Automatic energy-momentum conserving time integrators for hyperelastic waves

Autores: Amuthan Arunkumar Ramabathiran, S. Gopalakrishnan
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 236, Nº 18, 2012 (Ejemplar dedicado a: FEMTEC 2011: 3rd International Conference on Computational Methods in Engineering and Science, May 9-13, 2011), págs. 4700-4711
Idioma: inglés
DOI: 10.1016/j.cam.2012.02.040
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Resumen
- 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.