55 lines
1.5 KiB
Python
55 lines
1.5 KiB
Python
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"""
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This module contains all common functions used in variational form.
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All operators are defined with respect to the reference coordiantes.
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"""
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import fenics as fn
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__version__ = "0.1"
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__author__ = "Reidmen Arostica"
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__date__ = "25/06/2020"
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def F_(coordinates: fn.Function) -> fn.grad:
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"""
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Computes the deformation gradient operator (dx/dX).
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"""
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return fn.grad(coordinates)
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def inv_F_(coordinates: fn.Function) -> fn.inv:
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"""
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Computes the inverse of the deformation gradient.
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"""
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return fn.inv(F_(coordinates))
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def J_(coordinates: fn.Function) -> fn.det:
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"""
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Computes the determinant of the deformation gradient.
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"""
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return fn.det(F_(coordinates))
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def grad_(u: fn.Function, coordinates: fn.Function) -> fn.Function:
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"""
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Computes the grad operator on the reference configuration.
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"""
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inv_F = fn.inv(F_(coordinates))
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return fn.dot(fn.grad(u), inv_F)
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def nabla_grad_(u: fn.Function, coordinates: fn.Function) -> fn.Function:
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"""
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Computes the nabla_grad on the reference configuration.
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"""
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return grad_(u, coordinates).T
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def sym_grad_(u: fn.Function, coordinates: fn.Function) -> fn.Function:
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"""
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Computes the symmetric gradient operator w.r.t. the reference configuration.
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"""
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return 0.5*(grad_(u, coordinates) + grad_(u, coordinates).T)
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def div_(u: fn.Function, coordinates: fn.Function) -> fn.tr:
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"""
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Computes the Piola div operator w.r.t. the reference configuration.
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"""
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J = J_(coordinates)
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inv_F = inv_F_(coordinates)
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return fn.div(J*fn.dot(inv_F, u))
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