, n_c = self.get_data_shape(state) sym = (dim + 1) * dim // 2 return (n_el, 1, sym, 1), state.dtype
[docs]class VolumeTLTerm(HyperElasticTLBase): r""" Volume term (weak form) in the total Lagrangian formulation. :Definition: .. math:: \begin{array}{l} \int_{\Omega} q J(\ul{u}) \\ \mbox{volume mode: vector for } K \from \Ical_h: \int_{T_K} J(\ul{u}) \\ \mbox{rel\_volume mode: vector for } K \from \Ical_h: \int_{T_K} J(\ul{u}) / \int_{T_K} 1 \end{array} :Arguments: - virtual : :math:`q` - state : :math:`\ul{u}` """ name = 'dw_tl_volume' arg_types = ('virtual', 'state') arg_shapes = {'virtual' : (1, None), 'state' : 'D'} family_data_names = ['mtx_f', 'det_f', 'sym_inv_c'] function = staticmethod(terms.dw_tl_volume)
[docs] def get_fargs(self, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs): vgs, _ = self.get_mapping(virtual) vgv, _ = self.get_mapping(state) name = state.name fd = self.get_family_data(state, self.region, self.integral, self.geometry_types[name], self.arg_steps[name], self.arg_derivatives[name]) if mode == 'weak': if diff_var is None: fmode = 0 else: fmode = 1 elif (mode == 'eval') or (mode == 'el_avg'): if term_mode == 'volume': fmode = 2 elif term_mode == 'rel_volume': fmode = 3 else: raise ValueError('unsupported term evaluation mode in %s! (%s)' % (self.name, term_mode)) else: raise ValueError('unsupported evaluation mode in %s! (%s)' % (self.name, mode)) return fd.mtx_f, fd.sym_inv_c, fd.det_f, vgs, vgv, 0, fmode
[docs] def get_eval_shape(self, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs): n_el, n_qp, dim, n_en, n_c = self.get_data_shape(state) return (n_el, 1, 1, 1), state.dtype
[docs]class DiffusionTLTerm(HyperElasticTLBase): r""" Diffusion term in the total Lagrangian formulation with linearized deformation-dependent permeability :math:`\ull{K}(\ul{u}) = J \ull{F}^{-1} \ull{k} f(J) \ull{F}^{-T}`, where :math:`\ul{u}` relates to the previous time step :math:`(n-1)` and :math:`f(J) = \max\left(0, \left(1 + \frac{(J - 1)}{N_f}\right)\right)^2` expresses the dependence on volume compression/expansion. :Definition: .. math:: \int_{\Omega} \ull{K}(\ul{u}^{(n-1)}) : \pdiff{q}{\ul{X}} \pdiff{p}{\ul{X}} :Arguments: - material_1 : :math:`\ull{k}` - material_2 : :math:`N_f` - virtual : :math:`q` - state : :math:`p` - parameter : :math:`\ul{u}^{(n-1)}` """ name = 'dw_tl_diffusion' arg_types = ('material_1', 'material_2', 'virtual', 'state', 'parameter') arg_shapes = {'material_1' : 'D, D', 'material_2' : '1, 1', 'virtual' : (1, 'state'), 'state' : 1, 'parameter' : 'D'} family_data_names = ['mtx_f', 'det_f'] function = staticmethod(terms.dw_tl_diffusion)
[docs] def get_fargs(self, perm, ref_porosity, virtual, state, parameter, mode=None, term_mode=None, diff_var=None, **kwargs): vgv, _ = self.get_mapping(parameter) name = parameter.name fd = self.get_family_data(parameter, self.region, self.integral, self.geometry_types[name], self.arg_steps[name], self.arg_derivatives[name]) grad = self.get(state, 'grad') if mode == 'weak': if diff_var is None: fmode = 0 else: fmode = 1 elif mode == 'el_avg': if term_mode == 'diffusion_velocity': fmode = 2 else: raise ValueError('unsupported term evaluation mode in %s! (%s)' % (self.name, term_mode)) else: raise ValueError('unsupported evaluation mode in %s! (%s)' % (self.name, mode)) return grad, perm, ref_porosity, fd.mtx_f, fd.det_f, vgv, fmode
[docs] def get_eval_shape(self, perm, ref_porosity, virtual, state, parameter, mode=None, term_mode=None, diff_var=None, **kwargs): n_el, n_qp, dim, n_en, n_c = self.get_data_shape(state) return (n_el, 1, dim, 1), state.dtype
[docs]class HyperElasticSurfaceTLFamilyData(HyperElasticFamilyData): """ Family data for TL formulation applicable for surface terms. """ family_function = staticmethod(terms.dq_tl_finite_strain_surface) cache_name = 'tl_surface_common' data_names = ('mtx_f', 'det_f', 'inv_f') def __call__(self, state, region, integral, integration, step=0, derivative=None): sg, _ = state.field.get_mapping(region, integral, integration, get_saved=True) sd = state.field.surface_data[region.name] vec = state(step=step, derivative=derivative) st_shape = state.get_data_shape(integral, integration, region.name) data = self.init_data_struct(st_shape, name='surface_family_data') fargs = tuple([getattr(data, k) for k in self.data_names]) fargs = fargs + (vec, sg, sd.fis, state.field.econn) self.family_function(*fargs) return data
[docs]class HyperElasticSurfaceTLBase(HyperElasticTLBase): """ Base class for all hyperelastic surface terms in TL formulation family. """ get_family_data = HyperElasticSurfaceTLFamilyData()
