NDLI: An analysis of the stress formula for energy-momentum methods in nonlinear elastodynamics

Content Provider	Springer Nature Link
Author	Romero, Ignacio
Copyright Year	2012
Abstract	The energy-momentum method, a space–time discretization strategy for elastic problems in nonlinear solid, structural, and multibody mechanics relies critically on a discrete derivative operation that defines an approximation of the internal forces that guarantees the discrete conservation of energy and momenta. In the case of nonlinear elastodynamics, the formulation for general hyperelastic materials is due to Simo and Gonzalez, dating back to the mid-nineties. In this work we show that there are actually infinite second order energy-momentum methods for elastodynamics, all of them deriving from a modified midpoint integrator by an appropriate redefinition of the stress tensor at equilibrium. Such stress tensors can be interpreted as the solutions to local convex projections, whose precise definitions lead to different methods. The mathematical requirements of such projections are identified. Based on this geometrical interpretation several conserving methods are examined.
Starting Page	603
Ending Page	610
Page Count	8
File Format	PDF
ISSN	01787675
Journal	Computational Mechanics
Volume Number	50
Issue Number	5
e-ISSN	14320924
Language	English
Publisher	Springer-Verlag
Publisher Date	2012-02-29
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Energy-momentum Time integration Geometric integration Nonlinear elastodynamics Computational Science and Engineering Classical Continuum Physics Theoretical and Applied Mechanics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Ocean Engineering Computational Theory and Mathematics Mechanical Engineering Computational Mechanics Computational Mathematics

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