LIST OF PAPERS IN SECOND GRADIENT MATERIALS
[15] F. dell’Isola and G. Rotoli, “Validity of Laplace formula and dependence of surface tension on curvature in second gradient fluids”, Mechanics Research Communications, vol. 22 (5), 1995, pp. 485-490.Download Pdf
[16] F. dell’Isola, H. Gouin, and P. Seppecher, “Radius and surface tension of microscopic bubbles by second gradient theory”, Comptes Rendus de l’Academie de Sciences - Serie IIb: Mecanique, Physique, Chimie, Astronomie, vol. 320 (6), 1995, pp. 211-216. Download Pdf
[17] F. dell’Isola and P. Seppecher, “The relationship between edge contact forces, double forces and interstitial working allowed by the principle of virtual power”, Comptes Rendus de l’Academie de Sciences – Serie IIb: Mecanique, Physique, Chimie, Astronomie, vol. 321, 1995, pp. 303-308 Download Pdf
[21] F. dell’Isola, H. Gouin, and G. Rotoli, “Nucleation of spherical shell-like interfaces by second gradient theory: Numerical simulations”, European Journal of Mechanics, B/Fluids, vol. 15 (4), 1996, pp. 545-568. Download Pdf
[31] F. dell’Isola and P. Seppecher, “Edge Contact Forces and Quasi-Balanced Power,” Meccanica, vol. 32 (1), 1997, pp. 33-52. Download Pdf
[50] F. dell’Isola, M. Guarascio, and K. Hutter, “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, vol. 70 (5), 2000, pp. 323-337. Download Pdf
[64] J. Alibert, P. Seppecher, and F. dell’Isola, “Truss modular beams with deformation energy depending on higher displacement gradients”, Mathematics and Mechanics of Solids, vol. 8 (1), 2003, pp. 51-73.Download Pdf
[66] F. dell’Isola, G. Sciarra, and R. Batra, “Static Deformations of a Linear Elastic Porous Body Filled with an Inviscid Fluid”, Journal of Elasticity, vol. 72 (1-2), 2003, p. 99–120. Download Pdf
[88] G. Sciarra, F. dell’Isola, and K. Hutter, “Dilatational and compacting behavior around a cylindrical cavern leached out in a solid-fluid elastic rock salt”, International Journal of Geomechanics, vol. 5 (3), 2005, pp. 233-243. Download Pdf
[91] F. dell’Isola, G. Sciarra and R. Batra, “A second gradient model for deformable porous matrices filled with an inviscid fluid”, Solid Mechanics and its Applications – IUTAM Symposium on Physicochemical and Electromechanical Interactions in Porous Media, Vol. 125, 2005, pp. 221-229 Download Pdf
[95] G. Sciarra, F. dell’Isola, and O. Coussy, “Second gradient poromechanics”, International Journal of Solids and Structures, vol. 44 (20), 2007, p. 6607–6629. Download Pdf
[99] G. Sciarra, F. dell’Isola, N. Ianiro, and A. Madeo, “A variational deduction of second gradient poroelasticity part I: General theory”, Journal of Mechanics of Materials and Structures, vol. 3 (3), 2008, pp. 507-526. Download Pdf
[100]* A. Madeo, F. dell’Isola, N. Ianiro, G. Sciarra, “A second gradient poroelastic model of consolidation”, SIMAI 2008, Rome 15-19 September 2008
[101] A. Madeo, F. dell’Isola, N. Ianiro, and G. Sciarra, “A variational deduction of second gradient poroelasticity II: An application to the consolidation problem”, Journal of Mechanics of Materials and Structures, vol. 3 (4), 2008, pp. 607-625. Download Pdf
[103] F. dell’Isola, G. Sciarra, and S. Vidoli, “Generalized Hooke’s law for isotropic second gradient materials”, Royal Society of London, vol. 465 (107), 2009, pp. 2177-2196. Download Pdf
[104] F. dell’Isola, A. Madeo, and P. Seppecher, “Boundary conditions at fluid-permeable interfaces in porous media: A variational approach”, International Journal of Solids and Structures, vol. 46 (17), 2009Download Pdf
[108] F. dell’Isola and P. Seppecher, “Commentary about the paper ‘Hypertractions and hyperstresses convey the same mechanical information Continuum Mec. Thermodyn. (2010) 22:163-176 ‘ by Prof. Podio Guidugli and Prof. Vianello and some related papers on higher gradient theories”, Continuum Mechanics and Thermodynamics, vol. 23 (5), 2011, pp. 473-478 Download Pdf
[110] P. Seppecher, J.-J. Alibert and F. dell’Isola “Linear elastic trusses leading to continua with exotic mechanical interactions”, Journal of Physics: Conference Series vol. 319 (1), 2011, 13 pages. Download Pdf
