In general, the displacement field is expressed in terms of the material coordinates as
2.
This is because one index of the tensor describes the material coordinates X which are independent of the observer ( Holzapfel 2000 ).
3.
That this derivation is for a material element is implicit in the time constancy of the reference configuration : it is constant in material coordinates.
4.
While many heavy equipment items, such as main propulsion machinery, were furnished directly by the Navy, the balance of the procurement was handled centrally by the Material Coordinating Agency an adjunct of the Bureau of Ships so that the numerous builders in the program would not have to bid against one another.
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