Question: A rectangular parallelepiped with original volume V o is oriented such that its edges are parallel to the principal directions of strain as shown in

A rectangular parallelepiped with original volume V_o is oriented such that its edges are parallel to the principal directions of strain as shown in the following figure. For small strains, show that the dilatation is given by:

d = ekk change in volume_AV original volume Vo

3 2 1

d = ekk change in volume_AV original volume Vo

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