On Atypical Imperfect Transmission Conditions for Thin Poroelastic Interphase

Physical fields within thin poroelastic interphases often vary rapidly, making numerical resolution computationally expensive. Analytical approaches address this by replacing the interphase with imperfect transmission conditions along a zero-thickness interface via asymptotic methods while preserving leading order solution properties. This work examines transmission conditions when elastic and viscous effects occur in distinct asymptotic regimes, leading to atypical coupling between the fields. Such coupling poses mathematical challenges but also enables accurate representation of multiphysics processes at leading order. We develop a method for solving problems governed by these atypical conditions and apply it to two-dimensional poroelasticity in domains with mixed interface types. Exact solutions are derived using integral transforms and expressed as convergent series, with numerical simulations validating the analysis. The results highlight the limitations of classical interface models and demonstrate the importance of atypical conditions for capturing coupling phenomena.