M. Abbas, G. Drouet, and P. Hild, The local average contact (LAC) method, Comput. Methods Appl. Mech. Engrg, vol.339, pp.488-513, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01682901

M. Abbas, A. Ern, and N. Pignet, Hybrid High-Order methods for finite deformations of hyperelastic materials, Comput. Mech, vol.62, issue.4, pp.909-928, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01575370

M. Abbas, A. Ern, and N. Pignet, A Hybrid High-Order method for incremental associative plasticity with small deformations, Comput. Methods Appl. Mech. Engrg, vol.346, pp.891-912, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01768411

M. Abbas, A. Ern, and N. Pignet, A Hybrid High-Order method for finite elastoplastic deformations within a logarithmic strain framework, Int. J. Numer. Methods Eng, vol.120, issue.3, pp.303-327, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01978385

C. Adam, T. J. Hughes, S. Bouabdallah, M. Zarroug, and H. Maitournam, Selective and reduced numerical integrations for NURBS-based isogeometric analysis, Comput. Methods Appl. Mech. Engrg, vol.284, pp.732-761, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01214741

C. Agelet-de-saracibar, M. Chiumenti, Q. Valverde, and M. Cervera, On the orthogonal subgrid scale pressure stabilization of finite deformation J2 plasticity, Comput. Methods Appl. Mech. Eng, vol.195, issue.9, pp.1224-1251, 2006.

J. Aghili, D. A. Di-pietro, and B. Ruffini, An hp-Hybrid High-Order Method for Variable Diffusion on General Meshes, Comput. Methods Appl. Math, vol.17, issue.3, pp.359-376, 2017.

D. and A. Akhrass, Méthodeséléments finis mixtes robustes pour gérer l'incompréssibilité en grandes déformations dans un cadre industriel, 2014.

D. Akhrass, J. Bruchon, S. Drapier, and S. Fayolle, Integrating a logarithmic-strain based hyperelastic formulation into a three-field mixed finite element formulation to deal with incompressibility in finite-strain elastoplasticity, Finite Elem. Anal. Des, vol.86, pp.61-70, 2014.
URL : https://hal.archives-ouvertes.fr/emse-01063686

P. Alart, Méthode de Newton généralisée en mécanique du contact, J. Math. Pures Appl, vol.76, issue.9, pp.83-108, 1997.

J. Alberty, C. Carstensen, and D. Zarrabi, Adaptive numerical analysis in primal elastoplasticity with hardening, Comput. Methods Appl. Mech. Engrg, vol.171, issue.3-4, pp.175-204, 1999.

D. N. Arnold, F. Brezzi, B. Cockburn, and L. D. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM J. Numer. Anal, vol.39, issue.5, p.2, 2001.

E. Artioli, L. Beirão-da-veiga, C. Lovadina, and E. Sacco, Arbitrary order 2D virtual elements for polygonal meshes: part II, inelastic problem, Comput. Mech, vol.60, issue.4, pp.643-657, 2017.

F. Auricchio and L. Beirão-da-veiga, On a new integration scheme for von Mises plasticity with linear hardening, Int. J. Numer. Meth. Engrg, vol.56, pp.1375-1396, 2003.

F. Auricchio, L. Beirão-da-veiga, C. Lovadina, A. Reali, R. L. Taylor et al., Approximation of incompressible large deformation elastic problems: some unresolved issues, Comput. Mech, vol.52, issue.5, pp.1153-1167, 2013.

F. Auricchio, L. Beirão-da-veiga, C. Lovadina, and A. Reali, A stability study of some mixed finite elements for large deformation elasticity problems, Comput. Methods Appl. Mech. Engrg, vol.194, issue.9, pp.1075-1092, 2005.

F. Auricchio, L. Beirão-da-veiga, C. Lovadina, and A. Reali, The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: mixed FEMs versus NURBS-based approximations, Comput. Methods Appl. Mech. Engrg, vol.199, issue.5-8, pp.314-323, 2010.

B. Ayuso-de-dios, K. Lipnikov, and G. Manzini, The nonconforming virtual element method, ESAIM Math. Model. Numer. Anal, vol.50, issue.3, pp.879-904, 2016.

L. Baillet and T. Sassi, Méthode d'éléments finis avec hybridisation frontière pour les problèmes de contact avec frottement, C. R. Math. Acad. Sci, vol.334, issue.10, pp.917-922, 2002.

L. Baillet and T. Sassi, Mixed finite element methods for the Signorini problem with friction, Numer. Methods Partial Differential Equations, vol.22, issue.6, pp.1489-1508, 2006.
URL : https://hal.archives-ouvertes.fr/insu-00355157

J. M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal, vol.63, issue.4, p.77, 1976.

J. M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Philos. Trans. Roy. Soc. London Ser. A, vol.306, pp.557-611, 1496.

P. Ballard, Steady sliding frictional contact problems in linear elasticity, J. Elasticity, vol.110, issue.1, pp.33-61, 2013.

R. Bargellini, J. Besson, E. Lorentz, and S. Michel-ponnelle, A non-local finite element based on volumetric strain gradient: Application to ductile fracture, Computational Materials Science, vol.45, pp.762-767, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00379224

P. T. Barton, D. Drikakis, and E. I. Romenski, An Eulerian finite-volume scheme for large elastoplastic deformations in solids, Int. J. Numer. Meth. Engng, vol.81, pp.453-484, 2010.

