From the Cosserats mechanics backgrounds to modern field theory

ALBLAS J.B. 1969, Continuum mechanics of media with internal structure. Symposia Mathematica, (Inst. Naz. Alt. Mat.) 1, 229-251.
Crossref   Google Scholar

ANDRADE J. 1898, Leçons de mécanique physiquek Paris.   Google Scholar

ARIANO R. 1924, Deformacioni finite di sistemi continui. Annali di Matématica Pura ed Applicata, [ser4o] 2, 216-261.
Crossref   Google Scholar

ARMERO F., ROMERO I. 2003, Energy-dissipative momentum-conserving time-stepping algorithms for the dynamics of nonlinear Cosserat rods. Computational Mechanics 31 3–26.
Crossref   Google Scholar

ARON H. 1874, Das Geleichgewicht und die Bewegung einer unendlich dünnen beliebig gekrümmten elestischen Schale. J. reine angew. Math. (Crelle) 78, 136-174.
Crossref   Google Scholar

ATLURI S.N., CAZZANI A. 1995, Rotations in computational solid mechanics. Achieves
Crossref   Google Scholar

BADUR J., CHRÓŚCIELEWSKI J. 1983, Powłokowy element skończony oparty o kinematykę Cosseratów, Konf. Metod Num. Mech, Białystok.   Google Scholar

BADUR J., PIETRASZKIEWICZ W. 1986, On geometrically non-linear theory of elastic shells derived from pseudo-Cosserat continuum with constrained microrotations.[in:] Pietraszkiewicz, W. (Ed.) 1986, Finite Rotations in Structural Mechanics. Springer-Verlag, Wien, pp. 19–32.
Crossref   Google Scholar

BADUR J., STUMPF H. 1989, On the influence of E. and F. Cosserat on modern continuum mechanics and the field theory. Mitt. Aus dem Ins. F. Mechanik, Ruhr-Universität Bochum, no 72.   Google Scholar

BADUR J., YANG A. 1989, Mills type of equation for the compatibility conditions. Int. J. Eng. Sci. 27, 1439-1442.
Crossref   Google Scholar

BADUR J. 1990, Quasi-Abelian gauge theory of axisymmetric deformation of shells of revolution. Int. J. Eng. Sci. 28 563-572.
Crossref   Google Scholar

BADUR J. 1991, Extension of many-time Hamiltonian formalism to the theory of deformable Cosserat bodies. Int. J. Eng. Sci. 29, 69-77.
Crossref   Google Scholar

BADUR J. 1993, Pure gauge theory of the Cosserat surface. Int. J. Eng. Sci. 31, 41-59.
Crossref   Google Scholar

BADUR J. 1993, Space-time compatibility conditions for strains and velocities. Rendiconti di Matematica, 13, 1-29.   Google Scholar

BADUR J., POVSTIENKO Y. 1998, Cosserat boundle versus the motor calculus. Arch. Mech. 50, 367-376.   Google Scholar

BADUR J. 2009, Principles of Cosserat p-brane extended mechanics, [in:] ed. C. Capriz, M. Brocato; COSSERAT+100, int. Conf. on legacy of “Théorie des corps déformables by E.F. Cosserat, Paris 15-17 July (2009).   Google Scholar

BADUR J., CHRÓŚCIELEWSKI J. 2015, On a four-time unification of the Cosserats continua by the intrinsic approach. PCM, Gdańsk.   Google Scholar

BADUR J., ZIÓŁKOWSKI P., ZIÓŁKOWSKI P.J. 2015, On angular velocity slip in nonoflows. Microfluidics and Nanofluidics, 19, 191-199.
Crossref   Google Scholar

BADUR J. 2021, Eternal symmetries of Noether. IMP Press, Gdańsk, 1-514.   Google Scholar

BADUR J. 2022, Eternal relativity of Whitehead. IMP Press, Gdańsk, 1-501.   Google Scholar

BADUR J., OCHRYMIUK T., KOWALCZYK T., DUDDA W., ZIÓŁKOWSKI P. 2022, From fluid mechanics backgrounds to modern field theory. Acta Mech. 223, 3453-3465.
Crossref   Google Scholar

BASAR Y. 1987, A consistent theory of geometrically non-linear shells with an independent rotation vector. Int. J. Solids Struct. 23(10), 1401–1415.
Crossref   Google Scholar

BASAR Y., WEICHERT D. 2000, Nonlinear continuum mechanics of solids. Springer Verlag, Berlin.
Crossref   Google Scholar

BASSET A.B. 1894, On the deformation of thin elastic plates and shellsk Amer. J. Math. 16, 255-290.
Crossref   Google Scholar

BASSET A.B. 1895, On the deformation of thin elastic wiresk Amer. J. Math. 17, 281-317.
Crossref   Google Scholar

