  We show how microstructure can arise in first-order ferroelastic structural
transitions, in two and three spatial dimensions, through a local meanfield
approximation of their pseudospin hamiltonians, that include anisotropic
elastic interactions. Such transitions have symmetry-selected physical strains
as their $N_{OP}$-component order parameters, with Landau free energies that
have a single zero-strain 'austenite' minimum at high temperatures, and
spontaneous-strain 'martensite' minima of $N_V$ structural variants at low
temperatures. In a reduced description, the strains at Landau minima induce
temperature-dependent, clock-like $\mathbb{Z}_{N_V +1}$ hamiltonians, with
$N_{OP}$-component strain-pseudospin vectors ${\vec S}$ pointing to $N_V + 1$
discrete values (including zero). We study elastic texturing in five such
first-order structural transitions through a local meanfield approximation of
their pseudospin hamiltonians, that include the powerlaw interactions. As a
prototype, we consider the two-variant square/rectangle transition, with a
one-component, pseudospin taking $N_V +1 =3$ values of $S= 0, \pm 1$, as in a
generalized Blume-Capel model. We then consider transitions with two-component
($N_{OP} = 2$) pseudospins: the equilateral to centred-rectangle ($N_V =3$);
the square to oblique polygon ($N_V =4$); the triangle to oblique ($N_V =6$)
transitions; and finally the 3D cubic to tetragonal transition ($ N_V =3$). The
local meanfield solutions in 2D and 3D yield oriented domain-walls patterns as
from continuous-variable strain dynamics, showing the discrete-variable models
capture the essential ferroelastic texturings. Other related hamiltonians
illustrate that structural-transitions in materials science can be the source
of interesting spin models in statistical mechanics.
