E. Anderheggen and H. Knöpfel, Finite element limit analysis using linear programming. Interna-638 tional, Journal of Solids and Structures, vol.8, pp.1413-1431, 1972.

A. Ben-tal and A. Nemirovski, Lectures on modern convex optimization: analysis, algorithms, and 640 engineering applications, vol.2, 2001.

C. Bisbos and P. Pardalos, Second-order cone and semidefinite representations of material failure 642 criteria, Journal of Optimization Theory and Applications, vol.134, pp.275-301, 2007.

J. Bleyer, Advances in the simulation of viscoplastic fluid flows using interior-point methods, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01672045

, Computer Methods in Applied Mechanics and Engineering, vol.330, pp.368-394

J. Bleyer, Automating the formulation and resolution of convex variational problems: applications 646 from image processing to computational mechanics, 2019.

J. Bleyer, 2020. fenics-optim -Convex optimization interface in FEniCS. Version 1.0. Zenodo, p.648


J. Bleyer and P. De-buhan, A computational homogenization approach for the yield design of 650 periodic thin plates. Part I: Construction of the macroscopic strength criterion, International Journal 651 of Solids and Structures, vol.51, pp.2448-2459, 2014.

J. Bleyer and P. De-buhan, Lower bound static approach for the yield design of thick plates, International Journal for Numerical Methods in Engineering, vol.653, pp.814-833, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01082202

J. Bleyer and P. De-buhan, A numerical approach to the yield strength of shell structures, European 655 Journal of Mechanics-A/Solids, vol.59, pp.178-194, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01303348

J. Bleyer, C. V. Le, and P. De-buhan, Locking-free discontinuous finite elements for the upper bound 657 yield design of thick plates, International Journal for Numerical Methods in Engineering, vol.103, pp.894-913, 2015.

J. Bleyer, M. Maillard, P. De-buhan, and P. Coussot, Efficient numerical computations of yield 659 stress fluid flows using second-order cone programming, Computer Methods in Applied Mechanics and 660 Engineering, vol.283, pp.599-614, 2015.

S. Boyd and L. Vandenberghe, Convex optimization, 2004.

P. De-buhan, A fundamental approach to the yield design of reinforced soil structures, 1986.

M. Capurso, Limit analysis of continuous media with piecewise linear yeld condition, Meccanica, vol.665, issue.6, pp.53-58, 1971.

R. Casciaro and L. Cascini, A mixed formulation and mixed finite elements for limit analysis, 667 International Journal for Numerical Methods in Engineering, vol.18, pp.211-243, 1982.

W. F. Chen, Plasticity in reinforced concrete, 2007.

W. F. Chen, Limit analysis and soil plasticity, 2013.

E. Christiansen and K. Andersen, Computation of collapse states with von Mises type yield condition. 671, International Journal for Numerical Methods in Engineering, vol.46, pp.1185-1202, 1999.

G. B. Dantzig, A. Orden, and P. Wolfe, The generalized simplex method for minimizing a 673 linear form under linear inequality restraints, Pacific Journal of Mathematics, vol.5, pp.183-195, 1955.

P. De-buhan, J. Freard, D. Garnier, and S. Maghous, Failure properties of fractured rock masses as 675 anisotropic homogenized media, Journal of Engineering Mechanics, vol.128, pp.869-875, 2002.

A. Domahidi, E. Chu, and S. Boyd, Ecos: An socp solver for embedded systems, 2013.

, Control Conference (ECC), IEEE, pp.3071-3076

M. Frémond and A. Friaa, Analyse limite. comparaison des méthodes statique et cinématique, 1978.

, Comptes Rendus de l'Academie des Sciences, vol.286, pp.107-110

P. Germain, La méthode des puissances virtuelles en mécanique des milieux continus, premiere 681 partie: théorie du second gradient, Journal de mécanique, vol.12, pp.235-274, 1973.