BELTRAMI E. 1871, Sur principi fondamentali della idrodinamica. Memorie Reale Accademia Scienze Istituto Bologna (3), t.1, pp. 431-476; t.2 (1872), pp. 381-437; t.3 (1873), pp. 349-407; t.5 (1874), pp. 443-484.   Google Scholar

BELTRAMI E. 1911, Sulle equazioni generali dell’elasticità. Opere matematiche, tom III, pag. 383, U. Hoepli (Milano).   Google Scholar

BESDO D. 1974, Ein Beitrag zur nichtlinearen theorie des Cosserat-Kontinuums. Acta Mechanica, 20, 105-131.
Crossref   Google Scholar

BESSAN E. 1963, Sui sistemi continui nel case asimetrico. Ann. Mathem. Pura Appl. 62 169-222.
Crossref   Google Scholar

BROCATO M., CAPRIZ G. 2001, Gyrocontinua. Int. J. Solids Structures, 38, 1089-1103.
Crossref   Google Scholar

CAPRIZ G., PODIO-GUIDUGLI P. 1977, Formal structure and classification of theories of oriented media. Ann. Mat. Pura Appl., Ser. IV 115,17–39.
Crossref   Google Scholar

CAPRIZ G., VIRGA E. 1994, On singular surfaces in the dynamics of continua with microstructure, Quart. Appl. Math. 52, 509–517.
Crossref   Google Scholar

CAPRIZ G. 2008, On ephemeral continua. Physical Mesomechanics 11, 285-298.
Crossref   Google Scholar

CAPRIZ G. 2010, Hypocontinua. In Continuous Media with Microstructure (B. Albers,Editor). Springer: Berlin 61-70.
Crossref   Google Scholar

CARNOT L. 1793, Les Principes fondamentaux de l’équilibre et du movement. Paris.   Google Scholar

CARTAN E. 1925, Sur les variétés à connexion affine et la theorie de la relativité généralisée. Annales scientifiques de l’École Norm. Sup.40, 325-412 (1923); 41, 1-25 (1924); 42, 17-88.
Crossref   Google Scholar

CARTAN E. 1935, La méthóde du repére mobile, la théorie des groupes continus et les espaces generalisés. Hermann, Paris.   Google Scholar

CAUCHY A.-L. 1823, Reserches sur l’équilibre et le mouvement des corpes solides ou fluides, élastiques ou non élastiques. Bull. Soc. Philomatique, 9-13.   Google Scholar

CESARO E. 1926, Vorlesugen über Natüraliche Geometre. 2nd ed. Verlag und Druck von B.G. Teubner, (trans. G. Kowalewski) Leipzig.   Google Scholar

CHAICHIAN M., NELIPA N.F. 1984, Introduction to the Gauge Field Theories. Springer, Berlin.
Crossref   Google Scholar

CHEN W.Z. 1944, The intrinsic theory of thin shells and plates. I General theory, Quart. Appl. Math. 1, 297-327.
Crossref   Google Scholar

CHRÓŚCIELEWSKI J., MAKOWSKI J., STUMPF H. 1992, Genuinely resultant shell finite elements accounting for geometric and material nonlinearity. Int. J. Numer. Meth. Eng. 35, 63-94.
Crossref   Google Scholar

CHRÓŚCIELEWSKI J., MAKOWSKI J., PIETRASZKIEWICZ W. 2004, Statyka i Dynamika Powłok Wielopłatowych. Wyd. IPPT PAN, Warszawa.   Google Scholar

CHRÓŚCIELEWSKI J., PIETRASZKIEWICZ W., WITKOWSKI W. 2010, On shear correction factors in the nonlinear theory of elastic shells, Int. J. Solids Struct. 47, 3537–3445.
Crossref   Google Scholar

CLAYTON J.D. 2022, Finsler differential geometry in continuum mechanics: Fundamental concepts, history, and renewed application to ferromagnetic solids. Mathematics and Mechanics of Solids.
Crossref   Google Scholar

COSSERAT E. AND F. 1896, Sur la theorie de l’elasticitek Ann. Toulouse 10 1-116.
Crossref   Google Scholar

COSSERAT E. AND F. 1907, Sur la mécanique générale, Comptes Rendus 145, 1139-1142.   Google Scholar

COSSERAT E. AND F. 1909, Théorie des corps déformables. Paris, Hermann.   Google Scholar

COSSERAT E. AND F. 1909, Note sur la théorie de l’action euclidienne. [in:] Traité de mécanique rationelle (ed. P. Appell) t. III, pp 557-629, Paris, Gauthier-Villars 1909.   Google Scholar

CRAIG T. 1898, Displacement depending on one, two and three parameters in a space of four dimensionsk Amer. J. Math. 20, 135-156.
Crossref   Google Scholar

CRISFIELD M.A., JELENIĆ G. 1998, Objectivity of strain measures in geometrically exact 3D beam theory and its finite element implementation. Proc. Roy. Soc. London 455: 1125–1147.
Crossref   Google Scholar

