Abstract
A comparison of stress-based finite element methods is given for the prototype problem of linear elasticity and then extended to finite-strain hyperelasticity. Of particular interest is the accuracy of traction forces in reasonable Sobolev norms with an emphasis on uniform approximation behavior in the incompressible limit. The mixed formulation of Hellinger–Reissner type leading to a saddle-point problem as well as a first-order system least-squares approach are investigated and the strong connections between these two methods are studied. In addition, we also discuss stress reconstruction techniques based on displacement approximations by nonconforming finite elements.
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Acknowledgments
The work reported here was supported by the German Research Foundation (DFG) under grant STA 402/11-1. The authors would also like to thank Jörg Schröder and Alexander Schwarz for many discussions on the subject in the past years, especially related to the topic of Sect. 5.
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Müller, B., Starke, G. (2016). Stress-Based Finite Element Methods in Linear and Nonlinear Solid Mechanics. In: Schröder, J., Wriggers, P. (eds) Advanced Finite Element Technologies. CISM International Centre for Mechanical Sciences, vol 566. Springer, Cham. https://doi.org/10.1007/978-3-319-31925-4_4
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DOI: https://doi.org/10.1007/978-3-319-31925-4_4
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