H. R. Bayat, J. Krämer, L. Wunderlich, S. Wulfinghoff, S. Reese et al., Numerical evaluation of discontinuous and nonconforming finite element methods in nonlinear solid mechanics, Comput. Mech, vol.62, issue.6, pp.1413-1427, 2018.

H. R. Bayat, S. Wulfinghoff, S. Kastian, and S. Reese, On the use of reduced integration in combination with discontinuous galerkin discretization: application to volumetric and shear locking problems, Advanced Modeling and Simulation in Engineering Sciences, vol.5, issue.1, p.10, 2018.

L. Beirão-da-veiga, F. Brezzi, and L. D. Marini, Virtual elements for linear elasticity problems, SIAM J. Numer. Anal, vol.51, issue.2, pp.794-812, 2013.

L. Beirão-da-veiga, F. Brezzi, L. D. Marini, and A. Russo, Virtual element implementation for general elliptic equations, Building bridges: connections and challenges in modern approaches to numerical partial differential equations, vol.114, pp.39-71, 2016.

L. Beirão-da-veiga, C. Lovadina, and D. Mora, A virtual element method for elastic and inelastic problems on polytope meshes, Comput. Methods Appl. Mech. Engrg, vol.295, pp.327-346, 2015.

F. , B. Belgacem, and Y. Renard, Hybrid finite element methods for the Signorini problem, Math. Comp, vol.72, issue.243, pp.1117-1145, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00690588

D. Boffi, M. Botti, and D. A. Di-pietro, A nonconforming high-order method for the Biot problem on general meshes, SIAM J. Sci. Comput, vol.38, issue.3, pp.1508-1537, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01162976

F. Bonaldi, D. A. Di-pietro, G. Geymonat, and F. Krasucki, A Hybrid High-Order method for Kirchhoff-Love plate bending problems, ESAIM Math. Model. Numer. Anal, vol.52, issue.2, pp.393-421, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01541389

J. Bonelle, D. A. Di-pietro, and A. Ern, Low-order reconstruction operators on polyhedral meshes: application to compatible discrete operator schemes, Comput. Aided Geom. Design, vol.35, pp.27-41, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01097311

J. Bonelle and A. Ern, Analysis of compatible discrete operator schemes for elliptic problems on polyhedral meshes, ESAIM Math. Model. Numer. Anal, vol.48, issue.2, pp.553-581, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00751284

J. Bonet and R. D. Wood, Nonlinear continuum mechanics for finite element analysis, 1997.

V. Bostan and W. Han, A posteriori error analysis for finite element solutions of a frictional contact problem, Comput. Methods Appl. Mech. Engrg, vol.195, pp.1252-1274, 2006.

L. Botti and D. A. Di-pietro, Assessment of Hybrid High-Order methods on curved meshes and comparison with discontinuous Galerkin methods, J. Comput. Phys, vol.370, pp.58-84, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01581883

L. Botti, D. A. Di-pietro, and J. Droniou, A Hybrid High-Order method for the incompressible Navier-Stokes equations based on Temam's device, J. Comput. Phys, vol.376, pp.786-816, 2019.

M. Botti, D. A. Di-pietro, and P. Sochala, A Hybrid High-Order Method for Nonlinear Elasticity, SIAM J. Numer. Anal, vol.55, issue.6, pp.2687-2717, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01539510

H. Brezis, Équations et inéquations non linéaires dans les espaces vectoriels en dualité, vol.18, pp.115-175, 1968.

F. Brezzi, K. Lipnikov, and M. Shashkov, Convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes, SIAM J. Numer. Anal, vol.43, issue.5, pp.1872-1896, 2005.

F. Brezzi, K. Lipnikov, and V. Simoncini, A family of mimetic finite difference methods on polygonal and polyhedral meshes, Math. Models Methods Appl. Sci, vol.15, issue.10, pp.1533-1551, 2005.

U. Brink and E. Stein, On some mixed finite element methods for incompressible and nearly incompressible finite elasticity, Comput. Mech, vol.19, issue.1, pp.105-119, 1996.

E. Burman and A. Ern, An unfitted Hybrid High-Order method for elliptic interface problems, SIAM J. Numer. Anal, vol.56, issue.3, pp.1525-1546, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01625421

V. Calo, M. Cicuttin, Q. Deng, and A. Ern, Spectral approximation of elliptic operators by the Hybrid High-Order method, Math. Comp, vol.88, issue.318, pp.1559-1586, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01628698

P. Cardiff, A. Kara?, and A. Ivankovi?, A large strain finite volume method for orthotropic bodies with general material orientations, Comput. Methods Appl. Mech. Engrg, vol.268, pp.318-335, 2014.

C. Carstensen and F. Hellwig, Low-order discontinuous Petrov-Galerkin finite element methods for linear elasticity, SIAM J. Numer. Anal, vol.54, issue.6, pp.3388-3410, 2016.

K. L. Cascavita, J. Bleyer, X. Chateau, and A. Ern, Hybrid Discretization Methods with Adaptive Yield Surface Detection for Bingham Pipe Flows, J. Sci. Comput, vol.77, issue.3, pp.1424-1443, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01698983

K. L. Cascavita, F. Chouly, and A. Ern, Hybrid High-Order discretizations combined with nitsche's method for Dirichlet and Signorini boundary conditions, IMA J. Numer. Anal

M. Cervera, M. Chiumenti, L. Benedetti, and R. Codina, Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: compressible and incompressible plasticity, Comput. Methods Appl. Mech. Engrg, vol.285, pp.752-775, 2015.