DANIELSON D.A., HODGES D.H. 1984, Nonlinear beam kinematics by decomposition of the rotation tensor. ASME Journal of Applied Mechanics 54 258–262.
Crossref   Google Scholar

DARBOUX G. 1890, Leçons sur la théorie générale des surfacesk Paris.   Google Scholar

DARBOUX G. 1900, Sur les déformations finites et sur les systèmes triples de surfaces orthogonales. Proc. Lond. Math. Soc. 32, 377-383.
Crossref   Google Scholar

DE BORST R. 1991, Simulation of strain localization: a reappraisal of the Cosserat continuum. Eng. Comput. 8, 317–332.
Crossref   Google Scholar

DE LEÓN M., EPSTEIN V., JIMÉNEZ V. 2021, Material Geometry: Groupoids in Continuum Mechanics. Pergamon NY.
Crossref   Google Scholar

DELENS P.-C. 1927, Méthods et problèmes des géométries différentielles, Euclidienne et conforme. Gauther-Villars, Paris.   Google Scholar

DELL’ISOLA F., DELLA CROTE A., GIROGIO I. 2015, Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Tupin and some future research perspectives. Math. Mech. Sol. 20, (8) 887-928.   Google Scholar

DILL E.H. 1992, Kirchhoff's theory of rods. Arch. Hist. Exact Sci. 44 (1), 1-23.
Crossref   Google Scholar

DUHEM P. 1893, Le potentel thermodynamique et la pression hydrostatiquek Ann Ecole Norm. Sup., Ser 3, 10 187-230.
Crossref   Google Scholar

DUHEM P. 1901, Reserches sur l’hydrodynamique. Ann Toulouse (2) 3, 315-377, 379-431; 4 (1902), 101-169; 5 (1903), 5-61, 197-255, 353-404; [rep. separately Paris, 2 vols 1903, 1904].   Google Scholar

DUHEM P. 1904, Recherches sur l’elasticite. Ann. Ecole Norm. (3) 21 99-139, 375-414 (1904), 22 143-217 (1905), 23 169-223 (1906), repr. Separately, Paris 1906.   Google Scholar

EDELEN D.G.E., LAGOUDAS D.C. 1988, Gauge Theory of Defects in Solids. North-Holland, Amsterdam.   Google Scholar

EHLERS W., RAMM E., DIEBELS S., D’ADDETTA G.A. 2003, From particle ensembles to Cosserat continua: homogenization of contact forces towards stresses and couple stresses, Int. J. Solids Struct. 40 6681–6702.
Crossref   Google Scholar

EL NASCHIE M.S. 2016, Cosserat-Cartan and de Sitter-Witten spacetime setting for dark energy, Quantum Matter.
Crossref   Google Scholar

EPSTEIN M. , DE LEON M. 1998, Geometrical theory of uniform Cosserat media. Journal of Geometry and Physics 26, (1–2), 127-170.
Crossref   Google Scholar

ERICKSEN J.L., TRUESDELL C. 1958, Exact theory of stress and strain in rods and shells. Arch. Rational. Mech. Anal. 1, 295-323.
Crossref   Google Scholar

ERINGEN A.C., SUHUBI E.S. 1964, Nonlinear theory of simple microelastic solids. I and II. Int. J. Eng. Sci. 2, 189–203. 389–404.
Crossref   Google Scholar

EULER L.1752, Découverte d’un nouveau principle de mécanique, Mém. Acad. Sci. Et belles letters. Berlin, t 6, 185-217 (1752) [submitted 1750] [Euler Opera omia ser 2. t12, pp 81-108]   Google Scholar

FERRARESE G. 1959, Sulla velocita angolare nei moti rigidi e la rotazione locale nelle deformazioni finite. Rend. mat. E Appl. 18, 169-177.   Google Scholar

FERRARESE G. 1971, Sulla compatibilita dei continui alla Cosserat, Rendiconti di Matem. 4, 151-174.   Google Scholar

FERRARESE G. 1972, Intrinsic formulation of Cosserat continua dynamics, [in:] ed. H. Zorski, Trends in Applications of Pure Mathematics to Mechanics, II, pp 97-113 (1972).   Google Scholar

FERRARESE G. 1976, Sulla formulazione intrinseca della dinamica dei continui alla Cosserat. Ann. Mathem. Pura Appl. 108 109-124.
Crossref   Google Scholar

FINZI B. 1932, Equazioni intrinseche della meccanica dei sistemi continui perfettamente od imperfettamente flessibili. Annali Math. Pura Appl. 11, 215-245.
Crossref   Google Scholar

FOREST S., CAILLETAUD G., SIEVERT R. 1997, A Cosserat theory for elastoviscoplastic single crystals at finite deformation. Arch. Mech. 49 (4) 705–736.   Google Scholar

FOREST S., SIEVERT R. 2003, Elastoviscoplastic constitutive frameworks for generalized continua. Acta Mech. 160, 71–111.
Crossref   Google Scholar

