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In this paper, we propose a finite element–based immersed method to treat the mechanical coupling between a deformable porous medium model (PM) and an immersed solid model (ISM). The PM is formulated as a homogenized, volume‐coupled two‐field model, comprising a nearly incompressible solid phase that interacts with an incompressible Darcy‐Brinkman flow. The fluid phase is formulated with respect to...