Finite element model for a coupled thermo-mechanical system in nonlinear strain-limiting thermoelastic body

We investigate a specific finite element model to study the thermoelastic behavior 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, particularly in the neighborhood of crack tips. In the present communication, we consider a two-dimensional coupled system - linear and quasi-linear partial differential equations for temperature and displacements, respectively. A standard finite element method of continuous Galerkin is then employed to obtain the numerical solutions for the field variables, where two distinct temperature distribution of the Dirichlet type are considered for boundary condition. From a domain with an edge-crack, we find that the near-tip strain growth in the proposed model is slower than the growth of stress, which is the salient feature compared to the predictions of singular strain based on the classical linearized description of the elastic body. In essence, the model can be inherently consistent with the assumption of linearized elasticity and infinitesimal strain theory. This 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. (c) 2022 Elsevier B.V. All rights reserved.