[114] F. dell’Isola, A. Madeo and L. Placidi “Linear plane wave propagation and normal transmission and reflection at discontinuity surfaces in second gradient 3D Continua”, ZAMM – Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, vol. 92 (1), 2012, pp. 52-71. Download Pdf
[118] A.Madeo, F. dell’Isola and F. Darve “A continuum model for deformable, second gradient porous media partially saturated with compressible fluids”, Journal of the Mechanics and Physics of Solids, vol. 61 (11), 2013, pp. 2196-2211 . Download Pdf
[119] M. Ferretti, A. Madeo, F. dell’Isola and P. Boisse “Modelling the onset of shear boundary layers in fibrous composite reinforcements by second gradient theory”, ZAMP – Zeitschrift für angewandte Mathematik und Physik, vol. 65 (3), 2014, pp. 587-612. Download Pdf
[122] F. dell’Isola, and D. Steigmann “A two-dimensional gradient-elasticity theory for woven fabrics”, Journal of Elasticity, vol. 118 (1), 2015, pp. 113-125 . Download Pdf
[123] A. Madeo, M. Ferretti, F. dell’Isola and P. Boisse “Thick fibrous composite reinforcements behave as special second-gradient materials: three-point bending of 3D interlocks”, Zeitschrift für angewandte Mathematik und Physik, vol. 66 (4), 2015, pp. 2041-2060. Download Pdf
[124] A. Carcaterra, F. dell’Isola, R. Esposito and M. Pulvirenti “Macroscopic description of microscopically strongly inhomogenous systems: A mathematical basis for the synthesis of higher gradients metamaterials”, Archive for Rational Mechanics and Analysis, vol. 218 (3), 2015, pp. 1239-1262. Download Pdf
[126] D.J. Steigmann and F. dell’Isola “Mechanical response of fabric sheets to three-dimensional bending, twisting, and stretching”, Acta Mechanica Sinica, vol. 31 (3), 2015, pp. 373-382. Download Pdf
[127] I. Giorgio, R. Grygoruk, F. dell’Isola and D.J. Steigmann “Pattern formation in the three-dimensional deformations of fibered sheets”, Mechanics Research Communications, vol. 69, 2015, pp. 164–171. Download Pdf
[131] Y. Rahali, I. Giorgio, J.F. Ganghoffer and F. dell’Isola “Homogenization à la Piola produces second gradient continuum models for linear pantographic lattices”, International Journal of Engineering Science, vol. 97, 2015, pp. 148-172. Download Pdf
[134] A. Della Corte, A. Battista and F. dell’Isola “Referential description of the evolution of a 2D swarm of robots interacting with the closer neighbors: Perspectives of continuum modeling via higher gradient continua”, International Journal of Non-Linear Mechanics, vol. 80, 2016, pp. 209–220. (Published online before print 24 August 2015. DOI: 10.1016/j.ijnonlinmec.2015.06.016). Download Pdf
[135] F. dell’Isola, M.V. d’Agostino, A. Madeo, P. Boisse and D. Steigmann “Minimization of shear energy in two dimensional continua with two orthogonal families of inextensible fibers: The case of standard bias extension test”, Journal of Elasticity vol. 122 (2), 2016, pp 131-155. (Published online before print 09 July 2015). Download Pdf
[136] F. dell’Isola, A. Della Corte, L. Greco and A. Luongo “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, vol. 81, 2016, pp. 1-12. Download Pdf
[138] F. dell’Isola, I. Giorgio, M. Pawlikowski and N. L. Rizzi “Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium”, Proceedings of the Royal Society of London A, vol. 472 (2185), 2016, 23 pages. Download Pdf
[142] F. dell’Isola, A. Della Corte, I. Giorgio and D. Scerrato “Pantographic 2D sheets: Discussion of some numerical investigations and potential applications”, International Journal of Non-Linear Mechanics, vol. 80, 2016, pp. 200-208. Download Pdf
[143] I. Giorgio, A. Della Corte, F. dell’Isola and D. J. Steigmann “Buckling modes in pantographic lattices”, Comptes Rendus – Mécanique, vol. 344 (7), 2016 pp. 487-501. (DOI:10.1016/j.crme.2016.02.009). Download Pdf
[144] M. Cuomo, F. dell’Isola and L. Greco “Simplified analysis of a generalized bias-test for fabrics with two families of inextensible fibres”, Zeitschrift für angewandte Mathematik und Physik, 2016, 39 pages. (DOI: 10.1007/s00033-016-0653-z). Download Pdf
[148] E. Turco, F. dell’Isola, A. Cazzani and N. L. Rizzi “Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models”, Zeitschrift für angewandte Mathematik und Physik, vol. 67 (4), August 2016 (First online: 25 June 2016), 28 pages. (DOI: 10.1007/s00033-016-0681-8). Download Pdf
