ABSTRACT
We consider a body identified by the domain B which occupies a fixed configuration. A deformation of B is a smooth homeomorphism χ of B into a domain χ (B) in the three-dimensional Euclidean space E with det∇χ > 0. The point χ (x) is the place occupied by the material point x in the deformation χ, while
u (x) = χ (x)− x, (2.1.1)
is the displacement of x. The tensor fields
F = ∇χ and H = ∇u, (2.1.2)
are called, the deformation gradient and the displacement gradient, respectively. From (2.1.1) and (2.1.2), it results:
H = ∇u = F− 1, (2.1.3)
1 being the unit tensor.