P. Germain, The method of virtual power in continuum mechanics, 1973.

, SIAM Journal on Applied Mathematics, vol.25, pp.556-575

M. Gilbert, C. Casapulla, and H. Ahmed, Limit analysis of masonry block structures with non-685 associative frictional joints using linear programming, Computers & structures, vol.84, pp.873-887, 2006.

M. A. Herfelt, P. N. Poulsen, and L. C. Hoang, Strength-based topology optimisation of plastic 687 isotropic von mises materials, Structural and Multidisciplinary Optimization, vol.59, pp.893-906, 2019.

R. Hill, The mathematical theory of plasticity, 1950.

W. Hosford, A generalized isotropic yield criterion, Journal of Applied Mechanics, vol.39, pp.607-609, 1972.

W. F. Hosford, On the crystallographic basis of yield criteria. Textures and Microstructures 26-27, vol.691, pp.479-493, 1996.

A. Ilyushin, , 1956.

K. Johansen, Yield-line theory. Cement and Concrete Association London, 1962.

Z. Kammoun and H. Smaoui, A direct approach for continuous topology optimization subject to 695 admissible loading, Comptes Rendus Mécanique, vol.342, pp.520-531, 2014.

N. Karmarkar, A new polynomial-time algorithm for linear programming, Proceedings of the 697 sixteenth annual ACM symposium on Theory of computing, ACM, pp.302-311, 1984.

K. Krabbenhoft and L. Damkilde, Lower bound limit analysis of slabs with nonlinear yield criteria, 2002.

, Computers & structures, vol.80, pp.2043-2057

K. Krabbenhoft, M. Karim, A. Lyamin, and S. Sloan, Associated computational plasticity schemes 701 for nonassociated frictional materials, International Journal for Numerical Methods in Engineering, vol.90, pp.1089-1117, 2012.

K. Krabbenhoft, A. Lyamin, J. Huang, and M. V. Da-silva, Granular contact dynamics using 704 mathematical programming methods, Computers and Geotechnics, vol.43, pp.165-176, 2012.

K. Krabbenhøft, A. Lyamin, and S. Sloan, Formulation and solution of some plasticity problems as 706 conic programs, International Journal of Solids and Structures, vol.44, pp.1533-1549, 2007.

K. Krabbenhoft, A. Lyamin, S. Sloan, and P. Wriggers, An interior-point algorithm for elastoplas-708 ticity, International Journal for Numerical Methods in Engineering, vol.69, pp.592-626, 2007.

K. Krabbenhoft, A. V. Lyamin, M. Hjiaj, and S. W. Sloan, A new discontinuous upper bound limit 710 analysis formulation, International Journal for Numerical Methods in Engineering, vol.63, pp.1069-1088, 2005.

K. Krabbenhøft, A. V. Lyamin, and S. W. Sloan, Three-dimensional mohr-coulomb limit analysis 712 using semidefinite programming, Communications in Numerical Methods in Engineering, vol.24, pp.1107-1119, 2008.

J. Kumar and O. Rahaman, Lower bound limit analysis using power cone programming for solving 714 stability problems in rock mechanics for generalized hoek-brown criterion, p.715, 2020.

M. S. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret, Applications of second-order cone program-717 ming, Linear algebra and its applications, vol.284, pp.193-228, 1998.

R. W. Logan and W. F. Hosford, Upper-bound anisotropic yield locus calculations assuming¡ 111¿-719 pencil glide, International Journal of Mechanical Sciences, vol.22, pp.419-430, 1980.

J. Lysmer, Limit analysis of plane problems in soil mechanics, Journal of Soil Mechanics & 721 Foundations Div, vol.96, pp.1311-1334, 1970.

A. Makrodimopoulos, Remarks on some properties of conic yield restrictions in limit analysis, 723 International Journal for Numerical Methods in Biomedical Engineering, vol.26, pp.1449-1461, 2010.

A. Makrodimopoulos and C. Martin, Upper bound limit analysis using simplex strain elements 725 and second-order cone programming. International journal for numerical and analytical methods in 726 geomechanics 31, pp.835-865, 2007.

