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The Loss and Recovery of the Works by Piola and the Italian Tradition of Mechanics

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Evaluation of Scientific Sources in Mechanics

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 152))

Abstract

In this chapter, we look in detail at the aspects concerning the transmission of scientific knowledge of the Italian school of Continuum Mechanics, mainly headed by Gabrio Piola, which strongly supported the point of view of Archytas of Tarentum as rediscovered by D’Alembert and Lagrange. The process of systematically removing references to the name of Gabrio Piola in Continuum Mechanics (and part of his results) is just one of many examples of how some social groups have, over the centuries and in different cultural fields, rewritten more or less relevant parts of the cultural knowledge of a society. Specifically, Gabrio Piola’s contribution to mechanical sciences has been greatly underestimated in both the more theoretical mathematical-physics literature and in the more applied and engineering oriented one. We remark, in the discussion presented in this Chapter, that at the basis of this phenomenon one can always find common features as a sectarian vision of cultural progress or the conviction that the point of view of the own social group is clearly superior to that of all the others.

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References

  1. Abdoul-Anziz, H., Auffray, N., Desmorat, B.: Symmetry classes and matrix representations of the 2d flexoelectric law. Symmetry 12(4), 674:1–29 (2020)

    Google Scholar 

  2. Altenbach, H., Bîrsan, M., Eremeyev, V.A.: Cosserat-type rods. In: Generalized Continua from the Theory to Engineering Applications, pp. 179–248. Springer (2013)

    Google Scholar 

  3. Altenbach, H., Eremeyev, V.A.: On the theories of plates based on the cosserat approach. In: Mechanics of generalized continua, pp. 27–35. Springer (2010)

    Google Scholar 

  4. Altenbach, H., Eremeyev, V.A.: Cosserat media. In: Generalized Continua from the Theory to Engineering Applications, pp. 65–130. Springer (2013)

    Google Scholar 

  5. Altenbach, H., Eremeyev, V.A.: Cosserat-type shells. In: Generalized continua from the theory to engineering applications, pp. 131–178. Springer (2013)

    Google Scholar 

  6. Altenbach, J., Altenbach, H., Eremeyev, V.A.: On generalized Cosserat-type theories of plates and shells: a short review and bibliography. Archive of Applied Mechanics 80(1), 73–92 (2010)

    Google Scholar 

  7. Andreaus, U., Dell’Isola, F., Giorgio, I., Placidi, L., Lekszycki, T., Rizzi, N.L.: Numerical simulations of classical problems in two-dimensional (non) linear second gradient elasticity. International Journal of Engineering Science 108, 34–50 (2016)

    Google Scholar 

  8. Askari, E., Bobaru, F., Lehoucq, R., Parks, M., Silling, S., Weckner, O., et al.: Peridynamics for multiscale materials modeling. Journal of Physics: Conference Series 125(1), 012078:1–11 (2008)

    Google Scholar 

  9. Barchiesi, E., Eugster, S.R., dell’Isola, F., Hild, F.: Large in-plane elastic deformations of bipantographic fabrics: asymptotic homogenization and experimental validation. Mathematics and Mechanics of Solids 25(3), 739–767 (2020)

    Google Scholar 

  10. Barchiesi, E., Eugster, S.R., Placidi, L., dell’Isola, F.: Pantographic beam: a complete second gradient 1D-continuum in plane. Zeitschrift für angewandte Mathematik und Physik 70(5),135:1–24 (2019)

    Google Scholar 

  11. Barchiesi, E., Harsch, J., Ganzosch, G., Eugster, S.R.: Discrete versus homogenized continuum modeling in finite deformation bias extension test of bi-pantographic fabrics. Continuum Mechanics and Thermodynamics pp. 1–14 (2020)

    Google Scholar 

  12. Barchiesi, E., Yang, H., Tran, C., Placidi, L., Müller, W.: Computation of brittle fracture propagation in strain gradient materials by the FEniCS library. Mathematics and Mechanics of Solids pp. 1–16 (2020)

