We propose a component-based (CB) parametric model order reduction (pMOR) procedure for a class of problems in nonlinear mechanics with internal variables. The work is is motivated by applications to thermo-hydro-mechanical (THM) systems for radioactive waste disposal. The solution to this coupled system depends on several parameters, which might be related to the geometric configuration (e.g. the number of repositories, their distance or their size) or the material properties of the medium. The CB-pMOR formulation is based on overlapping subdomains. Our approach reads as a constrained optimization statement that penalizes the jump at the components’ interfaces subject to the approximate satisfaction of the partial differential equation in each local subdomain. Furthermore, the approach relies on the decomposition of the local states into a port component — associated with the solution on interior boundaries — and a bubble component that vanishes at ports: since the bubble components are uniquely determined by the solution value at the corresponding port, we can recast the constrained optimization statement into an unconstrained statement, which reads as a nonlinear least-squares problem and can be solved using the Gauss-Newton method.