  We seek a rational route to large-deformation, thermo-mechanical modeling of
solids with metrical defects. It assumes the reference and deformed geometries
to be of the Weyl type and introduces the Weyl one-form -- an additional set of
degrees of freedom that determine ratios of lengths in different tangent
spaces. The Weyl one-form prevents the metric from being compatible with the
connection and enables exploitation of the incompatibility for characterizing
metrical defects in the body. When such a body undergoes temperature changes,
additional incompatibilities appear and interact with the defects. This
interaction is modeled using the Weyl transform, which keeps the Weyl
connection invariant whilst changing the non-metricity of the configuration. An
immediate consequence of the Weyl connection is that the critical points of the
stored energy are shifted. We exploit this feature to represent the residual
stresses. In order to relate stress and strain in our non-Euclidean setting,
use is made of the Doyle-Ericksen formula, which is interpreted as a relation
between the intrinsic geometry of the body and the stresses developed. Thus the
Cauchy stress is conjugate to the Weyl transformed metric tensor of the
deformed configuration. The evolution equation for the Weyl one-form is
consistent with the two laws of thermodynamics. Our temperature evolution
equation, which couples temperature, deformation and Weyl one-form, follows
from the first law of thermodynamics. Using the model, the self-stress
generated by a point defect is calculated and compared with the linear elastic
solutions. We also obtain conditions on the defect distribution (Weyl one-form)
that render a thermo-mechanical deformation stress-free. Using this condition,
we compute specific stress-free deformation profiles for a class of prescribed
temperature changes.