    Google Scholar 

  13. Basdevant, J.L.: Feynman’s principle in quantum mechanics. In: Variational Principles in Physics, pp. 145–165. Springer (2007)

    Google Scholar 

  14. Benvenuto, E.: An introduction to the history of structural mechanics: Part I: Statics and resistance of solids. Springer Science & Business Media (2012)

    Google Scholar 

  15. Berrey, M.: Hellenistic science at court, vol. 5. Walter de Gruyter GmbH & Co KG (2017)

    Google Scholar 

  16. Burton Russell, J.: Inventing the flat earth: Columbus and modern historians (1991)

    Google Scholar 

  17. Capobianco, G., Eugster, S.R.: Time finite element based Moreau-type integrators. International Journal for Numerical Methods in Engineering 114(3), 215–231 (2018)

    Google Scholar 

  18. Capobianco, G., Eugster, S.R., Winandy, T.: Modeling planar pantographic sheets using a nonlinear Euler–Bernoulli beam element based on B-spline functions. Proceedings in Applied Mathematics and Mechanics 18(1), e201800220:1–2 (2018)

    Google Scholar 

  19. Capobianco, G., Winandy, T., Eugster, S.: The principle of virtual work and Hamilton’s principle on Galilean manifolds. Journal of Geometric Mechanics pp. 1–27 (2021)

    Google Scholar 

  20. Carcaterra, A., dell’Isola, F., Esposito, R., Pulvirenti, M.: Macroscopic description of microscopically strongly inhomogenous systems: A mathematical basis for the synthesis of higher gradients metamaterials. Archive for Rational Mechanics and Analysis 218(3), 1239–1262 (2015)

    Google Scholar 

  21. Cazzani, A., Atluri, S.: Four-noded mixed finite elements, using unsymmetric stresses, for linear analysis of membranes. Computational Mechanics 11(4), 229–251 (1993)

    Google Scholar 

  22. Cazzani, A., Malagù, M., Turco, E.: Isogeometric analysis of plane-curved beams. Mathematics and Mechanics of Solids 21(5), 562–577 (2016)

    Google Scholar 

  23. Cazzani, A., Malagù, M., Turco, E., Stochino, F.: Constitutive models for strongly curved beams in the frame of isogeometric analysis. Mathematics and Mechanics of Solids 21(2), 182–209 (2016)

    Google Scholar 

  24. Cazzani, A., Serra, M., Stochino, F., Turco, E.: A refined assumed strain finite element model for statics and dynamics of laminated plates. Continuum Mechanics and Thermodynamics 32(3), 665–692 (2020)

    Google Scholar 

  25. Cazzani, A., Stochino, F., Turco, E.: An analytical assessment of finite element and isogeometric analyses of the whole spectrum of Timoshenko beams. Zeitschrift für Angewandte Mathematik und Mechanik 96(10), 1220–1244 (2016)

    Google Scholar 

  26. Cohen, L.: Quantization problem and variational principle in the phase-space formulation of quantum mechanics. Journal of Mathematical Physics 17(10), 1863–1866 (1976)

    Google Scholar 

  27. Cosserat, E., Cosserat, F.: Théorie des corps déformables. A. Hermann et fils (1909)

    Google Scholar 

  28. Cremaschini, C., Tessarotto, M.: Synchronous Lagrangian variational principles in general relativity. The European Physical Journal Plus 130(6), 123 (2015)

    Google Scholar 

  29. Cuomo, M.: Continuum damage model for strain gradient materials with applications to 1d examples. Continuum Mechanics and Thermodynamics 31(4), 969–987 (2019)

    Google Scholar 

  30. Cuomo, M., Contrafatto, L., Greco, L.: A variational model based on isogeometric interpolation for the analysis of cracked bodies. International Journal of Engineering Science 80, 173–188 (2014)

    Google Scholar 

  31. Cuomo, S.: Pappus of Alexandria and the mathematics of late antiquity. Cambridge University Press (2000)

    Google Scholar 

  32. dell’Isola, F.: The academic and scientific activity of a “Maestro” in applied mechanics: Laudatio of Professor Antonio Di Carlo, Università di Roma TRE (Italy). Mathematics and Mechanics of Solids 18(8), 787 (2013)