A. Makrodimopoulos and C. Martin, Upper bound limit analysis using discontinuous quadratic 728 displacement fields, Communications in Numerical Methods in Engineering, vol.24, pp.911-927, 2008.

C. M. Martin and A. Makrodimopoulos, Finite-element limit analysis of Mohr-Coulomb materials in 730 3d using semidefinite programming, Journal of Engineering Mechanics, vol.134, pp.339-347, 2008.

,. Mosek-aps, The MOSEK optimization API for Python, 2018.

. Mosek-aps, MOSEK Modeling Cookbook, 2019.

J. C. Nagtegaal, D. M. Parks, and J. Rice, On numerically accurate finite element solutions in the 736 fully plastic range, Computer methods in applied mechanics and engineering, vol.4, pp.153-177, 1974.

B. Nayroles, Essai de théorie fonctionnelle des structures rigides plastiques parfaites, Journal de, p.738, 1970.

, Mécanique, vol.9, pp.491-506

Y. Nesterov, A. Nemirovskii, and Y. Ye, Interior-point polynomial algorithms in convex program-740 ming, vol.13, 1994.

H. Nguyen-xuan, L. V. Tran, C. H. Thai, and C. V. Le, Plastic collapse analysis of cracked structures 742 using extended isogeometric elements and second-order cone programming, Theoretical and Applied 743 Fracture Mechanics, vol.72, pp.13-27, 2014.

M. P. Nielsen and L. C. Hoang, Limit analysis and concrete plasticity, 2016.

J. Pastor and S. Turgeman, Mise en oeuvre numérique des méthodes de l'analyse limite pour les 746 matériaux de von mises et de coulomb standards en déformation plane, Mechanics Research Communi-747 cations, vol.3, pp.469-474, 1976.

F. Portioli, C. Casapulla, M. Gilbert, and L. Cascini, Limit analysis of 3d masonry block structures 749 with non-associative frictional joints using cone programming, Computers & Structures, vol.143, pp.108-121, 2014.

M. Robinson, A comparison of yield surfaces for thin shells, International Journal of Mechanical 751 Sciences, vol.13, pp.345-354, 1971.

J. Salençon, Calculà la rupture et analyse limite. Presses de l'Ecole Nationale des Ponts et 753 Chaussées, 1983.

J. Salençon, Yield Design. London, Hoboken : ISTE Ltd, 2013.

M. Save, M. A. Save, C. E. Massonnet, and G. De-saxce, Atlas of limit loads of metal plates, shells and disks. North-Holland Series in Applied, 1995.

J. Schlaich, K. Schäfer, and M. Jennewein, Toward a consistent design of structural concrete, PCI 760 journal, vol.32, pp.74-150, 1987.

S. W. Sloan, Lower bound limit analysis using finite elements and linear programming. Interna-762 tional, Journal for Numerical and Analytical Methods in Geomechanics, vol.12, pp.61-77, 1988.

S. W. Sloan and P. W. Kleeman, Upper bound limit analysis using discontinuous velocity fields, 1995.

, Computer Methods in Applied Mechanics and Engineering, vol.127, pp.293-314

P. Suquet, Elements of homogenization for inelastic solid mechanics. Homogenization techniques 766 for composite media 272, pp.193-278, 1985.

H. Vincent, M. Arquier, J. Bleyer, and P. De-buhan, Yield design-based numerical analysis of three-768 dimensional reinforced concrete structures, International Journal for Numerical and Analytical Methods, vol.769, pp.2177-2192, 2018.

A. Yan, Contributions to the Direct Limit State Analysis of Plastified and Cracked Structure, 1997.

W. H. Yang, Large deformation of structures by sequential limit analysis. International journal of 773 solids and structures, vol.30, pp.1001-1013, 1993.

X. Zhang, K. Krabbenhoft, and D. Sheng, Particle finite element analysis of the granular column 775 collapse problem, Granular Matter, vol.16, pp.609-619, 2014.