FOREST S., SIEVERT R. 2006, Nonlinear microstrain theories. Int. J. Solids Struct. 43, 7224–7245.
Crossref   Google Scholar

FORTUNE D., VALLEE C. 2001, Bianchi identities in case of large deformations. Int. J. Eng. Sci. 39 113-123.
Crossref   Google Scholar

FRANKE J. N. 1889, Mechanika Teoretyczna. Biblioteka Matematyczno-Fizyczna, Kasa J. Mianowskiego, tom X, pp 1- 645, Warszawa.   Google Scholar

FRENET F. 1847, Sur les courbes a double courbure. Toulouse: Thése.   Google Scholar

GOSIEWSKI W. 1877, O zasadach teorii bezwzględnej zjawisk materialnych. Pamiętnik Towarzystwa Nauk Ścisłych w Paryżu, 10,1-6.   Google Scholar

GREEN A.E. AND LAWS N. 1966, A general theory of rods. Proceedings of the Royal Society of London A293 145–155.
Crossref   Google Scholar

GREEN A.E., NAGHDI P.M. AND WAINWRIGHT W.L. 1965, A general theory of Cosserat surfaces. Arch. Rational Mech. Anal. 20, 287–308.
Crossref   Google Scholar

GRIOLI G. 1960, Elasticità asimmetrica. Ann. Mathem. Pura Appl. 50 389-417.
Crossref   Google Scholar

GRIOLI G. 1968, Questioni di compatibilità per continui di Cossarat. Sumposia Mathemetica, I, 271-287.   Google Scholar

GRUTTMANN F., STEIN E., WRIGGERS P. 1989, Theory and numerics of thin elastic shells with finite rotations, Ing.-Arch. 59, 54-67.
Crossref   Google Scholar

GRUTTMAN F., SAUER R., WAGNER W. 1998, A geometrically nonlinear eccentric 3D-beam element with arbitrary cross sections. Comput. Meth. Appl. Mech. Eng. 160: 383–400.
Crossref   Google Scholar

GÜNTHER W. 1958, Zur Statik und Kinematik des Cosseratschen Kontinuum. Abh. d. Brauschweigisch Wiss. Ges., 10, 195-213.   Google Scholar

GÜNTHER W. 1961, Analoge Systeme von Schalengeleichungen. Ing.-Arch., 30, 160-186.
Crossref   Google Scholar

HAY G.E. 1942, The finite displacement of thin rods, Trans. Am. Meth. Soc. 51, 65-102.
Crossref   Google Scholar

HEHL F., KRÖER E. 1965, Über den Spin in der allgemeinen Relativitätstheorie Eine notwendige Erweiterung der Einsteinschen Feldgleichungen. Zeitschrift für Physik, 187, 478-489.
Crossref   Google Scholar

HEHL F., KRÖER E. 1965, Zum materialgesetz eines elastischen Medius mit Momentenspannungen. Z. f. Naturforschg, 20, 336-350.
Crossref   Google Scholar

HEHL F.W. 1973, Spin and torsion in general relativity. I. Foundations, General relativity and gravitation 4, 333-349.
Crossref   Google Scholar

HEHL F.W., OBUKHOV Y.N. 2007, Élie Cartan's torsion in geometry and in field theory, an essay. arXiv preprint arXiv:0711.1535.   Google Scholar

HEHL F.W. 2017, Gauge theory of gravity and spacetime. [in:] Towards a Theory of Spacetime Theories, Springer Berlin, 145-169 (2017).
Crossref   Google Scholar

HELLINGER E. 1914, Die allgemein ansätze der mechanik der kontinua. In: Klein F, Müller CH (eds) Enz math wiss, vol 4, part 4, Article 30, Springer, Berlin, pp 602–694.   Google Scholar

HELMHOLTZ H. 1868, Über die Tataschen die Geometrie zugrunde liegen. Nachr. Ges. Wiss. Göttingen 9, 193-221.   Google Scholar

HENCKY H. 1915, Űber den Spannungszstand kreisrundem platten. Z. Math. Phys. 63, 311-317.   Google Scholar

HESS W. 1884, Ueber die Biegung und Drillung eines unendlich dünnen elastischen Stabes, dessen eines Ende von einem Kräftepaar angegriffen wied. Math. Ann. 23, 181-212.
Crossref   Google Scholar

HODGES D.H. 1990, A mixed variational formulation based on exact intrinsic equations for dynamics of moving beams. Int. J. Solids Struct. 26, 1253–1273.
Crossref   Google Scholar

HODGES D.H., ATILGAN A.R., DANIELSON D.A. 1993, A geometrically nonlinear theory of elastic plates. Journal of Applied Mechanics 60, 109–116.
Crossref   Google Scholar

IBRAHIMBEGOVIC A. 1994, Stress resultant geometrically nonlinear shell theory with drilling rotations. Part 1. A consistent formulation. Comput. Methods Appl. Mech. Eng. 118, 265-284.
Crossref   Google Scholar

