References¶
[AB-ER-PI2018] | M. Abbas, A. Ern, N. Pignet. Hybrid High-Order methods for finite deformations of hyperelastic materials. Computational Mechanics, 62(4), 909-928, 2018. |
[AB-ER-PI2019] | M. Abbas, A. Ern, N. Pignet. A Hybrid High-Order method for incremental associative plasticity with small deformations. Computer Methods in Applied Mechanics and Engineering, 346, 891-912, 2019. |
[AL-CU1991] | P. Alart, A. Curnier. A mixed formulation for frictional contact problems prone to newton like solution methods. Comput. Methods Appl. Mech. Engrg. 92, 353–375, 1991. |
[Al-Ge1997] | E.L. Allgower and K. Georg. Numerical Path Following, Handbook of Numerical Analysis, Vol. V (P.G. Ciarlet and J.L. Lions, eds.). Elsevier, pp. 3-207, 1997. |
[AM-MO-RE2014] | S. Amdouni, M. Moakher, Y. Renard, A local projection stabilization of fictitious domain method for elliptic boundary value problems. Appl. Numer. Math., 76:60-75, 2014. |
[AM-MO-RE2014b] | S. Amdouni, M. Moakher, Y. Renard. A stabilized Lagrange multiplier method for the enriched finite element approximation of Tresca contact problems of cracked elastic bodies. Comput. Methods Appl. Mech. Engrg., 270:178-200, 2014. |
[bank1983] | R.E. Bank, A.H. Sherman, A. Weiser. Refinement algorithms and data structures for regular local mesh refinement. In Scientific Computing IMACS, Amsterdam, North-Holland, pp 3-17, 1983. |
[ba-dv1985] | K.J. Bathe, E.N. Dvorkin, A four-node plate bending element based on Mindlin-Reissner plate theory and a mixed interpolation. Internat. J. Numer. Methods Engrg., 21, 367-383, 1985. |
[Be-Mi-Mo-Bu2005] | Bechet E, Minnebo H, Moës N, Burgardt B. Improved implementation and robustness study of the X-FEM for stress analysis around cracks. Internat. J. Numer. Methods Engrg., 64, 1033-1056, 2005. |
[BE-CO-DU2010] | M. Bergot, G. Cohen, M. Duruflé. Higher-order finite elements for hybrid meshes using new nodal pyramidal elements J. Sci. Comput., 42, 345-381, 2010. |
[br-ba-fo1989] | F. Brezzi, K.J. Bathe, M. Fortin. Mixed-interpolated element for Reissner-Mindlin plates. Internat. J. Numer. Methods Engrg., 28, 1787-1801, 1989. |
[bu-ha2010] | E. Burman, P. Hansbo. Fictitious domain finite element methods using cut elements: I. A stabilized Lagrange multiplier method. Computer Methods in Applied Mechanics, 199:41-44, 2680-2686, 2010. |
[ca-re-so1994] | D. Calvetti, L. Reichel and D.C. Sorensen. An implicitly restarted Lanczos method for large symmetric eigenvalue problems. Electronic Transaction on Numerical Analysis}. 2:1-21, 1994. |
[ca-ch-er2019] | K. Cascavita, F. Chouly and A. Ern Hybrid High-Order discretizations combined with Nitsche’s method for Dirichlet and Signorini boundary conditions. hal-02016378v2, 2019 |
[CH-LA-RE2008] | E. Chahine, P. Laborde, Y. Renard. Crack-tip enrichment in the Xfem method using a cut-off function. Int. J. Numer. Meth. Engng., 75(6):629-646, 2008. |
[CH-LA-RE2011] | E. Chahine, P. Laborde, Y. Renard. A non-conformal eXtended Finite Element approach: Integral matching Xfem. Applied Numerical Mathematics, 61:322-343, 2011. |
[ciarlet1978] | P.G. Ciarlet. The finite element method for elliptic problems. Studies in Mathematics and its Applications vol. 4, North-Holland, 1978. |
[ciarlet1988] | P.G. Ciarlet. Mathematical Elasticity. Volume 1: Three-Dimensional Elasticity. North-Holland, 1988. |
