def save_strain_and_params(self, iteration: int) -> None:
strain_vec = fenics.project(fenics.sym(fenics.grad(self.fields.u_new)),
V=self.tensor_space).vector()[:]
strain_tens = np.reshape(strain_vec,
newshape=(self.number_of_vertices, 2, 2))
parameters = fenics.project(
self.fields.new_constitutive_relation_multiplicative_parameters,
V=self.fields.new_constitutive_relation_multiplicative_parameters.
function_space()).vector()[:]
if self.fields.new_constitutive_relation_multiplicative_parameters.function_space(
).dim() == self.fields.tensor_space.dim():
parameters = np.reshape(parameters,
newshape=(self.number_of_vertices, 2, 2))
self.np_files.write(prefix='strain',
iteration=iteration,
array=strain_tens)
self.np_files.write(prefix='params',
iteration=iteration,
array=parameters)
def strain(v):
return fn.sym(fn.grad(v))
def k(u, v):
return inner(sigma(u), sym(grad(v))) * dx
def epsilon(u):
return fs.sym(fs.nabla_grad(u))
def get_new_value(self, r: fenics.Function) -> fenics.Expression:
return fenics.elem_mult(
self.fields.new_constitutive_relation_multiplicative_parameters,
fenics.sym(fenics.grad(r)))
def strain(u):
return fn.sym(fn.grad(u))
def eps(u):
return fn.sym(fn.grad(u))
def k(self, u: fenics.Function, w: fenics.Function,
constitutive_relation_function: Callable[[fenics.Function], fenics.Expression]) -> fenics.Expression:
return fenics.inner(constitutive_relation_function(u), fenics.sym(fenics.grad(w))) * fenics.dx
def get_new_value(self, r: fenics.Function) -> fenics.Expression:
return 2.0*self.lame_mu*fenics.sym(fenics.grad(r)) \
+ self.lame_lambda*fenics.tr(fenics.sym(fenics.grad(r)))*fenics.Identity(len(r))
def k(u, w):
return fnc.inner(sigma(u), fnc.sym(fnc.grad(w))) * fnc.dx
def sigma(r):
return 2.0 * mu * fnc.sym(fnc.grad(r)) + lmbda * fnc.tr(
fnc.sym(fnc.grad(r))) * fnc.Identity(len(r))
def eps(v):
return fnc.sym(fnc.grad(v))
def create_strain_tensor(self, u):
strain_vec = fenics.project(fenics.sym(fenics.grad((u))),
V=self.fields.tensor_space).vector()[:]
return np.reshape(strain_vec,
newshape=(self.fields.function_space.dim(), 2, 2))