JAUMANN R G. 1918, Physik der kontinuierlichen Medien. Denkschr. Akad. Wiss. Wien 95 461-562.   Google Scholar

KADIĆ A., EDELEN D.G. 1983, A gauge theory of dislocations and disclinations. Lect. Not. Phys. No. 174, Springer, Berlin.
Crossref   Google Scholar

KAFADAR C., ERINGEN A.C. 1971, Micropolar media, Part I – The classical theory, Int. J. Eng. Sci. 9, 271-329.
Crossref   Google Scholar

KESSEL S. 1970, Spannungsfelder einer Schraubenversetzung und einer Stufenversetzung im Cosseratschen Kontinuum. ZAMM, 50:547–553.   Google Scholar

KIRCHHOFF G. 1850, Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. J. reine angew. Math. 40, 51-88.
Crossref   Google Scholar

KIRCHHOFF G. 1852, Über die Gleichungen des Gleichgewichts eines elastischen Körpers bei nicht unendlich kleinen Verschiebungen seiner Teile. Sitzgsber. Akad. Wiss. Wien 9, 762-773.   Google Scholar

KIRCHHOFF G. 1859, Űber das Gleichgewicht und die Bewegung eines unendlich dünnen elastischen Stabes. J. reine angew. Math. 56, 285-313.
Crossref   Google Scholar

KIRCHHOFF G. 1883, Vorlesungen über mathematische Physik: Mechanik. Leipzig; (1876); 2nd ed. (1877); 3ed.   Google Scholar

KLINGER F. 1942, Die Statik und Kinematik des räumlich gekrümmten elastischen Stabes. Sitzun. Akad. Wiss. Wien, IIa, 151, 13-79.   Google Scholar

KLUGE G. 1969, Zur Dynamik der allgemeinen versetzungstheorie bei berücksichtigung von momentenspannungen. Int. J. Engng Sci. 7, 169-182.
Crossref   Google Scholar

KOITER W. T. 1964, Couple-stresses in the theory of elasticity. Proc. Kon. Ned. Acad. Wet., Amsterdam, 64, 17-44.   Google Scholar

KRAUß F. 1929, Űber die Grundleichungen der Elastizitätstheorie scheach deformirter Schalen. Math. Ann. 101, 61-92.
Crossref   Google Scholar

KRÖNER E. 1960, Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen. Arch. Rational Mech. Anal., Vol. 4, 273-334.
Crossref   Google Scholar

LACHNER D., LIPPMANN H., TOTH L.S. 1994, On Cosserat plasticity and plastic spin for isotropic materials. Archive Mech. 46, 531–539.   Google Scholar

LAGRANGE J.L. 1762, Application de la méthode exposée précédente a la solution de différmes problémes de dynamique. Misc. Taur, 2, 196-298.   Google Scholar

LAKES R. 1995, Experimental methods for study of Cosserat elastic solids and other generalized continua. [in:]Continuum models for materials with micro-structure, ed. H. Mühlhaus, J. Wiley, N. Y. Ch. 1, p. 1-22, (1995).   Google Scholar

LAME G., CLAPEYRON E. 1833, Mémoire sur l’équilibre intérieur des corps solides homogènes. Mémoires l’Acad. Royale des Sciences de l’Institut de France, tome 4, 465-562.   Google Scholar

LAMÉ G. 1852, Leçons sur la Théorie Mathématique de l’Élasticité. Paris.   Google Scholar

LANGE L. 1885, Über die wissenschaftliche Fassung des Galileischen Beharrungsgesetzes. Berl. Kgl. Ges. Wiss. Math-Phys. Kl. 333-351.   Google Scholar

LAZAR M., HEHL F.W. 2010, Cartan’s spiral staircase in physics and, in particular, in the gauge theory 2013of dislocations. Foundations of Physics 40, 1298-1325.
Crossref   Google Scholar

LE CORRE Y. 1965, La dissymétrie du tenseur des efforts et ses conséquences. J Phys Radium 17:934–939.
Crossref   Google Scholar

LE K.C., STUMPF H. 1998, Strain measures, integrability condition and frame indifference in the theory of oriented media. Int. J. Solids Struct 35 (9–10), 783–798.
Crossref   Google Scholar

LECORNU M.L. 1880, Sur l’équilibre des surfaces flexibiles at inextensibiles. J. De l’Ecole Polytech. 29, 1-100.   Google Scholar

LEHMANN TH. 1964, Formäderungen eines klassischen Kontinuum in vierdimensionaler Darstellung. Proc. 19 Int. Congers of Appl. Mech. Ed. H. Görtler, pp 376-382.
Crossref   Google Scholar

LIPPMANN H. 1969, Eine Cosserat-Theorie des plastischen Fließens. Acta Mech. 8, 255–284.
Crossref   Google Scholar