    Google Scholar 

  33. dell’Isola, F.: Big-(Wo)men, Tyrants, Chiefs, Dictators, Emperors and Presidents: Towards the Mathematical Understanding of Social Groups. Springer (2019)

    Google Scholar 

  34. dell’Isola, F., Andreaus, U., Placidi, L.: At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: an underestimated and still topical contribution of Gabrio Piola. Mathematics and Mechanics of Solids 20(8), 887–928 (2015)

    Google Scholar 

  35. dell’Isola, F., Bucci, S., Battista, A.: Against the fragmentation of knowledge: The power of multidisciplinary research for the design of metamaterials. In: Advanced Methods of Continuum Mechanics for Materials and Structures, pp. 523–545. Springer (2016)

    Google Scholar 

  36. dell’Isola, F., Corte, A.D., Giorgio, I.: Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives. Mathematics and Mechanics of Solids 22(4), 852–872 (2017)

    Google Scholar 

  37. dell’Isola, F., Della Corte, A., Greco, L., Luongo, A.: Plane bias extension test for a continuum with two inextensible families of fibers: a variational treatment with Lagrange multipliers and a perturbation solution. International Journal of Solids and Structures 81, 1–12 (2016)

    Google Scholar 

  38. dell’Isola, F., Gavrilyuk, S.: Variational models and methods in solid and fluid mechanics, vol. 535. Springer Science & Business Media (2012)

    Google Scholar 

  39. dell’Isola, F., Guarascio, M., Hutter, K.: A variational approach for the deformation of a saturated porous solid. A second-gradient theory extending Terzaghi’s effective stress principle. Archive of Applied Mechanics 70(5), 323–337 (2000)

    Google Scholar 

  40. dell’Isola, F., Madeo, A., Seppecher, P.: Boundary conditions at fluid-permeable interfaces in porous media: A variational approach. International Journal of Solids and Structures 46(17), 3150–3164 (2009)

    Google Scholar 

  41. dell’Isola, F., Madeo, A., Seppecher, P.: Cauchy tetrahedron argument applied to higher contact interactions. Archive for Rational Mechanics and Analysis 219(3), 1305–1341 (2016)

    Google Scholar 

  42. dell’Isola, F., Maier, G., Perego, U., et al.: The Complete Works of Gabrio Piola: Volume I (Advanced Structured Materials, vol. 38) (2014)

    Google Scholar 

  43. dell’Isola, F., Maier, G., Perego, U., et al.: The Complete Works of Gabrio Piola: Volume II. Cham, Switzerland: Springer (2019)

    Google Scholar 

  44. dell’Isola, F., Placidi, L.: Variational principles are a powerful tool also for formulating field theories. In: Variational models and methods in solid and fluid mechanics, pp. 1–15. Springer (2011)

    Google Scholar 

  45. dell’Isola, F., Seppecher, P.: Edge contact forces and quasi-balanced power. Meccanica 32(1), 33–52 (1997)

    Google Scholar 

  46. dell’Isola, F., Seppecher, P., Madeo, A.: How contact interactions may depend on the shape of Cauchy cuts in nth gradient continua: approach “à la D’Alembert”. Zeitschrift für angewandte Mathematik und Physik 63(6), 1119–1141 (2012)

    Google Scholar 

  47. dell’Isola, F., Steigmann, D.J.: Discrete and Continuum Models for Complex Metamaterials. Cambridge University Press (2020)

    Google Scholar 

  48. Deutschmann, B., Eugster, S.R., Ott, C.: Reduced models for the static simulation of an elastic continuum mechanism. IFAC-PapersOnLine 51(2), 403 – 408 (2018). 9th Vienna International Conference on Mathematical Modelling

    Google Scholar 

  49. Earman, J., Janssen, M., Norton, J.D.: The attraction of gravitation: new studies in the history of general relativity, vol. 5. Springer Science & Business Media (1993)

