  We investigate a specific finite element model to study the thermoelastic
behavior of an elastic body within the context of nonlinear strain-limiting
constitutive relation. As a special subclass of implicit relations, the
thermoelastic response of our interest is such that stresses can be arbitrarily
large, but strains remain small, especially in the neighborhood of crack-tips.
Thus, the proposed model can be inherently consistent with the assumption of
the small strain theory. In the present communication, we consider a
two-dimensional coupled system-linear and quasilinear partial differential
equations for temperature and displacements, respectively. Two distinct
temperature distributions of the Dirichlet type are considered for boundary
condition, and a standard finite element method of continuous Galerkin is
employed to obtain the numerical solutions for the field variables. For a
domain with an edge-crack, we find that the near-tip strain growth of our model
is much slower than the growth of stress, which is the salient feature compared
to the inconsistent results of the classical linearized description of the
elastic body. Current study can provide a theoretical and computational
framework to develop physically meaningful models and examine other coupled
multi-physics such as an evolution of complex network of cracks induced by
thermal shocks.
