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.
|Original language||English (US)|
|Number of pages||23|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|State||Published - Jun 15 2019|
Bibliographical noteFunding Information:
Zhilin Han gratefully acknowledges support from the China Scholarship Council that funded his long-term stay at the University of Minnesota, where this research was performed as part of a joint Ph.D. training program. Sofia Mogilevskaya gratefully acknowledges support provided by the Theodore W. Bennett Chair at the University of Minnesota . D. Schillinger gratefully acknowledges support from the National Science Foundation through the NSF CAREER Award No. 1651577 and the NSF grant CISE-156599 . The authors also acknowledge the Minnesota Supercomputing Institute (MSI) of the University of Minnesota for providing computing resources that have contributed to the research results reported within this paper ( https://www.msi.umn.edu/ ).
- Asymptotic models of thin interphases
- Cut-cell finite element methods
- Isogeometric analysis
- Theories of material surfaces
- Variational interface formulations