On Microstructural Inertia

Abstract

Microstructural inertia may be modified by the presence of a powerless term which derives from the partial indetermination of the kinetic coenergy of the microstructure.

Multi-Value Microstructural Descriptors for Complex Materials: Analysis of Ground States

“…Metric and connection bring with them physical meaning. The metric, in fact, is associated with the representation of possible microstructural kinetic energy, relative to the macroscopic motion-there are reasons to foresee such a kind of additional kinetics, at least in appropriate special circumstances (see [8,44]). The metric, also, can be associated with a dissipation potential, as in gradient systems.…”

“…Moreover, a connection over M is involved in the representation of first-neighbor interactions. Sometimes a physically significant connection seems to be not available (see [8]). Hence, we find it convenient to endow M with as skeletal as possible a geometric structure, unless technical instances impose on us the choice of additional properties.…”

Linear Wave Motions in Continua with Nano-Pores

“…(see, also, [23]). The kinetic co-energy χ,a sκ, must have the same value for all observers at rest, i.e., it must be invariant under the Galilean group and hence satisfy the conditioṅ…”

Ground states in complex bodies

“…Physics may suggest also that a connection on M has no physical meaning as in the case of liquids with 'dispersed' bubbles. Moreover, even when M is selected to be Riemannian, in some circumstances the gauge needed for N might not be the Levi-Civita one (see, e.g., [10]). In this case, if no prevalent role is given to the Levi-Civita connection, the parallel transport over geodetics may be non-isometric in general and also it can be even unbounded as a consequence of topological features of M itself.…”

“…As a consequence, the theorem below follows. 10) where P (x) ∈ Aut R 3 is the extended Hamilton-Eshelby tensor defined by…”