    Google Scholar 

  50. Eremeyev, V.A.: On non-holonomic boundary conditions within the nonlinear Cosserat continuum. In: New Achievements in Continuum Mechanics and Thermodynamics, pp. 93–104. Springer (2019)

    Google Scholar 

  51. Eremeyev,V.A., Lebedev, L.P., Altenbach, H.: Foundations of micropolar mechanics. Springer Science & Business Media (2012)

    Google Scholar 

  52. Eremeyev, V.A., Pietraszkiewicz,W.: Material symmetry group and constitutive equations of anisotropic Cosserat continuum. In: H. Altenbach, S. Forest, A. Krivtsov (eds.) Generalized continua as models for materials, Advanced Structures Materials, vol. 22. Springer (2012)

    Google Scholar 

  53. Eringen, A.C.: Nonlocal polar elastic continua. International Journal of Engineering Science 10(1), 1–16 (1972)

    Google Scholar 

  54. Eringen, A.C., Edelen, D.: On nonlocal elasticity. International Journal of Engineering Science 10(3), 233–248 (1972)

    Google Scholar 

  55. Eugster, S.R.: Geometric Continuum Mechanics and Induced Beam Theories, Lecture Notes in Applied and Computational Mechanics, vol. 75. Springer (2015)

    Google Scholar 

  56. Eugster, S.R.: Hellinger’s encyclopedia article on the fundamentals of the mechanics of continua. In: F. dell’Isola, S.R. Eugster, M. Spagnuolo, E. Barchiesi (eds.) Evaluation of Scientific Sources in Mechanics: Heiberg’s Prolegomena to the Works of Archimedes and Hellinger’s Encyclopedia Article. Springer (2021)

    Google Scholar 

  57. Eugster, S.R., dell’Isola, F.: Exegesis of the introduction and sect. I from “Fundamentals of the mechanics of continua” by E. Hellinger. Zeitschrift für angewandte Mathematik und Mechanik 97(4), 477–506 (2017)

    Google Scholar 

  58. Eugster, S.R., dell’Isola, F.: An ignored source in the foundations of continuum physics “Die Allgemeinen Ansätze der Mechanik der Kontinua” by E. Hellinger. Proceedings in Applied Mathematics and Mechanics 17(1), 413–414 (2017)

    Google Scholar 

  59. Eugster, S.R., dell’Isola, F.: Exegesis of sect. II and III.A from “Fundamentals of the mechanics of continua” by E. Hellinger. Zeitschrift für angewandte Mathematik und Mechanik 98(1), 31–68 (2018)

    Google Scholar 

  60. Eugster, S.R., dell’Isola, F.: Exegesis of sect. III.B from “Fundamentals of the mechanics of continua” by E. Hellinger. Zeitschrift für angewandte Mathematik und Mechanik 98(1), 69–105 (2018)

    Google Scholar 

  61. Eugster, S.R., dell’Isola, F., Steigmann, D.: Continuum theory for mechanical metamaterials with a cubic lattice substructure. Mathematics and Mechanics of Complex Systems 7(1),75–98 (2019)

    Google Scholar 

  62. Eugster, S.R., Deutschmann, B.: A nonlinear Timoshenko beam formulation for modeling a tendon-driven compliant neck mechanism. Proceedings in Applied Mathematics and Mechanics 18(1), e201800208:1–2 (2018)

    Google Scholar 

  63. Eugster, S.R., Glocker, Ch.: Constraints in structural and rigid body mechanics: a frictional contact problem. Annals of Solid and Structural Mechanics 5(1-2), 1–13 (2013)

    Google Scholar 

  64. Eugster, S.R., Glocker, Ch.: On the notion of stress in classical continuum mechanics. Mathematics and Mechanics of Complex Systems 5(3-4), 299–338 (2017)

    Google Scholar 

  65. Eugster, S.R., Harsch, J.: A variational formulation of classical nonlinear beam theories. In: B.E. Abali, I. Giorgio (eds.) Developments and Novel Approaches in Nonlinear Solid Body Mechanics, pp. 95–121. Springer International Publishing (2020)

