space ${\mathbb R }^{3}$ and $x^{0}=t$ on the time axes ${\mathbb R}$. We have $H=dt^2+h=dt^2+\sum_{i}dx^{i\ 2}.$

Hyperplanes $t=c$ are endowed with the 3D Euclidean metric $h$ induced by $H$. We extend 3D tensor $h$ to the degenerate (0,2)-tensor $\hat{h}$ in $M$, taking ${\hat{h}}_{0i}={\hat{h}}_{i0}={\hat h}_{00}=0$.

A solid is considered here, in a conventional way as a 3D manifold $B$ with the boundary $\partial B$, i.e. a set of “idealized” material points. We will use local coordinates $X^{I},I=1,2,3$ which, incidently, may be global coordinates induced by a [**reference configuration**]{} i.e., a diffeomorphic embedding $\phi _{0\
3}: B \longmapsto {\mathbb R}^{3}$ ([@MH]).

Cylinder $P={\mathbb R}\times {\bar B}$ (with the coordinates $(X^{0}=T,X^{I},I=1,2,3)$) is equipped with the 4D Riemannian metric $G$ (material metric) with the components $G_{IJ}$ relative to the coordinates $X^{0}=T,\ X^I, I=1,2,3$. Space $(P,G)$ is further referred to as the [**material “space-time”**]{}.

Metric $G$ defines the 4D volume form $dV=\sqrt{\vert G\vert
}d^{4}X$, where $\vert G\vert $ is the determinant of the matrix $(G_{IJ})$.

An example of such a material metric $G$ can be constructed as follows. Extend the reference configuration $\phi _{0\ 3}$ to the diffeomorphic embedding $\phi _{0}: P \longmapsto M,\ \phi
_{0}(T,X^I )=(T,x^i=\phi^{i}_{0\ 3}(X^I ))$. Let $G_{0}$ be the metric $\phi 