TY - JOUR
T1 - Higher-order imperfect interface modeling via complex variables based asymptotic analysis
AU - Baranova, S.
AU - Mogilevskaya, S. G.
AU - Nguyen, T. H.
AU - Schillinger, D.
N1 - Publisher Copyright:
© 2020 Elsevier Ltd
PY - 2020/12
Y1 - 2020/12
N2 - 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.
AB - 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.
KW - Asymptotic analysis
KW - Higher-order imperfect interface models
KW - Interphase layer
KW - Potential problems
KW - Theory of complex-valued functions
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U2 - 10.1016/j.ijengsci.2020.103399
DO - 10.1016/j.ijengsci.2020.103399
M3 - Article
AN - SCOPUS:85092249295
SN - 0020-7225
VL - 157
JO - International Journal of Engineering Science
JF - International Journal of Engineering Science
M1 - 103399
ER -