M. Cervera, M. Chiumenti, and R. Codina, Mixed stabilized finite element methods in nonlinear solid mechanics Part I: formulation, Comput. Methods Appl. Mech. Engrg, vol.199, pp.2559-2570, 2010.

M. Cervera, M. Chiumenti, Q. Valverde, and C. Agelet-de-saracibar, Mixed linear/-linear simplicial elements for incompressible elasticity and plasticity, Comput. Methods Appl. Mech. Engrg, vol.192, issue.49, pp.5249-5263, 2003.

F. Chave, D. A. Di-pietro, and L. Formaggia, A Hybrid High-Order method for Darcy flows in fractured porous media, SIAM J. Sci. Comput, vol.40, issue.2, pp.1063-1094, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01482925

F. Chave, D. A. Di-pietro, and L. Formaggia, A Hybrid High-Order method for passive transport in fractured porous media, Int. J. Geomath, vol.10, issue.12, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01784181

F. Chave, D. A. Di-pietro, F. Marche, and F. Pigeonneau, A Hybrid High-Order method for the Cahn-Hilliard problem in mixed form, SIAM J. Numer. Anal, vol.54, issue.3, pp.1873-1898, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01477247

A. Chernov, M. Maischak, and E. Stephan, A priori error estimates for hp penalty BEM for contact problems in elasticity, Comput. Methods Appl. Mech. Engrg, vol.196, pp.3871-3880, 2007.

H. Chi, L. Beirão-da-veiga, and G. H. Paulino, Some basic formulations of the virtual element method (VEM) for finite deformations, Comput. Methods Appl. Mech. Engrg, vol.318, pp.148-192, 2017.

M. Chiumenti, M. Cervera, and R. Codina, A mixed three-field FE formulation for stress accurate analysis including the incompressible limit, Comput. Methods Appl. Mech. Engrg, vol.283, pp.1095-1116, 2015.

M. Chiumenti, Q. Valverde, C. Agelet-de-saracibar, and M. Cervera, A stabilized formulation for incompressible plasticity using linear triangles and tetrahedra, Int. J. Plasticity, vol.20, issue.8, pp.1487-1504, 2004.

F. Chouly, An adaptation of Nitsche's method to the Tresca friction problem, J. Math. Anal. Appl, vol.411, pp.329-339, 2014.

F. Chouly, A. Ern, and N. Pignet, A Hybrid High-Order discretization combined with Nitsche's method for contact and Tresca friction in small strain elasticity

F. Chouly, M. Fabre, P. Hild, R. Mlika, J. Pousin et al., An overview of recent results on Nitsche's method for contact problems, Geometrically unfitted finite element methods and applications, vol.121, pp.93-141, 2017.

F. Chouly and P. Hild, A Nitsche-based method for unilateral contact problems: numerical analysis, SIAM J. Numer. Anal, vol.51, issue.2, pp.1295-1307, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00717711

F. Chouly and P. Hild, On convergence of the penalty method for unilateral contact problems, Appl. Numer. Math, vol.65, pp.27-40, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00688641

F. Chouly, P. Hild, V. Lleras, and Y. Renard, Nitsche-based finite element method for contact with Coulomb friction, Numerical Mathematics and Advanced Applications ENUMATH 2017, vol.126, pp.839-847, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01654487

F. Chouly, P. Hild, and Y. Renard, Symmetric and non-symmetric variants of Nitsche's method for contact problems in elasticity: theory and numerical experiments, Math. Comp, vol.84, issue.293, pp.1089-1112, 2015.

F. Chouly, R. Mlika, and Y. Renard, An unbiased Nitsche's approximation of the frictional contact between two elastic structures, Numer. Math, vol.139, issue.3, pp.593-631, 2018.

P. G. Ciarlet, The Finite Element Method for Elliptic Problems, 1978.

P. G. , Three-dimensional elasticity, Studies in Mathematics and its Applications, vol.I, 1988.

M. Cicuttin, D. A. Di-pietro, and A. Ern, Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming, J. Comput. Appl. Math, vol.344, pp.852-874, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01429292

M. Cicuttin, A. Ern, and S. Lemaire, A Hybrid High-Order method for highly oscillatory elliptic problems, Comput. Methods Appl. Math, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01467434

B. Cockburn, Discontinuous Galerkin methods. ZAMM Z. Angew. Math. Mech, vol.83, issue.11, pp.731-754, 2003.

B. Cockburn, D. A. Di-pietro, and A. Ern, Bridging the Hybrid High-Order and hybridizable discontinuous Galerkin methods, ESAIM Math. Model. Numer. Anal, vol.50, issue.3, pp.635-650, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01115318

B. Cockburn, O. Dubois, J. Gopalakrishnan, and S. Tan, Multigrid for an HDG method, IMA J. Numer. Anal, vol.34, issue.4, pp.1386-1425, 2014.

B. Cockburn, J. Gopalakrishnan, and R. Lazarov, Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems, SIAM J. Numer. Anal, vol.47, issue.2, pp.1319-1365, 2009.

B. Cockburn, J. Gopalakrishnan, N. C. Nguyen, J. Peraire, and F. Sayas, Analysis of HDG methods for Stokes flow, Math. Comp, vol.80, issue.274, pp.723-760, 2011.

B. Cockburn, D. Schötzau, and J. Wang, Discontinuous Galerkin methods for incompressible elastic materials, Comput. Methods Appl. Mech. Engrg, vol.195, pp.3184-3204, 2006.