[EncyclopCubature] | R. Cools, An Encyclopedia of Cubature Formulas, J. Complexity. |
[Dh-Go-Ku2003] | A. Dhooge, W. Govaerts and Y. A. Kuznetsov. MATCONT: A MATLAB Package for Numerical Bifurcation Analysis of ODEs. ACM Trans. Math. Software 31, 141-164, 2003. |
[Di-Er2015] | D.A. Di Pietro, A. Ern. A hybrid high-order locking free method for linear elasticity on general meshes. Comput. Methods Appl. Mech. Engrg., 283:1-21, 2015 |
[Di-Er2017] | D.A. Di Pietro, A. Ern. Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes. IMA Journal of Numerical Analysis, 37(1), 40-63. 2017 |
[Duan2014] | H. Duan. A finite element method for Reissner-Mindlin plates. Math. Comp., 83:286, 701-733, 2014. |
[Dr-La-Ek2014] | A. Draganis, F. Larsson, A. Ekberg. Finite element analysis of transient thermomechanical rolling contact using an efficient arbitrary Lagrangian-Eulerian description. Comput. Mech., 54, 389-405, 2014. |
[Fa-Po-Re2015] | M. Fabre, J. Pousin, Y. Renard. A fictitious domain method for frictionless contact problems in elasticity using Nitsche’s method. preprint, https://hal.archives-ouvertes.fr/hal-00960996v1 |
[Fa-Pa2003] | F. Facchinei and J.-S. Pang. Finite-Dimensional Variational Inequalities and Complementarity Problems, Vol. II. Springer Series in Operations Research, Springer, New York, 2003. |
[Georg2001] | K. Georg. Matrix-free numerical continuation and bifurcation. Numer. Funct. Anal. Optimization 22, 303-320, 2001. |
[GR-GH1999] | R.D. Graglia, I.-L. Gheorma. Higher order interpolatory vector bases on pyramidal elements IEEE transactions on antennas and propagation, 47:5, 775-782, 1999. |
[GR-ST2015] | D. Grandi, U. Stefanelli. The Souza-Auricchio model for shape-memory alloys Discrete and Continuous Dynamical Systems, Series S, 8(4):723-747, 2015. |
[HA-WO2009] | C. Hager, B.I. Wohlmuth. Nonlinear complementarity functions for plasticity problems with frictional contact. Comput. Methods Appl. Mech. Engrg., 198:3411-3427, 2009 |
[HA-HA2004] | A Hansbo, P Hansbo. A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput. Methods Appl. Mech. Engrg. 193 (33-35), 3523-3540, 2004. |
[HA-RE2009] | J. Haslinger, Y. Renard. A new fictitious domain approach inspired by the extended finite element method. Siam J. on Numer. Anal., 47(2):1474-1499, 2009. |
[HI-RE2010] | Hild P., Renard Y. Stabilized lagrange multiplier method for the finite element approximation of contact problems in elastostatics. Numer. Math. 15:1, 101–129, 2010. |
[KH-PO-RE2006] | Khenous H., Pommier J., Renard Y. Hybrid discretization of the Signorini problem with Coulomb friction, theoretical aspects and comparison of some numerical solvers. Applied Numerical Mathematics, 56/2:163-192, 2006. |
[KI-OD1988] | N. Kikuchi, J.T. Oden. Contact problems in elasticity. SIAM, 1988. |
[LA-PO-RE-SA2005] | Laborde P., Pommier J., Renard Y., Salaun M. High order extended finite element method for cracked domains. Int. J. Numer. Meth. Engng., 64:354-381, 2005. |
[LA-RE-SA2010] | J. Lasry, Y. Renard, M. Salaun. eXtended Finite Element Method for thin cracked plates with Kirchhoff-Love theory. Int. J. Numer. Meth. Engng., 84(9):1115-1138, 2010. |
[KO-RE2014] | K. Poulios, Y. Renard, An unconstrained integral approximation of large sliding frictional contact between deformable solids. Computers and Structures, 153:75-90, 2015. |