LOVE A.E.H. 1888, The small free vibrations and deformations of a thin elastic shell. Phil. Trans. Roy. Soc. London, A 179, 491-546.
Crossref   Google Scholar

LUO A.C.J., 2010, On a nonlinear theory of thin rods. Comm. Nonlinear Sci Numer Simulat 15 4181–4197.
Crossref   Google Scholar

MAC CULLAGH J. 1839, An essay towards a dynamical theory of crystalline reflexion and refraction. Transactions of the Royal Irish Academy, 21 17-50.   Google Scholar

MAKOWSKI J., STUMPF H. 1990, Buckling equations for elastic shells with rotational degrees of freedom undergoing finite strain deformation. Int. J. Solids Struct. 26 (3), 353–368.
Crossref   Google Scholar

MALCOLM D.J., GLOCKNER P.G. 1972, Nonlinear sandwich shell and Cosserat surface theory. Trans. ASCE J. Eng. Mech.Div. 98(EM5), 1183–1203.
Crossref   Google Scholar

MAUGIN G. A. 2014, Continuum Mechanics Through the Eighteenth and Nineteenth Centuries 2014 Historical Perspectives from John Bernoulli (1727) to Ernst Hellinger (1914). Springer Cham, pp 1-269.
Crossref   Google Scholar

MAUGIN G.A. 1998, On the structure of the theory of polar elasticity. Philos. Trans. R. Soc. Lond. A 356, 1367–1395.
Crossref   Google Scholar

MEISSNER K. 2013, Classical Field Theory. PWN Press, 1-162, Warszawa.   Google Scholar

MINDLIN R. D., TRIESTEN H. 1962, Effects of complex-stress in linear elasticity. Arch. Rat. Mech. Anal. 11, 415-448.
Crossref   Google Scholar

MINDLIN R.D. 1964, Microstructure in linear elasticity. Arch. Rat. Mech. Anal. 16, 51-78.
Crossref   Google Scholar

NADLER B., RUBIN M.B. 2003, A new 3-D finite element for nonlinear elasticity using the theory of a Cosserat point. Int. J. Solids Structures, 40, 4585–4614.
Crossref   Google Scholar

NEFF P. 2006, A finite-strain elastic–plastic Cosserat theory for polycrystals with grain rotations. Int. J. of Engineering Sci. 44 574–594.
Crossref   Google Scholar

NEFF P. 2019, Cosserat Theory by Prof. Dr. Patrizio Neff. Lehrstuhl für Nichtlineare Analysis, Universität Duisburg-Essen - from http://www.uni-due.de/mathematik/ag_neff/cosserat .   Google Scholar

NOWACKI W. 1966, Couple-stresses in the theory of thermoelasticity. Bull. de L’Acad. Polonaise des Sci. 14 97-106, 203-212.   Google Scholar

NOWACKI W. 1986, Theory of Asymmetric Elasticity. Pergamon-Press, Oxford.   Google Scholar

O’REILLY O. M., TURCOTTE J.S. 1997, Elastic rods with moderate rotation, Journal of Elasticity 48: 193–216.
Crossref   Google Scholar

OPOKA S., PIETRASZKIEWICZ W. 2004, Intrinsic equation of nonlinear deformation and stability of thin elastic shells. Int. J. Solids Struct. 41, 3275–3292.
Crossref   Google Scholar

PAPENFUSS C., FOREST S. 2006, Thermodynamical frameworks for higher grade material theories with internal variables or additional degrees of freedom. J. Non-Equilib. Therm, 31:319–353.
Crossref   Google Scholar

PASTORI M. 1934, Equilibro di lastre a membrane elastiche. Rend. Cirolo Math. Palermo, 58, 1-48.
Crossref   Google Scholar

PIETRASZKIEWICZ W. 1979, Finite rotation and lagrangean description in the non-linear theory of shells. PWN, Warszawa, pp 1-109.   Google Scholar

PIETRASZKIEWICZ W., BADUR J. 1983, Finite rotations in the description of continuum deformation. Int. J. Eng Sci. 21, 1097-1115.
Crossref   Google Scholar

PIETRASZKIEWICZ W., BADUR J. 1983, On non-classical forms of compatibility conditions in continuum mechanics, [in:] Trends in Applications of Pure Math. Mech., vol IV, pp 197-227.   Google Scholar

PIETRASZKIEWICZ W. 1988, Geometrically non-linear theories of thin elastic shells. Mitt. Aus dem Ins. F. Mechanik, Ruhr-Universität Bochum, no 55.   Google Scholar

PIOLA G. 1833, La meccanica de’corpi naturalmente esteci trattata col calcolo delle variazioni. Opuscoli matematici e fisici di diversi autori, 201-236.   Google Scholar

PIOLA G. 1848, Intorno alle equazioni fondamentali del movimento di copri qualsivoglino, considerati second la naturale loro forma e costituzione. Mem. Mat. Fis. Soc. Ital. Moderna 24 1-186.   Google Scholar

