Abstract
Stress equilibration is investigated for hyperelastic deformation models in this contribution. From the displacement-pressure approximation computed with a stable finite element pair, an \(H (\mathrm{div})\)-conforming approximation to the first Piola-Kirchhoff stress tensor is computed. This is done in the usual way in a vertex-patch-wise manner involving local problems of small dimension. The corresponding reconstructed Cauchy stress is not symmetric but its skew-symmetric part is controlled by the computed correction. This difference between the reconstructed stress and the stress approximation obtained directly from the Galerkin approximation also serves as an upper bound for the discretization error. These properties are illustrated by computational experiments for an incompressible rigid block loaded on one half of its top boundary.
The funding by the Deutsche Forschungsgemeinschaft (DFG) under grants BE6511/1-1 and STA 402/14-1 within the priority program SPP 1748 is gratefully acknowledged.
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Bertrand, F., Moldenhauer, M., Starke, G. (2022). Stress Equilibration for Hyperelastic Models. In: Schröder, J., Wriggers, P. (eds) Non-standard Discretisation Methods in Solid Mechanics. Lecture Notes in Applied and Computational Mechanics, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-030-92672-4_4
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