An adaptive projection?based model reduction method for nonlinear mechanics with internal variables: Application to thermo?hydro?mechanical systems

We propose a projection-based monolithic model order reduction procedure for class of problems in nonlinear mechanics with internal variables. The work is motivated by applications to thermo-hydro-mechanical (THM) systems radioactive waste disposal. THM equations the behavior temperature, pore water pressure, and solid displacement neighborhood geological repositories, which contain are responsible significant thermal flux toward Earth's surface. develop an adaptive sampling strategy based on POD-Greedy method, we element-wise empirical quadrature hyper-reduction reduce assembling costs. present numerical results two-dimensional system illustrate validate proposed methodology.