POINCARÉ H. 1898, Leçons sur la théorie de l’Élasticité. Paris.   Google Scholar

POISSON S.-D. 1831, Mémoire sur la equations generales de la l’équilibre et du mouvement des corps solides élastiques et des fluides. J. École Polytech. 13 cahier 20, 1-174.   Google Scholar

POISSON S.-D. 1833, Traité de Mécanique. Paris.   Google Scholar

POMMARIET J.-F. 1989, Gauge Theory and General Relativity. Reports on Mathematical Physics, 3, 27, 313-344.
Crossref   Google Scholar

POMMARET J.-F. 1997, F. Cosserat et le secret de la théorie mathématique de l’élasticité. Ann. Ponts et Chaussées, Nouvelle série, no. 82, 59–66.   Google Scholar

POMMARET J.-F. 2010, Parametrization of Cosserat Equations, Acta Mechanica, 215, 43- 55.
Crossref   Google Scholar

POMMARET J.-F. 2014, The mathematical foundations of gauge theory revisited, Journal of Modern Physics, 5, 157-170.
Crossref   Google Scholar

POMMARET J.-F. 2016, Deformation Theory of Algebraic and Geometric Structures. LAP-publishing, Saarbrucken, Germany, 200.   Google Scholar

RANKINE W.J.M. 1851, Laws of the elasticity of solids bodies. Camb. Dubl. Math J. 6, 41-80, 178-181, 185-186.   Google Scholar

REECH F. 1852, Cours de mécanique, d’après la nature généralement flexible et élastique des corps. Paris.   Google Scholar

REISSNER E. 1950, On axisymmetrical deformation of thin shells of revolution. Proc. Symposia in Appl. Mech. 3, 27-52.
Crossref   Google Scholar

REISSNER E., WAN F.M. 1968, A note on Günther’s analysis of couple stress. [in:] ed. E. Kröner; Mechanics of Generalized Continua, Springer-Verlag, Berlin.
Crossref   Google Scholar

REISSNER E. 1972, On finite symmetrical strain in thin shells of revolution. J. App. Mech. 39 1137-1138.
Crossref   Google Scholar

REISSNER E. 1974, Linear and nonlinear theory of shells. [in:] Thin Shell Structures, 29-44, Prentice-Hall, Englewood Cliffs (1974).   Google Scholar

REISSNER E. 1981, On finite deformation of space-curved beams. J. Appl. Math. Phys. 32, 734–744.
Crossref   Google Scholar

RUBIN M.B. 2000, Cosserat Theories: Shells, Rods and Points. Kluwer Academic Publishers, Dordrecht.
Crossref   Google Scholar

SANSOUR C., BUER H. 1992, An exact finite rotation shell theory, its mixed variational formulation and its fnite element implementation. Int. J. Num. Methods Engrg. 34, 73-115.
Crossref   Google Scholar

SANSOUR C. 1998, A unified concept of elastic–viscoplastic Cosserat and micromorphic continua. Journal de Physique IV Proceedings 8, 341–348.
Crossref   Google Scholar

SANSOUR C. 1998, A theory of the elastic–viscoplastic Cosserat continuum. Arch. Mech. 50 577–597.   Google Scholar

SANSOUR C., SKATULLA S. 2008, A non-linear Cosserat continuum-based formulation and moving least square approximations in computations of size-scale effects in elasticity. Computational Materials Science 41, 589–601.
Crossref   Google Scholar

SAWCZUK A. 1967, On the yielding of Cosserat-Continua. Arch. Mech. Stosow. 19, 471-492.   Google Scholar

SCHAEFER H. 1967, Analysis der Motorfelder im Cosserat-Kontinuum. ZAMM, 47, 319-328.
Crossref   Google Scholar

SCHAEFER H. 1967, Das Cosserat-Kontinuum. ZAMM, 47, 485-498.
Crossref   Google Scholar

SCHOUTEN J. A. 1954, Calculus Ricci. 2nd ed. Springer Verlag Berlin.   Google Scholar

SHIELD R.T. 1973, The rotation associated with large strains. SIAM Journal on Applied Mathematics 25 483–491.
Crossref   Google Scholar

SIGNORINI A. 1943, Transformazioni termoelastiche finite, Annali Math. Pura et Applicata, 22, 33-143.
Crossref   Google Scholar

SIMMONDS J.G., DANIELSON D.A. 1972, Nonlinear shell theory with finite rotation and stress function vectors. J. Appl. Mech. 39, 1085-1090.
Crossref   Google Scholar

SIMO J.C. 1992, The (symmetric) hessian for geometrically nonlinear models in solid mechanics: Intrinsic definition and geometric interpretation. Com. Meth. Appl. Mech. Eng., 96:189–200.
Crossref   Google Scholar

SIMON E.R., DELL’ISOLA F. 2018, Exegesis from “fundamentals of the mechanics of continua by E. Hellinger. Z. Angew. Math. Mech. 97(4) a477-506 (2017); 98(1), 31-68 (2018); 98(1), 69-105.   Google Scholar

