Automatic energy-momentum conserving time integrators for hyperelastic waves

Ramabathiran, Amuthan Arunkumar and Gopalakrishnan, S (2012) Automatic energy-momentum conserving time integrators for hyperelastic waves. In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 236 (18, SI). pp. 4700-4711.

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Abstract

An energy-momentum conserving time integrator coupled with an automatic finite element algorithm is developed to study longitudinal wave propagation in hyperelastic layers. The Murnaghan strain energy function is used to model material nonlinearity and full geometric nonlinearity is considered. An automatic assembly algorithm using algorithmic differentiation is developed within a discrete Hamiltonian framework to directly formulate the finite element matrices without recourse to an explicit derivation of their algebraic form or the governing equations. The algorithm is illustrated with applications to longitudinal wave propagation in a thin hyperelastic layer modeled with a two-mode kinematic model. Solution obtained using a standard nonlinear finite element model with Newmark time stepping is provided for comparison. (C) 2012 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
Publication:	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Publisher:	ELSEVIER SCIENCE BV
Additional Information:	Copy right for this article belongs to Elsevier Science Netherlands.
Keywords:	Hyperelasticity;Energy-momentum conserving integrators; Murnaghan strain energy function;Automatic finite element assembly;Automatic differentiation;Higher order structural model
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	04 Oct 2012 12:28
Last Modified:	04 Oct 2012 12:28
URI:	http://eprints.iisc.ac.in/id/eprint/45071

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