    Google Scholar 

  66. Eugster, S.R., Hesch, C., Betsch, P., Glocker, Ch.: Director-based beam finite elements relying on the geometrically exact beam theory formulated in skew coordinates. International Journal for Numerical Methods in Engineering 97(2), 111–129 (2014)

    Google Scholar 

  67. Eugster, S.R., Steigmann, D.J.: Variational methods in the theory of beams and lattices. In: H. Altenbach, A. Öchsner (eds.) Encyclopedia of Continuum Mechanics, pp. 1–9. Springer (2018)

    Google Scholar 

  68. Feynman, R.P., Brown, L.M.: Feynman’s thesis: a new approach to quantum theory. World Scientific (2005)

    Google Scholar 

  69. Feynman, R.P., Hibbs, A.R., Styer, D.F.: Quantum mechanics and path integrals. Courier Corporation (2010)

    Google Scholar 

  70. Feynman, R.P., Leighton, B.R., Sands, M.: The Feynman Lectures on Physics, Volume I. Basic Books (2018)

    Google Scholar 

  71. Forest, S.: Mechanics of Cosserat media – an introduction. Ecole des Mines de Paris, Paris pp. 1–20 (2005)

    Google Scholar 

  72. George, D., Spingarn, C., Dissaux, C., Nierenberger, M., Rahman, R.A., Rémond, Y.: Examples of multiscale and multiphysics numerical modeling of biological tissues. Bio-Medical Materials and Engineering 28(s1), S15–S27 (2017)

    Google Scholar 

  73. Germain, P.: Functional concepts in continuum mechanics. Meccanica 33(5), 433–444 (1998)

    Google Scholar 

  74. Germain, P.: My discovery of mechanics. Continuum Thermomechanics, P. Germain’s Anniversary Volume pp. 1–24 (2000)

    Google Scholar 

  75. Germain, P.: The method of virtual power in the mechanics of continuous media, I: Secondgradient theory. Mathematics and Mechanics of Complex Systems 8(2), 153–190 (2020)

    Google Scholar 

  76. Germain, P., Nayroles, B.: Applications of Methods of Functional Analysis to Problems in Mechanics: Joint Symposium IUTAM/IMU Held in Marseille, Sept. 1–6, 1975, vol. 503. Springer (2006)

    Google Scholar 

  77. Gingerich, O.: Did Copernicus owe a debt to Aristarchus? Journal for the History of Astronomy 16(1), 37–42 (1985)

    Google Scholar 

  78. Giorgio, I., Andreaus, U., Dell’Isola, F., Lekszycki, T.: Viscous second gradient porous materials for bones reconstructed with bio-resorbable grafts. Extreme Mechanics Letters 13, 141–147 (2017)

    Google Scholar 

  79. Giorgio, I., Ciallella, A., Scerrato, D.:Astudy about the impact of the topological arrangement of fibers on fiber-reinforced composites: Some guidelines aiming at the development of new ultra-stiff and ultra-soft metamaterials. International Journal of Solids and Structures 203, 73–83 (2020)

    Google Scholar 

  80. Giorgio, I., Harrison, P., dell’Isola, F., Alsayednoor, J., Turco, E.: Wrinkling in engineering fabrics: a comparison between two different comprehensive modelling approaches. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474(2216), 20180063:1–20 (2018)

    Google Scholar 

  81. Giorgio, I., Scerrato, D.: Multi-scale concrete model with rate-dependent internal friction. European Journal of Environmental and Civil Engineering 21(7-8), 821–839 (2017)

    Google Scholar 

  82. Harsch, J., Capobianco, G., Eugster, S.R.: Finite element formulations for constrainted spatial nonlinear beam theories. Mathematics and Mechanics of Solids pp. 1–26 (2021)

    Google Scholar 

  83. Harsch, J., Eugster, S.R.: Finite element analysis of planar nonlinear classical beam theories. In: B.E. Abali, I. Giorgio (eds.) Developments and Novel Approaches in Nonlinear Solid Body Mechanics, pp. 123–157. Springer International Publishing (2020)