A. Curnier and P. Alart, A generalized Newton method for contact problems with friction, J. Méc. Théor. Appl, vol.7, pp.67-82, 1988.
URL : https://hal.archives-ouvertes.fr/hal-01433772

G. Maso, A. Desimone, and M. G. Mora, Quasistatic evolution problems for linearly elastic-perfectly plastic materials, Arch. Ration. Mech. Anal, vol.180, issue.2, pp.237-291, 2006.

P. Daniel, A. Ern, I. Smears, and M. Vohralík, An adaptive hp-refinement strategy with computable guaranteed bound on the error reduction factor, Comput. Math. Appl, vol.76, issue.5, pp.967-983, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01666763

E. A. De-souza-neto, F. M. Andrade-pires, and D. R. Owen, F-bar-based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: formulation and benchmarking, Int. J. Numer. Meth. Engng, vol.62, pp.353-383, 2005.

E. A. De-souza-neto, D. Peric, and D. R. Owen, Computational methods for plasticity: theory and applications, 2011.

D. A. Di-pietro and J. Droniou, A Hybrid High-Order method for Leray-Lions elliptic equations on general meshes, Math. Comp, vol.86, issue.307, pp.2159-2191, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01183484

D. A. Di-pietro and J. Droniou, W s,p -approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray-Lions problems, Math. Models Methods Appl. Sci, vol.27, issue.5, pp.879-908, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01326818

D. A. Di-pietro, J. Droniou, and A. Ern, A discontinuous-skeletal method for advectiondiffusion-reaction on general meshes, SIAM J. Numer. Anal, vol.53, issue.5, pp.2135-2157, 2015.

D. A. Di-pietro, J. Droniou, and G. Manzini, Discontinuous Skeletal Gradient Discretisation Methods on polytopal meshes, J. Comput. Phys, vol.355, pp.397-425, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01564598

D. A. Di-pietro and A. Ern, Mathematical aspects of discontinuous Galerkin methods, vol.69, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01820185

D. A. Di-pietro and A. Ern, A Hybrid High-Order locking-free method for linear elasticity on general meshes, Comput. Methods Appl. Mech. Engrg, vol.283, pp.1-21, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00979435

D. A. Di-pietro and A. Ern, Hybrid High-Order methods for variable-diffusion problems on general meshes, C. R. Math. Acad. Sci, vol.353, issue.1, pp.31-34, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01023302

D. A. Di-pietro, A. Ern, and S. Lemaire, An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators, Comput. Methods Appl. Math, vol.14, issue.4, pp.461-472, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00978198

D. A. Di-pietro, A. Ern, and S. Lemaire, A review of Hybrid High-Order methods: formulations, computational aspects, comparison with other methods, Building bridges: connections and challenges in modern approaches to numerical partial differential equations, vol.114, pp.205-236, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01163569

D. A. Di-pietro, A. Ern, A. Linke, and F. Schieweck, A discontinuous skeletal method for the viscosity-dependent Stokes problem, Comput. Methods Appl. Mech. Engrg, vol.306, pp.175-195, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01244387

D. A. Di-pietro and S. Krell, A Hybrid High-Order method for the steady incompressible Navier-Stokes problem, J. Sci. Comput, vol.74, issue.3, pp.1677-1705, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01349519

D. A. Di-pietro and R. Tittarelli, An introduction to Hybrid High-Order methods, Numerical methods for PDEs, vol.15, pp.75-128, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01490524

I. Dione, Optimal convergence analysis of the unilateral contact problem with and without Tresca friction conditions by the penalty method, J. Math. Anal. Appl, vol.472, issue.1, pp.266-284, 2019.

J. K. Djoko, F. Ebobisse, A. T. Mcbride, and B. D. Reddy, A discontinuous Galerkin formulation for classical and gradient plasticity. I. Formulation and analysis, Comput. Methods Appl. Mech. Engrg, vol.196, pp.3881-3897, 2007.

J. K. Djoko, F. Ebobisse, A. T. Mcbride, and B. D. Reddy, A discontinuous Galerkin formulation for classical and gradient plasticity. II. Algorithms and numerical analysis, Comput. Methods Appl. Mech. Engrg, vol.197, issue.1-4, pp.1-21, 2007.

M. Dobrowolski, A mixed finite element method for approximating incompressible materials, SIAM J. Numer. Anal, vol.29, issue.2, pp.365-389, 1992.

W. P. Doherty, E. L. Wilson, and R. L. Taylor, Stress analysis of axisymmetric solids utilizing higher-order quadrilateral finite elements, 1969.

J. Droniou and R. Eymard, A mixed finite volume scheme for anisotropic diffusion problems on any grid, Numer. Math, vol.105, issue.1, pp.35-71, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00005565

J. Droniou and R. Eymard, Study of the mixed finite volume method for Stokes and Navier-Stokes equations, Numer. Methods Partial Differential Equations, vol.25, issue.1, pp.137-171, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00110911

J. Droniou, R. Eymard, T. Gallouët, and R. Herbin, A unified approach to mimetic finite difference, hybrid finite volume and mixed finite volume methods, Math. Models Methods Appl. Sci, vol.20, issue.2, pp.265-295, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00346077

J. Droniou, R. Eymard, T. Gallouët, and R. Herbin, Gradient schemes: a generic framework for the discretisation of linear, nonlinear and nonlocal elliptic and parabolic equations, Math. Models Methods Appl. Sci, vol.23, issue.13, pp.2395-2432, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00751551

J. Droniou, R. Eymard, and R. Herbin, Gradient schemes: generic tools for the numerical analysis of diffusion equations, ESAIM Math. Model. Numer. Anal, vol.50, issue.3, pp.749-781, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01150517

J. Droniou and B. P. Lamichhane, Gradient schemes for linear and non-linear elasticity equations, Numer. Math, vol.129, issue.2, pp.251-277, 2015.

