Journal
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
Volume 157, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijengsci.2020.103399
Keywords
Interphase layer; Asymptotic analysis; Theory of complex-valued functions; Higher-order imperfect interface models; Potential problems
Categories
Funding
- International Student Work Opportunity Program (ISWOP) at the University of Minnesota
- Theodore W. Bennett Chair at the University of Minnesota
- Isaac Newton Institute for Mathematical Sciences (INI) at Cambridge University (EPSRC grant) [EP/R014604/1]
- Simons Foundation through a Simons INI Fellowship
- German Research Foundation through the DFG Emmy Noether Award [SCH 1249/2-1]
- EPSRC [EP/R014604/1] Funding Source: UKRI
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We present a new methodology to derive imperfect interface models for the problems with interphase layers. The test case is potential problems, e.g., thermal conductivity, antiplane elasticity, etc. The methodology combines classical asymptotic analysis with concepts from the theory of complex-valued functions. Its major advantage over existing asymptotic approaches is the straightforward derivation of jump conditions that involve surface differential operators of arbitrary order, resulting in a hierarchy of models that maintain arbitrary-order accuracy with respect to the layer thickness and its curvature. Unlike low-order models, the derived higher-order models can accurately represent layers that are significantly softer or stiffer than the adjacent bulk materials, exhibit varying curvature, or are of finite thickness with respect to the characteristic length scale of the adjacent bulk regions. The interface models obtained via our methodology are compared with existing models of different orders, their limiting behavior is validated with respect to known interface regimes, and the improved accuracy of higher-order variants is illustrated for a benchmark example. While here we limited ourselves to scalar problems in two dimensions, the extension to vector problems in two-dimensions is straightforward. We also discuss the pathway to extend our methodology to scalar and vector problems in three-dimensions. (C) 2020 Elsevier Ltd. All rights reserved.
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