Coherent Phase Interfaces

Abstract

The ensuing discussion is valid for both finite and infinitesimal deformations. The compatibility conditions (10-2) take the form

$$ [\dot u] = - V[\nabla u]m, $$

(14-1a)

$$ [\nabla u]P = 0, $$

(14-1b)

when expressed in terms of displacement. The working now has the form

with q and v velocity fields for ∂P and S, and with ů and

, respectively, corresponding time derivatives of u following the evolutions of ∂P and S. (The field

is defined by (10-4) with y replaced by u and transforms in the same manner as do $\dot u$ and ů; cf. (10-4) and the paragraph containing (13-5).) The second law remains (6-4), but with W(P) given by (14-2).