G. Drouet and P. Hild, Optimal convergence for discrete variational inequalities modelling Signorini contact in 2D and 3D without additional assumptions on the unknown contact set, SIAM J. Numer. Anal, vol.53, issue.3, pp.1488-1507, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01969534

D. A. Dunavant, High degree efficient symmetrical Gaussian quadrature rules for the triangle, Int. J. Numer. Methods Eng, vol.21, issue.6, pp.1129-1148, 1985.

G. Duvaut and J. Lions, Les inéquations en mécanique et en physique, Travaux et Recherches Mathématiques. Dunod, vol.21, 1972.

C. Eck, J. Jaru?ek, and M. Krbec, Unilateral contact problems, Pure and Applied Mathematics, vol.270, 2005.

F. Electricité-de, Finite element code aster , structures and thermomechanics analysis for studies and research. Open source on www, pp.1989-2019

T. Elguedj, Y. Bazilevs, V. M. Calo, and T. J. Hughes, B andF projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higherorder NURBS elements, Comput. Methods Appl. Mech. Eng, vol.197, issue.33, pp.2732-2762, 2008.

T. Elguedj and T. J. Hughes, Isogeometric analysis of nearly incompressible large strain plasticity, Comput. Methods Appl. Mech. Engrg, vol.268, pp.388-416, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00938598

A. Ern and J. Guermond, Finite element quasi-interpolation and best approximation, ESAIM Math. Model. Numer. Anal, vol.51, issue.4, pp.1367-1385, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01155412

A. T. Eyck, F. Celiker, and A. Lew, Adaptive stabilization of discontinuous Galerkin methods for nonlinear elasticity: analytical estimates, Comput. Methods Appl. Mech. Engrg, vol.197, pp.2989-3000, 2008.

A. T. Eyck, F. Celiker, and A. Lew, Adaptive stabilization of discontinuous Galerkin methods for nonlinear elasticity: motivation, formulation, and numerical examples, Comput. Methods Appl. Mech. Engrg, vol.197, pp.3605-3622, 2008.

A. T. Eyck and A. Lew, Discontinuous Galerkin methods for non-linear elasticity, Int. J. Numer. Methods Eng, vol.67, issue.9, pp.1204-1243, 2006.

A. T. Eyck and A. Lew, An adaptive stabilization strategy for enhanced strain methods in non-linear elasticity, Int. J. Numer. Methods Eng, vol.81, issue.11, pp.1387-1416, 2010.

R. Eymard, T. Gallouët, and R. Herbin, A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysis, C. R. Math. Acad. Sci, vol.344, issue.6, pp.403-406, 2007.

R. Eymard, T. Gallouët, and R. Herbin, Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces, IMA J. Numer. Anal, vol.30, issue.4, pp.1009-1043, 2010.

R. Eymard and C. Guichard, Discontinuous Galerkin gradient discretisations for the approximation of second-order differential operators in divergence form, Comput. Appl. Math, vol.37, issue.4, pp.4023-4054, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01535147

G. Fu, B. Cockburn, and H. Stolarski, Analysis of an HDG method for linear elasticity, Int. J. Numer. Methods Eng, vol.102, issue.3-4, pp.551-575, 2015.

R. Glowinski, Numerical methods for nonlinear variational problems, 2008.

A. Grundmann and M. Moeller, Invariant integration formulas for the n-simplex by combinatorial methods, SIAM J. Numer. Anal, vol.15, issue.2, pp.282-290, 1978.

Q. Guan, M. Gunzburger, and W. Zhao, Weak-Galerkin finite element methods for a second-order elliptic variational inequality, Comput. Methods Appl. Mech. Engrg, vol.337, pp.677-688, 2018.

C. Hager, P. Hauret, P. L. Tallec, and B. I. Wohlmuth, Solving dynamic contact problems with local refinement in space and time, Comput. Methods Appl. Mech. Engrg, vol.201, pp.25-41, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01393141

B. Halphen and Q. S. Nguyen, Sur les matériaux standard généralisés, J. Mecanique, vol.14, pp.39-63, 1975.

W. Han and B. D. Reddy, Plasticity: Mathematical Theory and Numerical Analysis, 2013.

W. Han and M. Sofonea, Quasistatic contact problems in viscoelasticity and viscoplasticity, AMS/IP Studies in Advanced Mathematics, vol.30, 2002.

P. Hansbo, Nitsche's method for interface problems in computational mechanics, vol.28, pp.183-206, 2005.

P. Hansbo, A discontinuous finite element method for elasto-plasticity, Int. J. Numer. Meth. Biomed. Engng, vol.26, issue.6, pp.780-789, 2010.

P. Hansbo and M. G. Larson, Discontinuous Galerkin methods for incompressible and nearly incompressible elasticity by Nitsche's method, Comput. Methods Appl. Mech. Engrg, vol.191, pp.1895-1908, 2002.

J. Haslinger and I. Hlavá?ek, Approximation of the Signorini problem with friction by a mixed finite element method, J. Math. Anal. Appl, vol.86, issue.1, pp.99-122, 1982.

