TY - JOUR
T1 - Consistent discretization of higher-order interface models for thin layers and elastic material surfaces, enabled by isogeometric cut-cell methods
AU - Han, Zhilin
AU - Stoter, Stein K.F.
AU - Wu, Chien Ting
AU - Cheng, Changzheng
AU - Mantzaflaris, Angelos
AU - Mogilevskaya, Sofia G.
AU - Schillinger, Dominik
N1 - Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/6/15
Y1 - 2019/6/15
N2 - Many interface formulations, e.g. based on asymptotic thin interphase models or material surface theories, involve higher-order differential operators and discontinuous solution fields. In this article, we are taking first steps towards a variationally consistent discretization framework that naturally accommodates these two challenges by synergistically combining recent developments in isogeometric analysis and cut-cell finite element methods. Its basis is the mixed variational formulation of the elastic interface problem that provides access to jumps in displacements and stresses for incorporating general interface conditions. Upon discretization with smooth splines, derivatives of arbitrary order can be consistently evaluated, while cut-cell meshes enable discontinuous solutions at potentially complex interfaces. We demonstrate via numerical tests for three specific nontrivial interfaces (two regimes of the Benveniste–Miloh classification of thin layers and the Gurtin–Murdoch material surface model) that our framework is geometrically flexible and provides optimal higher-order accuracy in the bulk and at the interface.
AB - Many interface formulations, e.g. based on asymptotic thin interphase models or material surface theories, involve higher-order differential operators and discontinuous solution fields. In this article, we are taking first steps towards a variationally consistent discretization framework that naturally accommodates these two challenges by synergistically combining recent developments in isogeometric analysis and cut-cell finite element methods. Its basis is the mixed variational formulation of the elastic interface problem that provides access to jumps in displacements and stresses for incorporating general interface conditions. Upon discretization with smooth splines, derivatives of arbitrary order can be consistently evaluated, while cut-cell meshes enable discontinuous solutions at potentially complex interfaces. We demonstrate via numerical tests for three specific nontrivial interfaces (two regimes of the Benveniste–Miloh classification of thin layers and the Gurtin–Murdoch material surface model) that our framework is geometrically flexible and provides optimal higher-order accuracy in the bulk and at the interface.
KW - Asymptotic models of thin interphases
KW - Cut-cell finite element methods
KW - Isogeometric analysis
KW - Theories of material surfaces
KW - Variational interface formulations
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U2 - 10.1016/j.cma.2019.03.010
DO - 10.1016/j.cma.2019.03.010
M3 - Article
AN - SCOPUS:85063096431
SN - 0045-7825
VL - 350
SP - 245
EP - 267
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -