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Reference documentation for deal.II version 8.5.1
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Namespaces | |
Contravariant | |
Covariant | |
Piola | |
Rotations | |
Functions | |
Special operations | |
template<int dim, typename Number > | |
Tensor< 1, dim, Number > | nansons_formula (const Tensor< 1, dim, Number > &N, const Tensor< 2, dim, Number > &F) |
A collection of operations to assist in the transformation of tensor quantities from the reference to spatial configuration, and vice versa. These types of transformation are typically used to re-express quantities measured or computed in one configuration in terms of a second configuration.
We will use the same notation for the coordinates , transformations
, differential operator
and deformation gradient
as discussed for namespace Physics::Elasticity.
As a further point on notation, we will follow Holzapfel (2007) and denote the push forward transformation as and the pull back transformation as
. We will also use the annotation
to indicate that a tensor
is a contravariant tensor, and
that it is covariant. In other words, these indices do not actually change the tensor, they just indicate the kind of object a particular tensor is.
Tensor<1,dim,Number> Physics::Transformations::nansons_formula | ( | const Tensor< 1, dim, Number > & | N, |
const Tensor< 2, dim, Number > & | F | ||
) |
Returns the result of applying Nanson's formula for the transformation of the material surface area element to the current surfaces area element
under the nonlinear transformation map
.
The returned result is the spatial normal scaled by the ratio of areas between the reference and spatial surface elements, i.e.
[in] | N | The referential normal unit vector ![]() |
[in] | F | The deformation gradient tensor ![]() |