    Google Scholar 

  84. Hartle, J.B., Sharp, D.H.: Variational principle for the equilibrium of a relativistic, rotating star. The Astrophysical Journal 147, 317 (1967)

    Google Scholar 

  85. Heath, T.: Aristarchus of Samos, the Ancient Copernicus: A History of Greek Astronomy to Aristarchus, Together with Aristarchus’s Treatise on the Sizes and Distances of the Sun and Moon. Cambridge University Press (2013)

    Google Scholar 

  86. Hellinger, E.: Die allgemeinen Ansätze der Mechanik der Kontinua. In: Encyklopädie der mathematischen Wissenschaften, vol. 5. B.G. Teubner Verlag (1913)

    Google Scholar 

  87. Hesch, C., Schuß, S., Dittmann, M., Eugster, S.R., Favino, M., Krause, R.: Variational space–time elements for large-scale systems. Computer Methods in Applied Mechanics and Engineering 326, 541–572 (2017)

    Google Scholar 

  88. Huffman, C.: Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King. Cambridge University Press (2005)

    Google Scholar 

  89. Irby-Massie, G.L.,Keyser, P.T., Rihll, T.E.: Greek science of the Hellenistic era:Asourcebook. Aestimatio: Critical Reviews in the History of Science 1, 44–50 (2004)

    Google Scholar 

  90. Khakalo, S., Niiranen, J.: Anisotropic strain gradient thermoelasticity for cellular structures: Plate models, homogenization and isogeometric analysis. Journal of the Mechanics and Physics of Solids 134, 103728 (2020)

    Google Scholar 

  91. Kuhn, T.S.: The structure of scientific revolutions. University of Chicago press (2012)

    Google Scholar 

  92. de Lagrange, J.L.: Mécanique analytique, vol. 1. Mallet-Bachelier (1853)

    Google Scholar 

  93. Lagrange, J.L.: Analytical mechanics, vol. 191. Springer Science & Business Media (2013)

    Google Scholar 

  94. Landau, L.D., Lifshitz, E.M.: Quantum mechanics: non-relativistic theory, vol. 3. Elsevier (2013)

    Google Scholar 

  95. Lloyd, J., Mitchinson, J.: QI: The Book of General Ignorance-The Noticeably Stouter Edition. Faber & Faber (2010)

    Google Scholar 

  96. Lloyd, J., Mitchinson, J.: The Second Book of General Ignorance: Everything You Think You Know is (still) Wrong. Crown (2011)

    Google Scholar 

  97. Maugin, G., Trimarco, C.: Pseudomomentum and material forces in nonlinear elasticity: variational formulations and application to brittle fracture. Acta mechanica 94(1-2), 1–28 (1992)

    Google Scholar 

  98. Maugin, G.A.: A selection of scientific works and publications by Paul Germain. In: G.A. Maugin, R. Drouot, F. Sidoroff (eds.) Continuum Thermodynamics: The Art and Science of Modelling Material Behaviour, Solid Mechanics and Its Applications, vol. 76, pp. 25–27. Kluwer Academic Publishers (2000)

    Google Scholar 

  99. Maugin, G.A.: Generalized continuum mechanics: what do we mean by that? In: Mechanics of Generalized Continua, pp. 3–13. Springer (2010)

    Google Scholar 

  100. Maugin, G.A.: A historical perspective of generalized continuum mechanics. In: Mechanics of generalized continua, pp. 3–19. Springer (2011)

    Google Scholar 

  101. Maugin, G.A.: Continuum mechanics through the twentieth century. Springer (2013)

    Google Scholar 

  102. Maugin, G.A., Eringen, A.C.: Variational formulation of the relativistic theory of microelectromagnetism. Journal of Mathematical Physics 15(9), 1494–1499 (1974)

    Google Scholar 

  103. Meissner, H.: Ernst Hellinger. In: Topics in operator theory: Ernst D. Hellinger memorial volume, Operator Theory: Advances and Applications, vol. 48. Birkhäuser Verlag, Basel (1990)

