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A coordinate-free variational continuum interface model for thin interphases: Ellipticity and convergence analysis.

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Title: A coordinate-free variational continuum interface model for thin interphases: Ellipticity and convergence analysis.
Authors: Stathas, Alexandros1 (AUTHOR) alexandros.stathas@boku.ac.at, Neuner, Matthias1 (AUTHOR)
Source: International Journal of Engineering Science. Aug2026, Vol. 225, pN.PAG-N.PAG. 1p.
Subjects: Elliptic equations, Continuum mechanics, Mathematical analysis, Engineering simulations, Inhomogeneous materials
Abstract: Thin interphase layers arise in many engineered joints and coatings, yet resolving them with full 3D models is costly and often impractical. This work introduces an elliptic interface model (EGI) that replaces a thin interphase by effective interface conditions while retaining the key kinematics of the original three-body configuration. In contrast to many existing reduced models, the proposed formulation explicitly accounts for displacement-gradient jumps generated around the interphase and is written in a general Cartesian setting, so interfaces at arbitrary orientation can be handled without special treatment. We provide a rigorous derivation of the EGI model, highlight its main differences from available approaches, and show that it preserves ellipticity for all material combinations for which the underlying full model is elliptic. Through a set of convergence analysis studies, we show that the EGI model provides an accurate and stable reduced description of thin interphases, suitable for engineering simulations involving complex interface orientations and strong material contrasts, and offers a practical basis for future extensions to viscoelastic and nonlinear interphase behavior. • We develop a novel Coordinate-Free Variational Continuum Interface Model for Thin Generalized Elliptic Interphases (EGI). • We show that the proposed model preserves ellipticity over a broader range of interphase material properties than existing approaches available in the literature. • We assess the performance of the EGI model in two demanding three-dimensional applications involving shear and torsion. • We demonstrate improved performance of the proposed model compared with related approaches reported in the literature. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:Thin interphase layers arise in many engineered joints and coatings, yet resolving them with full 3D models is costly and often impractical. This work introduces an elliptic interface model (EGI) that replaces a thin interphase by effective interface conditions while retaining the key kinematics of the original three-body configuration. In contrast to many existing reduced models, the proposed formulation explicitly accounts for displacement-gradient jumps generated around the interphase and is written in a general Cartesian setting, so interfaces at arbitrary orientation can be handled without special treatment. We provide a rigorous derivation of the EGI model, highlight its main differences from available approaches, and show that it preserves ellipticity for all material combinations for which the underlying full model is elliptic. Through a set of convergence analysis studies, we show that the EGI model provides an accurate and stable reduced description of thin interphases, suitable for engineering simulations involving complex interface orientations and strong material contrasts, and offers a practical basis for future extensions to viscoelastic and nonlinear interphase behavior. • We develop a novel Coordinate-Free Variational Continuum Interface Model for Thin Generalized Elliptic Interphases (EGI). • We show that the proposed model preserves ellipticity over a broader range of interphase material properties than existing approaches available in the literature. • We assess the performance of the EGI model in two demanding three-dimensional applications involving shear and torsion. • We demonstrate improved performance of the proposed model compared with related approaches reported in the literature. [ABSTRACT FROM AUTHOR]
ISSN:00207225
DOI:10.1016/j.ijengsci.2026.104553