Error estimation and adaptivity for incompressible hyperelasticity
KAUST Grant NumberKUK-C1-013-04
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AbstractSUMMARY: A Galerkin FEM is developed for nonlinear, incompressible (hyper) elasticity that takes account of nonlinearities in both the strain tensor and the relationship between the strain tensor and the stress tensor. By using suitably defined linearised dual problems with appropriate boundary conditions, a posteriori error estimates are then derived for both linear functionals of the solution and linear functionals of the stress on a boundary, where Dirichlet boundary conditions are applied. A second, higher order method for calculating a linear functional of the stress on a Dirichlet boundary is also presented together with an a posteriori error estimator for this approach. An implementation for a 2D model problem with known solution, where the entries of the strain tensor exhibit large, rapid variations, demonstrates the accuracy and sharpness of the error estimators. Finally, using a selection of model problems, the a posteriori error estimate is shown to provide a basis for effective mesh adaptivity. © 2014 John Wiley & Sons, Ltd.
CitationWhiteley JP, Tavener SJ (2014) Error estimation and adaptivity for incompressible hyperelasticity. Int J Numer Meth Engng 99: 313–332. Available: http://dx.doi.org/10.1002/nme.4677.
SponsorsThis research was supported in part by award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). Both authors would also like to acknowledge financial support through the Colorado State University, College of Natural Sciences International Scholars program.