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Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods
Author(s) -
Annavarapu Chandrasekhar,
Hautefeuille Martin,
Dolbow John E.
Publication year - 2012
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4343
Subject(s) - finite element method , benchmark (surveying) , constraint (computer aided design) , mathematical optimization , computer science , transient (computer programming) , boundary value problem , mathematics , boundary (topology) , dual (grammatical number) , focus (optics) , element (criminal law) , kinematics , mathematical analysis , geometry , engineering , classical mechanics , structural engineering , physics , literature , art , geodesy , optics , law , political science , geography , operating system
SUMMARY We investigate various strategies to enforce the kinematics at an embedded interface for transient problems within the extended finite element method. In particular, we focus on explicit time integration of the semi‐discrete equations of motion and extend both dual and primal variational frameworks for constraint enforcement to a transient regime. We reiterate the incompatibility of the dual formulation with purely explicit time integration and the severe restrictions placed by the Courant–Friedrichs–Levy condition on primal formulations. We propose an alternate, consistent formulation for the primal method and derive an estimate for the stabilization parameter, which is more amenable in an explicit dynamics framework. Importantly, the use of the new estimate circumvents the need for any tolerances as an interface approaches an element boundary. We also show that with interfacial constraints, existing mass lumping schemes can lead to prohibitively small critical time steps. Accordingly, we propose a mass lumping procedure, which provides a more favorable estimate. These techniques are then demonstrated on several benchmark numerical examples, where we compare and contrast the accuracy of the primal methods against the dual methods in enforcing the constraints. Copyright © 2012 John Wiley & Sons, Ltd.