    Google Scholar 

  104. Misra, A., Poorsolhjouy, P.: Granular micromechanics model for damage and plasticity of cementitious materials based upon thermomechanics. Mathematics and Mechanics of Solids 25(10), 1778–1803 (2020)

    Google Scholar 

  105. Müller, C.H., Timpe, A.: Die Grundgleichungen der mathematische Elastizitätstheorie. In: Mechanik, Enzyklopädie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, vol. IV/4, pp. 1–54. B.G. Teubner Verlag (1906)

    Google Scholar 

  106. Neugebauer, O.: The history of ancient astronomy problems and methods. Journal of Near Eastern Studies 4(1), 1–38 (1945)

    Google Scholar 

  107. Parks, M.L., Lehoucq, R.B., Plimpton, S.J., Silling, S.A.: Implementing peridynamics within a molecular dynamics code. Computer Physics Communications 179(11), 777–783 (2008)

    Google Scholar 

  108. Pietraszkiewicz, W., Eremeyev, V.: On vectorially parameterized natural strain measures of the non-linear Cosserat continuum. International Journal of Solids and Structures 46(11-12), 2477–2480 (2009)

    Google Scholar 

  109. Piola, G.: Intorno alle equazioni fondamentali del movimento dei corpi qualsivogliono, considerati secondo naturale loro formae costituzione (1845)

    Google Scholar 

  110. Piola, G.: Memoria intorno alle equazioni fondamentali del movimento di corpi qualsivogliono considerati secondo la naturale loro forma e costituzione. Modena, Tipi del RD Camera (1846)

    Google Scholar 

  111. Pipkin, A.C.: Equilibrium of Tchebychev nets. In: The Breadth and Depth of Continuum Mechanics, pp. 287–303. Springer (1986)

    Google Scholar 

  112. Placidi, L.: A variational approach for a nonlinear 1-dimensional second gradient continuum damage model. Continuum Mechanics and Thermodynamics 27(4-5), 623–638 (2015)

    Google Scholar 

  113. Placidi, L., Barchiesi, E.: Energy approach to brittle fracture in strain-gradient modelling. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474(2210), 20170878:1–19 (2018)

    Google Scholar 

  114. Placidi, L., Barchiesi, E., Misra, A.: A strain gradient variational approach to damage: a comparison with damage gradient models and numerical results. Mathematics and Mechanics of Complex Systems 6(2), 77–100 (2018)

    Google Scholar 

  115. Placidi, L., Barchiesi, E., Misra, A., Andreaus, U.: Variational methods in continuum damage and fracture mechanics. Encyclopedia of Continuum Mechanics. Springer (2018)

    Google Scholar 

  116. Placidi, L., Misra, A., Barchiesi, E.: Two-dimensional strain gradient damage modeling: a variational approach. Zeitschrift für angewandte Mathematik und Physik 69(3), 56 (2018)

    Google Scholar 

  117. Placidi, L., Misra, A., Barchiesi, E.: Simulation results for damage with evolving microstructure and growing strain gradient moduli. Continuum Mechanics and Thermodynamics 31(4), 1143–1163 (2019)

    Google Scholar 

  118. Poisson, M.: Mémoire sur l’équilibre et le mouvement des corps élastique. In: Mémoires de l’académie royale des sciences, pp. 357–570 (1829)

    Google Scholar 

  119. Polizzotto, C.: Nonlocal elasticity and related variational principles. International Journal of Solids and Structures 38(42-43), 7359–7380 (2001)

    Google Scholar 

  120. Rodriguez-Ramos, R., Pobedria, B., Padilla, P., Bravo-Castillero, J., Guinovart-Diaz, R., Maugin, G.: Variational principles for nonlinear piezoelectric materials. Archive of Applied Mechanics 74(3-4), 191–200 (2004)

