of body at different moments of time $T$ sees the different rate of the local time in comparison with the laboratory clocks.

Moreover, the lapse function S can be considered as an intrinsic measure of material age, associated with its cohesiveness. It can be normalized to be equal 1 in the reference state of the solid. As a result of energy dissipation in various inelastic processes, material loses its cohesiveness with aging. In the formalism presented here it is manifested in slowing down of the material (intrinsic) time, i.e. increasing of $S(X,T)$.

Here we do not consider thermodynamics. However, monotonic increase of $S(X,T)$ resembles and can be linked to the principle of non-negative entropy production of the thermodynamics of irreversible processes: $ \frac{dS_{in}}{dt}>0.$

The requirement $S>1$ leads to the strong constraints on the form of the “ground state term” of the material Lagrangian $L_{m}$, (see Sec. 5).

In this context, the shift vector field $\vec{N}$ in the metric $G$ reflects a propagation of the phase transition or chemical transformation boundary through the material as reflected, for instance in the mass conservation law (see below).

The separation of the evolution of 3D material metric $g$, material transformation process in $B_t$, characterized 