Reduced order variational multiscale enrichment method for thermo-mechanical problems

This manuscript presents the formulation and implementation of the reduced order variational multiscale enrichment (ROVME) method for thermo-mechanical problems. ROVME is extended to model the inelastic behavior of heterogeneous structures, in which the constituent properties are temperature sensitive. The temperature-dependent coefficient tensors of the reduced order method are approximated in an efficient manner, retaining the computational efficiency of the reduced order model in the presence of spatial/temporal temperature variations. A Newton–Raphson iterative scheme is formulated and implemented for the numerical evaluation of nonlinear system of equations associated with the proposed ROVME method. Numerical verifications are performed to assess the efficiency and accuracy of the proposed computational framework. The results of the verifications reveal that ROVME retains reasonable accuracy and achieves high efficiency in the presence of hermo-mechanical loads.