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An error-estimate-free and remapping-free variational mesh refinement and coarsening method for dissipative solids at finite strains

Mosler, J. and Ortiz, M. (2009) An error-estimate-free and remapping-free variational mesh refinement and coarsening method for dissipative solids at finite strains. International Journal for Numerical Methods in Engineering, 77 (3). pp. 437-450. ISSN 0029-5981. https://resolver.caltech.edu/CaltechAUTHORS:MOSijnme09

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Abstract

A variational h-adaptive finite element formulation is proposed. The distinguishing feature of this method is that mesh refinement and coarsening are governed by the same minimization principle characterizing the underlying physical problem. Hence, no error estimates are invoked at any stage of the adaption procedure. As a consequence, linearity of the problem and a corresponding Hilbert-space functional framework are not required and the proposed formulation can be applied to highly non-linear phenomena. The basic strategy is to refine (respectively, unrefine) the spatial discretization locally if such refinement (respectively, unrefinement) results in a sufficiently large reduction (respectively, sufficiently small increase) in the energy. This strategy leads to an adaption algorithm having O(N) complexity. Local refinement is effected by edge-bisection and local unrefinement by the deletion of terminal vertices. Dissipation is accounted for within a time-discretized variational framework resulting in an incremental potential energy. In addition, the entire hierarchy of successive refinements is stored and the internal state of parent elements is updated so that no mesh-transfer operator is required upon unrefinement. The versatility and robustness of the resulting variational adaptive finite element formulation is illustrated by means of selected numerical examples.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1002/nme.2428DOIUNSPECIFIED
http://www3.interscience.wiley.com/journal/121375960/abstractPublisherUNSPECIFIED
ORCID:
AuthorORCID
Ortiz, M.0000-0001-5877-4824
Additional Information:Copyright © 2008 John Wiley & Sons, Ltd. Received 20 September 2007; Revised 17 June 2008; Accepted 18 June 2008. Support from the DoE through Caltech’s ASC/ASAP Center for the Simulation of the Dynamic Response of Solids is gratefully acknowledged. J. M. is also grateful for support from the Deutsche Forschungsgemeinschaft (DFG) under contract/grant number: Mo 1389/1-1.
Funders:
Funding AgencyGrant Number
Department of EnergyUNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG);Mo 1389/1-1
Subject Keywords:h-adaption; variational formulation; dissipative solids; finite deformations; mesh-to-mesh-transfer operator; remapping
Issue or Number:3
Record Number:CaltechAUTHORS:MOSijnme09
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:MOSijnme09
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13419
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:17 Apr 2009 17:13
Last Modified:24 Feb 2020 10:30

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