Identity

Calculate the identity tensor. Two functions for generating identities are implemented:

• Eye = identity2(C) calculate Eye with the same tensor data type as C. The components of C are ignored.
• I4 = identity4(Eye) calculate the symmetric fourth order identity tensor with the property C = I4 : C

For the fourth order variant the function argument is not only used for defining the data type. For example the fourth order “inverse-identity” tensor may be obtained with I4invC = identity4(inv(C)) with the property invC = I4invC : C

Property	Value
Result	Tensor-valued function
Data Types	Tensor2, Tensor2s

Example

type(Tensor2)  :: C, invC, Eye
! type(Tensor2s) :: C, invC, Eye

type(Tensor4)  :: I4, I4invC
! type(Tensor4s) :: I4, I4invC

! the argument is only used for setting the data type
Eye = identity2(Eye)
Eye = identity2(C)

I4 = identity4(Eye)
C = I4**C
I4invC = identity4(inv(C))
invC = I4invC**C

Note: the operator ** for two tensor data types represents a double contraction. See double contraction for details. Eye.cdya.Eye is equivalent to identity4(Eye). See crossed-dyadic product for details.