    Google Scholar 

  121. Rosenbrock, H.: A variational principle for quantum mechanics. Physics letters A 110(7-8), 343–346 (1985)

    Google Scholar 

  122. Rowbotham, S.B., et al.: Zetetic astronomy: Earth not a globe. Ravenio Books (2015)

    Google Scholar 

  123. Sarton, G.: A history of science: Ancient science through the golden age of Greece. Oxford University Press London (1953)

    Google Scholar 

  124. Sarton, G.: Hellenistic science and culture in the last three centuries BC. Courier Corporation (1993)

    Google Scholar 

  125. Scholtz, F., Geyer, H., Hahne, F.: Quasi-Hermitian operators in quantum mechanics and the variational principle. Annals of Physics 213(1), 74–101 (1992)

    Google Scholar 

  126. Schulte, J., Dittmann, M., Eugster, S.R., Hesch, S., Reinicke, T., dell’Isola, F., Hesch, C.: Isogeometric analysis of fiber reinforced composites using Kirchhoff–Love shell elements. Computer Methods in Applied Mechanics and Engineering 362, 112845:1–34 (2020)

    Google Scholar 

  127. Segev, R.: Locality and continuity in constitutive theory. Archive for Rational Mechanics and Analysis 101(1), 29–39 (1988)

    Google Scholar 

  128. Silling, S.A.: Reformulation of elasticity theory for discontinuities and long-range forces. Journal of the Mechanics and Physics of Solids 48(1), 175–209 (2000)

    Google Scholar 

  129. Silling, S.A., Epton, M., Weckner, O., Xu, J., Askari, E.: Peridynamic states and constitutive modeling. Journal of Elasticity 88(2), 151–184 (2007)

    Google Scholar 

  130. Silling, S.A., Lehoucq, R.B.: Convergence of peridynamics to classical elasticity theory. Journal of Elasticity 93(1), 13 (2008)

    Google Scholar 

  131. Stahl, W.H.: Aristarchus of Samos. Dictionary of scientific biography 1, 246–250 (1970)

    Google Scholar 

  132. Taub, A.: Variational principles in general relativity. In: Relativistic Fluid Dynamics, pp. 205–300. Springer (2011)

    Google Scholar 

  133. Taub, A.H.: General relativistic variational principle for perfect fluids. Physical Review 94(6),1468 (1954)

    Google Scholar 

  134. Toupin, R.A.: Theories of elasticity with couple-stress. Archive for Rational Mechanics and Analysis 17(2), 85–112 (1964)

    Google Scholar 

  135. Truesdell, C., Toupin, R.: The classical field theories. In: S. Flügge (ed.) Principles of Classical Mechanics and Field Theory, Encyclopedia of Physics, vol. III/1. Springer (1960)

    Google Scholar 

  136. Turco, E., Barchiesi, E., Giorgio, I., dell’Isola, F.: A Lagrangian Hencky-type non-linear model suitable for metamaterials design of shearable and extensible slender deformable bodies alternative to Timoshenko theory. International Journal of Non-Linear Mechanics p. 103481 (2020)

    Google Scholar 

  137. Turco, E., dell’Isola, F., Cazzani, A., Rizzi,N.L.: Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models. Zeitschrift für angewandte Mathematik und Physik 67(4), 85 (2016)

    Google Scholar 

  138. Turco, E., Golaszewski, M., Cazzani, A., Rizzi, N.L.: Large deformations induced in planar pantographic sheets by loads applied on fibers: experimental validation of a discrete Lagrangian model. Mechanics Research Communications 76, 51–56 (2016)

    Google Scholar 

  139. Winter, T.N.: The mechanical problems in the corpus of Aristotle. Faculty Publications, Classics and Religious Studies Department (2007)

    Google Scholar 

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Spagnuolo, M., Ciallella, A., Scerrato, D. (2022). The Loss and Recovery of the Works by Piola and the Italian Tradition of Mechanics. In: dell'Isola, F., Eugster, S.R., Spagnuolo, M., Barchiesi, E. (eds) Evaluation of Scientific Sources in Mechanics. Advanced Structured Materials, vol 152. Springer, Cham. https://doi.org/10.1007/978-3-030-80550-0_4

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