J. Haslinger, I. Hlavá?ek, and J. Ne?as, Numerical methods for unilateral problems in solid mechanics, volume IV of Handbook of Numerical Analysis, 1996.

P. Hauret and P. L. Tallec, Energy-controlling time integration methods for nonlinear elastodynamics and low-velocity impact, Comput. Methods Appl. Mech. Engrg, vol.195, pp.4890-4916, 2006.
URL : https://hal.archives-ouvertes.fr/hal-01630695

P. Hauret and P. L. Tallec, A discontinuous stabilized mortar method for general 3D elastic problems, Comput. Methods Appl. Mech. Engrg, vol.196, pp.4881-4900, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00175620

T. Helfer, B. Michel, J. Proix, M. Salvo, J. Sercombe et al., Introducing the open-source mfront code generator: Application to mechanical behaviours and material knowledge management within the PLEIADES fuel element modelling platform, Comput. Math. Appl, vol.70, issue.5, pp.994-1023, 2015.

P. Hild, Éléments finis non conformes pour un problème de contact unilatéral avec frottement, C. R. Acad. Sci. Paris Sér. I Math, vol.324, issue.6, pp.707-710, 1997.

P. Hild, Numerical implementation of two nonconforming finite element methods for unilateral contact, Comput. Methods Appl. Mech. Engrg, vol.184, issue.1, pp.99-123, 2000.
URL : https://hal.archives-ouvertes.fr/hal-01390457

P. Hild and Y. Renard, A stabilized Lagrange multiplier method for the finite element approximation of contact problems in elastostatics, Numer. Math, vol.115, issue.1, pp.101-129, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00464274

P. Hild and Y. Renard, An improved a priori error analysis for finite element approximations of Signorini's problem, SIAM J. Numer. Anal, vol.50, issue.5, pp.2400-2419, 2012.

R. Hill, A general theory of uniqueness and stability in elastic-plastic solids, J. Mech. Phys. Solids, vol.6, issue.3, pp.236-249, 1958.

B. Hudobivnik, F. Aldakheel, and P. Wriggers, A low order 3D virtual element formulation for finite elasto-plastic deformations, Comput. Mech, 2018.

S. Hüeber and B. I. Wohlmuth, An optimal a priori error estimate for nonlinear multibody contact problems, SIAM J. Numer. Anal, vol.43, issue.1, pp.156-173, 2005.

T. J. Hughes, Generalization of selective integration procedures to anisotropic and nonlinear media, Int. J. Numer. Meth. Engrg, vol.15, issue.9, pp.1413-1418, 1980.

L. John, M. Neilan, and I. Smears, Stable discontinuous galerkin fem without penalty parameters, Numerical Mathematics and Advanced Applications ENUMATH 2015, pp.165-173, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01428664

H. Kabaria, A. J. Lew, and B. Cockburn, A hybridizable discontinuous Galerkin formulation for non-linear elasticity, Comput. Methods Appl. Mech. Engrg, vol.283, pp.303-329, 2015.

N. Kikuchi and J. T. Oden, Contact problems in elasticity: a study of variational inequalities and finite element methods, SIAM Studies in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), vol.8, 1988.

N. Kikuchi and Y. J. Song, Penalty-finite-element approximation of a class of unilateral problems in linear elasticity, Quart. Appl. Math, vol.39, pp.1-22, 1981.

O. Klaas, A. Maniatty, and M. S. Shephard, A stabilized mixed finite element method for finite elasticity.: Formulation for linear displacement and pressure interpolation, Computer Methods in Applied Mechanics and Engineering, vol.180, issue.1, pp.65-79, 1999.

J. Krämer, C. Wieners, B. Wohlmuth, and L. Wunderlich, A hybrid weakly nonconforming discretization for linear elasticity, Proc. Appl. Math. Mech, vol.16, issue.1, pp.849-850, 2016.

P. , Mean-strain eight-node hexahedron with optimized energy-sampling stabilization for large-strain deformation, Int. J. Numer. Methods Eng, vol.103, issue.9, pp.650-670, 2015.

P. , Mean-strain 8-node hexahedron with optimized energy-sampling stabilization, Finite Elem. Anal. Des, vol.108, pp.41-53, 2016.

Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The mimetic finite difference method on polygonal meshes for diffusion-type problems, Comput. Geosci, vol.8, issue.4, pp.301-324, 2004.

P. Laborde and Y. Renard, Fixed point strategies for elastostatic frictional contact problems, Math. Methods Appl. Sci, vol.31, issue.4, pp.415-441, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01330376

T. A. Laursen, Computational contact and impact mechanics, 2002.

P. L. Tallec, C. Rahier, and A. Kaiss, Three-dimensional incompressible viscoelasticity in large strains: formulation and numerical approximation, Comput. Methods Appl. Mech. Engrg, vol.109, issue.3-4, pp.233-258, 1993.

C. Lehrenfeld, Hybrid Discontinuous Galerkin methods for solving incompressible flow problems, Rheinisch-Westfälischen Technischen Hochschule Aachen, 2010.

J. Lemaitre and J. Chaboche, Mechanics of Solid Materials, 1994.

A. Lew, P. Neff, D. Sulsky, and M. Ortiz, Optimal BV estimates for a discontinuous Galerkin method for linear elasticity, AMRX Appl. Math. Res. Express, issue.3, pp.73-106, 2004.

Y. Lian and Z. Li, A numerical study on cavitation in nonlinear elasticity-defects and configurational forces, Math. Models Methods Appl. Sci, vol.21, issue.12, pp.2551-2574, 2011.