[docs]class SurfaceFluxTLTerm(HyperElasticSurfaceTLBase): r""" Surface flux term in the total Lagrangian formulation, consistent with :class:`DiffusionTLTerm`. :Definition: .. math:: \int_{\Gamma} \ul{\nu} \cdot \ull{K}(\ul{u}^{(n-1)}) \pdiff{p}{\ul{X}} :Arguments: - material_1 : :math:`\ull{k}` - material_2 : :math:`N_f` - parameter_1 : :math:`p` - parameter_2 : :math:`\ul{u}^{(n-1)}` """ name = 'd_tl_surface_flux' arg_types = ('material_1', 'material_2', 'parameter_1', 'parameter_2') arg_shapes = {'material_1' : 'D, D', 'material_2' : '1, 1', 'parameter_1' : 1, 'parameter_2' : 'D'} family_data_names = ['det_f', 'inv_f'] integration = 'surface_extra' function = staticmethod(terms.d_tl_surface_flux)
[docs] def get_fargs(self, perm, ref_porosity, pressure, displacement, mode=None, term_mode=None, diff_var=None, **kwargs): sg, _ = self.get_mapping(displacement) name = displacement.name fd = self.get_family_data(displacement, self.region, self.integral, self.geometry_types[name], self.arg_steps[name], self.arg_derivatives[name]) grad = self.get(pressure, 'grad') fmode = {'eval' : 0, 'el_avg' : 1}.get(mode, 0) return grad, perm, ref_porosity, fd.inv_f, fd.det_f, sg, fmode
[docs] def get_eval_shape(self, perm, ref_porosity, pressure, displacement, mode=None, term_mode=None, diff_var=None, **kwargs): n_fa, n_qp, dim, n_en, n_c = self.get_data_shape(displacement) return (n_fa, 1, 1, 1), pressure.dtype
[docs]class SurfaceTractionTLTerm(HyperElasticSurfaceTLBase): r""" Surface traction term in the total Lagrangian formulation, expressed using :math:`\ul{\nu}`, the outward unit normal vector w.r.t. the undeformed surface, :math:`\ull{F}(\ul{u})`, the deformation gradient, :math:`J = \det(\ull{F})`, and :math:`\ull{\sigma}` a given traction, often equal to a given pressure, i.e. :math:`\ull{\sigma} = \pi \ull{I}`. :Definition: .. math:: \int_{\Gamma} \ul{\nu} \cdot \ull{F}^{-1} \cdot \ull{\sigma} \cdot \ul{v} J :Arguments: - material : :math:`\ull{\sigma}` - virtual : :math:`\ul{v}` - state : :math:`\ul{u}` """ name = 'dw_tl_surface_traction' arg_types = ('opt_material', 'virtual', 'state') arg_shapes = [{'opt_material' : 'D, D', 'virtual' : ('D', 'state'), 'state' : 'D'}, {'opt_material' : None}] family_data_names = ['det_f', 'inv_f'] integration = 'surface_extra' function = staticmethod(terms.dw_tl_surface_traction)
[docs] def get_fargs(self, mat, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs): sg, _ = self.get_mapping(virtual) sd = virtual.field.surface_data[self.region.name] bf = virtual.field.get_base(sd.bkey, 0, self.integral) name = state.name fd = self.get_family_data(state, self.region, self.integral, self.geometry_types[name], self.arg_steps[name], self.arg_derivatives[name]) if mat is None: eye = nm.eye(sg.dim, dtype=nm.float64) mat = nm.tile(eye, ((1, sg.n_qp, 1, 1))) if diff_var is None: fmode = 0 else: fmode = 1 return mat, fd.det_f, fd.inv_f, bf, sg, sd.fis, fmode
[docs]class VolumeSurfaceTLTerm(HyperElasticSurfaceTLBase): r""" Volume of a :math:`D`-dimensional domain, using a surface integral in the total Lagrangian formulation, expressed using :math:`\ul{\nu}`, the outward unit normal vector w.r.t. the undeformed surface, :math:`\ull{F}(\ul{u})`, the deformation gradient, and :math:`J = \det(\ull{F})`. Uses the approximation of :math:`\ul{u}` for the deformed surface coordinates :math:`\ul{x}`. :Definition: .. math:: 1 / D \int_{\Gamma} \ul{\nu} \cdot \ull{F}^{-1} \cdot \ul{x} J :Arguments: - parameter : :math:`\ul{u}` """ name = 'd_tl_volume_surface' arg_types = ('parameter',) arg_shapes = {'parameter' : 'D'} family_data_names = ['det_f', 'inv_f'] integration = 'surface_extra' function = staticmethod(terms.d_tl_volume_surface)
[docs] def get_fargs(self, parameter, mode=None, term_mode=None, diff_var=None, **kwargs): sg, _ = self.get_mapping(parameter) sd = parameter.field.surface_data[self.region.name] bf = parameter.field.get_base(sd.bkey, 0, self.integral) name = parameter.name fd = self.get_family_data(parameter, self.region, self.integral, self.geometry_types[name], self.arg_steps[name], self.arg_derivatives[name]) asc = nm.ascontiguousarray coors0 = parameter.field.get_coor() coors = asc(coors0 + parameter().reshape(coors0.shape)) return coors, fd.det_f, fd.inv_f, bf, sg, asc(sd.econn)
[docs] def get_eval_shape(self, parameter, mode=None, term_mode=None, diff_var=None, **kwargs): n_el, n_qp, dim, n_en, n_c = self.get_data_shape(parameter) return (n_el, 1, 1, 1), parameter.dtype