Page 69 - Introduction to Continuum Mechanics

54 Tensors Calculus

thus,

so that the Cartesian components of (Vv) are

That is,

A geometrical interpretation of Vv will be given later in connection with the kinematics of
deformation.

2C4 Divergence of a Vector Field and Divergence of a Tensor Field.
Let v(r) be a vector field. The divergence of v(r) is defined to be a scalar field given by the
trace of the gradient of v. That is,

With reference to rectangular Cartesian basis, the diagonal elements of Vv are and

Thus

Let T(r) be a second order tensor field. The divergence of T is defined to be a vector field,
denoted by div T, such that for any vector a