SKIBA E. 1874, Przyczynek do teorii strun. Pamiętnik Akademii Umiejętności w Krakowie, 3,130-154.   Google Scholar

STAZI L. 1976, Sulla mechanica intrinseca dei continui iperelastici. Rend. Circ. Matem. Palermo.   Google Scholar

STEINMANN P. 1994, A micropolar theory of finite deformation and finite rotation multiplicative elastoplasticity. Int. J. Solids Struct. 31 (8) 1063–1084.
Crossref   Google Scholar

STEINMANN P., STEIN E. 1997, A uniform treatment of variational principles for two types of micropolar continua. Acta Mechanica 121, 215–232.
Crossref   Google Scholar

STOJANOVIĆ R. 1972, Nonlinear micropolar elasticity. In: Nowacki, W., Olszak, W. (Eds.), Micropolar Elasticity. CISM, Udine, pp. 73–103 (1972).
Crossref   Google Scholar

STUMPF H., BADUR J. 1990, On the non-Abelian motor calculus. ZAMM, 70, 551-555.
Crossref   Google Scholar

SUDRIA J. 1925, Contribution à la théorie de l’action euclidienne. Ann Fac Sci Toulouse, 3ème série, 17:63–152.
Crossref   Google Scholar

SUDRIA J. 1935, L’action éuclidéenne de déformation et de mouvement, Mém. Sci. Phys. Paris no 29 pp56.   Google Scholar

SYNGE J.L., CHIEN W.Z. 1941, The intrinsic theory of elastic shells and plates. [in:] von Kàrmàn anniv. vol. Pasadena pp 103-120 (1941).   Google Scholar

THOMSON W., TAIT P.G. 1883, Treatise on Natural Philosophy. Cambridge University Press vol. I (1879), vol II.   Google Scholar

TONOLO A. 1930, Equaqzioni intrinseche di equilibro dell’elasticità negli spazî a curvatura costante. Rend. del Sem. Matem. della Univ. Di Padova, 1, 73-84.   Google Scholar

TONTI E. 1976, On the formal structure of Physical Theories. Ins. di Matemetica Politecnico di Milano.   Google Scholar

TOUPIN R. 1962, Elastic materials with couple stresses. Arch. Rat. Mech. Anal. 11 385–413.
Crossref   Google Scholar

TOUPIN R. 1964, Theories of elasticity with couple-stress. Arch. Rat. Mech. Anal. 17, 85-112.
Crossref   Google Scholar

TRUESDELL C. 1953, The mechanical foundation of elasticity and fluid dynamics. Jour. Rat. Mech. Anal. 1 125-300 (1952) errata 2 593-616.
Crossref   Google Scholar

TRUESDELL C. 1960, The Rational Mechanics of Elastic or Flexible Bodies. L. Euler Opera Omnia, vol. II, 1-435.   Google Scholar

TRUESDELL C., TOUPIN R.A. 1960, The Classical Field Theories. Hand. der Physik III/1, ed. S. Fluge, 226-793.
Crossref   Google Scholar

VALID R. 1979, An intrinsic formulation for the nonlinear theory of shells and some approximations. Computers and Structures, 10 183-194.
Crossref   Google Scholar

VARDOULAKIS I. 2019, Cosserat Continuum Mechanics, Lecture Notes in Applied and Computational Mechanics 87. Springer International Publishing.
Crossref   Google Scholar

VOIGT W. 1887, Teoretische Studien über Elasticitätverhältinsse der Krystalle. I.II. Abh K Ges Wissen Göttingen 34:3–52, 53–100.   Google Scholar

MISES R. 1924, Motorrechnung, ein neues Hilfsmittel der mechanic. ZAMM, 4, 155-181.
Crossref   Google Scholar

WEATHEBURN C.E. 1927, On small deformation of surfaces and of thin elastic shells. The Quarterly Jour. Pure Appl. Math. 50, 272-296.   Google Scholar

WILSON E.B. 1913, An advance in theoretical mechanics: Théorie des corps déformables by E. and F. Cosserat. Bull Amer Math Soc 19(5):242–246.
Crossref   Google Scholar

WIŚNIEWSKI K. 1998, A shell theory with independent rotations for relaxed Biot stress and right stretch strain. Comput. Mech. 21 (2) 101-122.
Crossref   Google Scholar

ZERNA W. 1950, Beitrag zur allgemeinen Schalenbiegetheore. Ing.-Arch. 17 147-164.
Crossref   Google Scholar

ZHONG-HENG G. 1963, Homographic representation of the theory of finite thermoelastic deformations. Arch. Mech. Stos. 15 475-505.   Google Scholar

ZHOUNG-HENG G. 1983, “Method of principal axes” in nonlinear continuum mechanics. Adv. in Mech. 13 1-17.   Google Scholar