[LA-RE2006] | P. Laborde, Y. Renard. Fixed point strategies for elastostatic frictional contact problems. Math. Meth. Appl. Sci., 31:415-441, 2008. |
[Li-Re2014] | T. Ligurský and Y. Renard. A Continuation Problem for Computing Solutions of Discretised Evolution Problems with Application to Plane Quasi-Static Contact Problems with Friction. Comput. Methods Appl. Mech. Engrg. 280, 222-262, 2014. |
[Li-Re2014hal] | T. Ligurský and Y. Renard. Bifurcations in Piecewise-Smooth Steady-State Problems: Abstract Study and Application to Plane Contact Problems with Friction. Computational Mechanics, 56:1:39-62, 2015. |
[Li-Re2015hal] | T. Ligurský and Y. Renard. A Method of Piecewise-Smooth Numerical Branching. Z. Angew. Math. Mech., 97:7:815–827, 2017. |
[Mi-Zh2002] | P. Ming and Z. Shi, Optimal L2 error bounds for MITC3 type element. Numer. Math. 91, 77-91, 2002. |
[Xfem] | N. Moës, J. Dolbow and T. Belytschko, A finite element method for crack growth without remeshing. Internat. J. Numer. Methods Engrg., 46, 131-150, 1999. |
[Nackenhorst2004] | U. Nackenhorst, The ALE formulation of bodies in rolling contact. Theoretical foundation and finite element approach. Comput. Methods Appl. Mech. Engrg., 193:4299-4322, 2004. |
[NI-RE-CH2011] | S. Nicaise, Y. Renard, E. Chahine, Optimal convergence analysis for the eXtended Finite Element Method. Int. J. Numer. Meth. Engng., 86:528-548, 2011. |
[Pantz2008] | O. Pantz The Modeling of Deformable Bodies with Frictionless (Self-)Contacts. Archive for Rational Mechanics and Analysis, Volume 188, Issue 2, pp 183-212, 2008. |
[SCHADD] | L.F. Pavarino. Domain decomposition algorithms for the p-version finite element method for elliptic problems. Luca F. Pavarino. PhD thesis, Courant Institute of Mathematical Sciences}. 1992. |
[PO-NI2016] | K. Poulios, C.F. Niordson, Homogenization of long fiber reinforced composites including fiber bending effects. Journal of the Mechanics and Physics of Solids, 94, pp 433-452, 2016. |
[GetFEM2020] | Y. Renard, K. Poulios GetFEM: Automated FE modeling of multiphysics problems based on a generic weak form language. Preprint, https://hal.archives-ouvertes.fr/hal-02532422/document |
[remacle2003] | J.-F. Remacle, M.S. Shephard; An algorithm oriented mesh database. International Journal for Numerical Methods in Engineering, 58:2, pp 349-374, 2003. |
[SE-PO-WO2015] | A. Seitz, A. Popp, W.A. Wall, A semi-smooth Newton method for orthotropic plasticity and frictional contact at finite strains. Comput. Methods Appl. Mech. Engrg. 285:228-254, 2015. |
[SI-HU1998] | J.C. Simo, T.J.R. Hughes. Computational Inelasticity. Interdisciplinary Applied Mathematics, vol 7, Springer, New York 1998. |
[SO-PE-OW2008] | E.A. de Souza Neto, D Perić, D.R.J. Owen. Computational methods for plasticity. J. Wiley & Sons, New York, 2008. |
[renard2013] | Y. Renard, Generalized Newton’s methods for the approximation and resolution of frictional contact problems in elasticity. Comput. Methods Appl. Mech. Engrg., 256:38-55, 2013. |
[SU-CH-MO-BE2001] | Sukumar N., Chopp D.L., Moës N., Belytschko T. Modeling holes and inclusions by level sets in the extended finite-element method. Comput. Methods Appl. Mech. Engrg., 190:46-47, 2001. |
[ZT1989] | Zienkiewicz and Taylor. The finite element method. 5th edition, volume 3 : Fluids Dynamics. |