Automatic energy–momentum conserving time integrators for hyperelastic waves

Ramabathiran, Amuthan Arunkumar ; Gopalakrishnan, S. (2012) Automatic energy–momentum conserving time integrators for hyperelastic waves Journal of Computational and Applied Mathematics, 236 (18). pp. 4700-4711. ISSN 0377-0427

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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.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Hyperelasticity; Energy–momentum Conserving Integrators; Murnaghan Strain Energy Function; Automatic Finite Element Assembly; Automatic Differentiation; Higher Order Structural Model
ID Code:99066
Deposited On:03 Sep 2015 05:31
Last Modified:03 Sep 2015 05:31

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