mu]v] cannot be obtained directly from the embedding functions, but should be computed from the

covariant components as their inverse matrix.

j] are the

covariant components of the acceleration of the volume in the deformed body.

The Green strain tensor (E) may then be defined in terms of its covariant components as

Meanwhile, the covariant components of the displacement vector u(t) are

1), it is defined by a skew-symmetrical S[THETA](4)-invariant tensor field of degree 2 which may be expressed either by its

covariant componentsThe covariant components of the metric tensor on the deformed middle surface are

Alpha][Beta]] is the Kronecker delta, while the covariant components of the metric tensor and its determinant in the current configuration read

Here 2 = [alpha] 1 and nffand nff respectively are the contravariant and covariant components of the unit vector field n normal to the hypersurface of material coordinates [F.

It is customary to give the fully covariant components of the Riemann-Christoffel curvature tensor.

Therefore, we can express the fully covariant components of the generalized four-dimensional elasticity tensor in terms of the covariant components of the symmetric metric tensor [g.

the covariant components of the "dilation" and intrinsic spin tensors, respectively.

are the

covariant components of the tangent velocity vector field satisfying [u.