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1297 1313 121 6 ; S ; "This is the peer reviewed version of the following article: Navarro-Jiménez, José M., Héctor Navarro-García, Manuel Tur, and Juan J. Ródenas. 2019. Superconvergent Patch Recovery with Constraints for Three-dimensional Contact Problems within the Cartesian Grid Finite Element Method. International Journal for Numerical Methods in Engineering 121 (6). Wiley: 1297 1313. doi:10.1002/nme.6266, which has been published in final form at https://doi.org/10.1002/nme.6266. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving." [EN] The superconvergent patch recovery technique with constraints (SPR-C) consists in improving the accuracy of the recovered stresses obtained with the original SPR technique by considering known information about the exact solution, like the internal equilibrium equation, the compatibility equation or the Neumann boundary conditions, during the recovery process. In this paper the SPR-C is extended to consider the equilibrium around the contact area when solving contact problems with the Cartesian grid Finite Element Method. In the proposed method, the Finite Element stress fields of both bodies in contact are considered during the recovery process and the equilibrium is enforced by means of the continuity of tractions along the contact surface. The authors would like to thank Generalitat Valenciana (PROMETEO/2016/007), the Spanish Ministerio de Economía, Industria y Competitividad (DPI2017-89816-R), the Spanish Ministerio de Ciencia, Innovación y Universidades (FPU17/03993), and Universitat Politècnica de València (FPI2015) for the financial support to this work. Navarro-Jiménez, J.; Navarro-García, H.; Tur Valiente, M.; Ródenas, JJ. (2020). Superconvergent patch recovery with constraints for three-dimensional contact problems within the Cartesian grid Finite Element Method. International Journal for Numerical Methods in Engineering. 121(6):1297-1313. https://doi.org/10.1002/nme.6266 Wriggers, P. (2006). ...

853 870 62 4 ; S Piegl L, Tiller W (1995) The NURBS Book. Springer, Berlin ; Wriggers P (2008) Nonlinear finite element methods. Springer, Berlin. https://doi.org/10.1007/978-3-540-71001-1 ; [EN] This paper proposes a method of solving 3D large deformation frictional contact problems with the Cartesian Grid Finite Element Method. A stabilized augmented Lagrangian contact formulation is developed using a smooth stress field as stabilizing term, calculated by Zienckiewicz and Zhu Superconvergent Patch Recovery. The parametric definition of the CAD surfaces (usually NURBS) is considered in the definition of the contact kinematics in order to obtain an enhanced measure of the contact gap. The numerical examples show the performance of the method. The authors wish to thank the Spanish Ministerio de Economia y Competitividad the Generalitat Valenciana and the Universitat Politecnica de Valencia for their financial support received through the projects DPI2013-46317-R, Prometeo 2016/007 and the FPI2015 program. Navarro-Jiménez, J.; Tur Valiente, M.; Albelda Vitoria, J.; Ródenas, JJ. (2018). Large deformation frictional contact analysis with immersed boundary method. Computational Mechanics. 62(4):853-870. https://doi.org/10.1007/s00466-017-1533-x ANSYS$$^{\textregistered }$$® Academic Research Mechanical, Release 16.2 Alart P, Curnier A (1991) A mixed formulation for frictional contact problems prone to Newton like solution methods. Comput Methods Appl Mech Eng 92(3):353–375. https://doi.org/10.1016/0045-7825(91)90022-X Annavarapu C, Hautefeuille M, Dolbow JE (2012) Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods. Int J Numer Methods Eng 92(June):206–228. https://doi.org/10.1002/nme.4343 Annavarapu C, Hautefeuille M, Dolbow JE (2014) A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. Part I: single interface. Comput Methods Appl Mech Eng 268:417–436. https://doi.org/10.1016/j.cma.2013.09.002 Annavarapu C, Settgast RR, Johnson SM, Fu ...