R. Liu, M. F. Wheeler, C. N. Dawson, and R. H. Dean, A fast convergent rate preserving discontinuous Galerkin framework for rate-independent plasticity problems, Comput. Methods Appl. Mech. Engrg, vol.199, pp.3213-3226, 2010.

R. Liu, M. F. Wheeler, and I. Yotov, On the spatial formulation of discontinuous Galerkin methods for finite elastoplasticity, Comput. Methods Appl. Mech. Engrg, vol.253, pp.219-236, 2013.

E. Lorentz and V. Godard, Gradient damage models: Toward full-scale computations, Comput. Methods Appl. Mech. Engrg, vol.200, pp.1927-1944, 2011.

D. S. Malkus and T. J. Hughes, Mixed finite element methods -reduced and selective integration techniques: A unification of concepts, Computer Methods in Applied Mechanics and Engineering, vol.15, issue.1, pp.63-81, 1978.

A. T. Mcbride and B. D. Reddy, A discontinuous Galerkin formulation of a model of gradient plasticity at finite strains, Comput. Methods Appl. Mech. Engrg, vol.198, pp.1805-1820, 2009.

C. Miehe, N. Apel, and M. Lambrecht, Anisotropic additive plasticity in the logarithmic strain space: modular kinematic formulation and implementation based on incremental minimization principles for standard materials, Comput. Methods Appl. Mech. Engrg, vol.191, pp.5383-5425, 2002.

R. Mlika, Y. Renard, and F. Chouly, An unbiased Nitsche's formulation of large deformation frictional contact and self-contact, Comput. Methods Appl. Mech. Engrg, vol.325, pp.265-288, 2017.

L. Molari, G. Wells, K. Garikipati, and F. Ubertini, A discontinuous Galerkin method for strain gradient-dependent damage: study of interpolations and convergence, Comput. Methods Appl. Mech. Engrg, vol.195, pp.1480-1498, 2006.

M. Moussaoui and K. Khodja, Régularité des solutions d'un problème mêlé DirichletSignorini dans un domaine polygonal plan, Comm. Partial Differential Equations, vol.17, issue.5-6, pp.805-826, 1992.

N. C. Nguyen and J. Peraire, Hybridizable discontinuous Galerkin methods for partial differential equations in continuum mechanics, J. Comput. Phys, vol.231, issue.18, pp.5955-5988, 2012.

N. C. Nguyen, J. Peraire, and B. Cockburn, High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics, J. Comput. Phys, vol.230, issue.10, pp.3695-3718, 2011.

J. Nitsche, Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind, Abh. Math. Sem. Univ. Hamburg, vol.36, pp.9-15, 1971.

L. Noels and R. Radovitzky, A general discontinuous Galerkin method for finite hyperelasticity. Formulation and numerical applications, Int. J. Numer. Methods Eng, vol.68, issue.1, pp.64-97, 2006.

J. T. Oden and N. Kikuchi, Finite element methods for constrained problems in elasticity, Internat. J. Numer. Meth. Engrg, vol.18, pp.701-705, 1982.

J. T. Oden and S. J. Kim, Interior penalty methods for finite element approximations of the Signorini problem in elastostatics, Comput. Math. Appl, vol.8, issue.1, pp.35-56, 1982.

R. W. Ogden, Non-linear elastic deformations, 1997.

E. Pipping, O. Sander, and R. Kornhuber, Variational formulation of rate-and statedependent friction problems, ZAMM Z. Angew. Math. Mech, vol.95, issue.4, pp.377-395, 2015.

J. P. Ponthot, Mécanique des milieux continus en grandes transformations et traitement unifié par la méthode deséléments finis, 1995.

K. Poulios and Y. Renard, An unconstrained integral approximation of large sliding frictional contact between deformable solids, Comp. Struct, vol.153, pp.75-90, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00937569

S. Reese, On a consistent hourglass stabilization technique to treat large inelastic deformations and thermo-mechanical coupling in plane strain problems, Int. J. Numer. Meth. Engrg, vol.57, issue.8, pp.1095-1127, 2003.

S. Reese, H. R. Bayat, and S. Wulfinghoff, On an equivalence between a discontinuous Galerkin method and reduced integration with hourglass stabilization for finite elasticity, Comput. Methods Appl. Mech. Engrg, vol.325, pp.175-197, 2017.

S. Reese, M. Küssner, and B. D. Reddy, A new stabilization technique for finite elements in non-linear elasticity, Int. J. Numer. Meth. Engrg, vol.44, issue.11, pp.1617-1652, 1999.

S. Reese and P. Wriggers, A stabilization technique to avoid hourglassing in finite elasticity, Int. J. Numer. Meth. Engrg, vol.48, issue.1, pp.79-109, 2000.

Y. Renard, Generalized Newton's methods for the approximation and resolution of frictional contact problems in elasticity, Comput. Methods Appl. Mech. Engrg, vol.256, pp.38-55, 2013.

A. Seitz, W. A. Wall, and A. Popp, Nitsche's method for finite deformation thermomechanical contact problems, Comput. Mech, vol.63, issue.6, pp.1091-1110, 2019.

R. Sevilla, M. Giacomini, and A. Huerta, A locking-free face-centred finite volume (FCFV) method for linear elastostatics, Computers and Structures, vol.212, pp.43-57, 2019.

A. Signorini, Questioni di elasticità non linearizzata e semi-linearizzata. Rend. di Matematica, vol.18, pp.95-139, 1959.

J. C. Simo, A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. I. Continuum formulation, Comput. Methods Appl. Mech. Engrg, vol.66, issue.2, pp.199-219, 1988.

J. C. Simo, Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory, Comput. Methods Appl. Mech. Engrg, vol.99, pp.61-112, 1992.

J. C. Simo and F. Armero, Geometrically nonlinear enhanced strain mixed methods and the method of incompatible modes, Int. J. Numer. Methods Eng, vol.33, issue.7, pp.1413-1449, 1992.

J. C. Simo, F. Armero, and R. L. Taylor, Improved versions of assumed enhanced strain trilinear elements for 3D finite deformation problems, Comput. Methods Appl. Mech. Engrg, vol.110, issue.3-4, pp.359-386, 1993.

J. C. Simo and T. J. Hughes, Computational Inelasticity. Springer, 1998.

J. C. Simo and M. S. Rifai, A class of mixed assumed strain methods and the method of incompatible modes, Int. J. Numer. Methods Eng, vol.29, issue.8, pp.1595-1638, 1990.

J. C. Simo and R. L. Taylor, Consistent tangent operators for rate-independent elastoplasticity, Comput. Methods Appl. Mech. Engrg, vol.48, issue.1, pp.101-118, 1985.

J. C. Simo, R. L. Taylor, and K. S. Pister, Variational and projection methods for the volume constraint in finite deformation elasto-plasticity, Comput. Methods Appl. Mech. Engrg, vol.51, issue.1, pp.177-208, 1985.

S. Soon, Hybridizable Discontinuous Galerkin Method for Solid Mechanics, 2008.

S. Soon, B. Cockburn, and H. K. Stolarski, A hybridizable discontinuous Galerkin method for linear elasticity, Int. J. Numer. Methods Eng, vol.80, issue.8, pp.1058-1092, 2009.

R. Stenberg, On some techniques for approximating boundary conditions in the finite element method, J. Comput. Appl. Math, vol.63, issue.1-3, pp.139-148, 1995.

L. Szabó, On the eigenvalues of the fourth-order constitutive tensor and loss of strong ellipticity in elastoplasticity, Int. J. Plasticity, vol.13, issue.10, pp.809-835, 1998.

L. Szabó, A semi-analytical integration method for J2 flow theory of plasticity with linear isotropic hardening, Comput. Methods Appl. Mech. Engrg, vol.198, pp.2151-2166, 2009.

G. A. Taylor, C. Bailey, and M. Cross, A vertex-based finite volume method applied to non-linear material problems in computational solid mechanics, Int. J. Numer. Meth. Engng, vol.56, pp.507-529, 2003.

S. Terrana, N. C. Nguyen, J. Bonet, and J. Peraire, A hybridizable discontinuous Galerkin method for both thin and 3D nonlinear elastic structures, Comput. Methods Appl. Mech. Engrg, vol.352, pp.561-585, 2019.

C. Wang, J. Wang, R. Wang, and R. Zhang, A locking-free weak Galerkin finite element method for elasticity problems in the primal formulation, J. Comput. Appl. Math, vol.307, pp.346-366, 2016.

F. Wang, W. Han, and X. Cheng, Discontinuous Galerkin methods for solving the Signorini problem, IMA J. Numer. Anal, vol.31, issue.4, pp.1754-1772, 2011.

F. Wang and H. Wei, Virtual element method for simplified friction problem, Appl. Math. Letters, vol.85, pp.125-131, 2018.

B. Wohlmuth, Variationally consistent discretization schemes and numerical algorithms for contact problems, Acta Numer, vol.20, pp.569-734, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01382364

P. Wriggers, Computational Contact Mechanics, 2002.

P. Wriggers and B. Hudobivnik, A low order virtual element formulation for finite elasto-plastic deformations, Comput. Methods Appl. Mech. Engrg, vol.327, pp.459-477, 2017.

P. Wriggers, B. D. Reddy, W. Rust, and B. Hudobivnik, Efficient virtual element formulations for compressible and incompressible finite deformations, Comput. Mech, vol.60, issue.2, pp.253-268, 2017.

P. Wriggers, W. T. Rust, and B. D. Reddy, A virtual element method for contact, Comput. Mech, vol.58, issue.6, pp.1039-1050, 2016.

S. Wulfinghoff, H. R. Bayat, A. Alipour, and S. Reese, A low-order locking-free hybrid discontinuous Galerkin element formulation for large deformations, Comput. Methods Appl. Mech. Engrg, vol.323, pp.353-372, 2017.

X. Xu and D. Henao, An efficient numerical method for cavitation in nonlinear elasticity, Math. Models Methods Appl. Sci, vol.21, issue.8, pp.1733-1760, 2011.

S. Yadav, A. K. Pani, and E. J. Park, Superconvergent discontinuous Galerkin methods for nonlinear elliptic equations, Math. Comp, vol.82, pp.1297-1335, 2013.

Y. Zhang, E. Lorentz, and J. Besson, Ductile damage modelling with locking-free regularised GTN model, Int. J. Numer. Methods Eng, vol.113, pp.1871-1903, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01758768

M. Zhao, H. Wu, and C. Xiong, Error analysis of HDG approximations for elliptic variational inequality: obstacle problem, Numer. Algorithms, vol.81, issue.2, pp.445-463, 2019.

O. C. Zienkiewicz, R. L. Taylor, and J. M. Too, Reduced integration technique in general analysis of plates and shells, Int. J. Numer. Methods Eng, vol.3, issue.2, pp.275-290, 1971.