[150] F. dell’Isola, M. Cuomo, L. Greco and A. Della Corte “Bias extension test for pantographic sheets: numerical simulations based on second gradient shear energies”, Journal of Engineering Mathematics, 2016, pp. 1-31 (DOI: 10.1007/s10665-016-9865-7). Download Pdf
[151] U. Andreaus, F. dell’Isola, I. Giorgio, L. Placidi, T. Lekszycki and N. L. Rizzi “Numerical simulations of classical problems in two-dimensional (non) linear second gradient elasticity”, International Journal of Engineering Science, vol. 108, 2016, pp. 34-50. Download Pdf
[154] M. Cuomo, F. dell’Isola, L. Greco and N. L. Rizzi “First versus second gradient energies for planar sheets with two families of inextensible fibres: Investigation on deformation boundary layers, discontinuities and geometrical instabilities”, Composites Part B Engineering, vol. 115, 2017, pp. 423-448. (DOI: 0.1016/j.compositesb.2016.08.043). Download Pdf
[157] I. Giorgio, U. Andreaus, F. dell’Isola and T. Lekszycki “Viscous second gradient porous materials for bones reconstructed with bio-resorbable grafts”, Extreme Mechanics Letters., vol. 13, 2017, pp. 141-147. (DOI: 10.1016/j.eml.2017.02.008). Download Pdf
[162] B. E. Abali, W. H. Müller and F. dell’Isola “Theory and computation of higher gradient elasticity theories based on action principles”, Archive of Applied Mechanics, vol. 87 (9), 2017, pp. 1495-1510. (FIRST ONLINE 05 June 2017). (DOI: 10.1007/s00419-017-1266-5). Download Pdf
[165] V. A. Eremeyev, F. dell’Isola, C. Boutin and D. Steigmann “Linear pantographic sheets: Existence and uniqueness of weak solutions”, Journal of Elasticity, First Online: 06 November 2017, pp. 1-22. (DOI 10.1007/s10659-017-9660-3). Download Pdf
[177] I. Giorgio, F. dell’Isola and D. J. Steigmann “Axisymmetric deformations of a 2nd grade elastic cylinder”, Mechanics Research Communications, Available online 8 September 2018. [DOI: https://doi.org/10.1016/j.mechrescom.2018.09.004]. Download Pdf
[181] E. Barchiesi, S. R. Eugster, L. Placidi and F. dell’Isola “Pantographic beam: a complete second gradient 1D-continuum in plane”, ZAMP – Zeitschrift für angewandte Mathematik und Physik, FIRST ONLINE 16 August 2019, 24 pages. [DOI: https://doi.org/10.1007/s00033-019-1181-4]. Download Pdf
[202] L. Placidi, F. dell’Isola and E. Barchiesi “Heuristic homogenization of Euler and pantographic beams”, Mechanics of Fibrous Materials and Applications – Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 596), 2020, pp.123-155. [FIRST ONLINE: 28 July 2019]Download Pdf
[214] V. A. Eremeyev and F. dell’Isola “Weak Solutions within the Gradient-Incomplete Strain-Gradient Elasticity”, Lobachevskii Journal of Mathematics, 2020, vol. 41 (10), pp. 191-197. [DOI: 10.1134/S1995080220100078]. Download Pdf
[215] V. A. Eremeyev, S. A. Lurie, Y. O. Solyaev and F. dell’Isola “On the well posedness of static boundary value problem within the linear dilatational strain gradient elasticity”, Zeitschrift für angewandte Mathematik und Physik ZAMP, 71:82, 2020, 16 pages. [DOI: https://doi.org/10.1007/s00033-020-01395-5]. Download Pdf
[223] I. Giorgio, V. Varano, F. dell’Isola, N.L. Rizzi “Two layers pantographs: a 2D continuum model accounting for the beams’ offset and relative rotations as averages in SO (3) Lie groups”, International Journal of Solids and Structures, 2021, vol. 216, pp. 43-58. Download Pdf
[224] C. Boutin, F. dell’Isola “Green’s functions and integral representation of generalized continua: the case of orthogonal pantographic lattices” Zeitschrift für angewandte Mathematik und Physik, 2021, vol. 72 (2), 26 pages. [DOI: https://doi.org/DOI: 10.1007/s00033-021-01480-3]. Download Pdf
[230] S.R. Eugster, F. Dell’Isola, R. Fedele, P. Seppecher “Piola transformations in second-gradient continua” Mechanics Research Communications, 2022, 103836. Download Pdf
[232] F. dell’Isola, S.R. Eugster, R. Fedele, P. Seppecher “Second-gradient continua: From Lagrangian to Eulerian and back” Mathematics and Mechanics of Solids, 2022, 10812865221078822. Download Pdf
[242] L. Placidi, E. Barchiesi, F. dell’Isola, V. Maksimov, A. Misra, N. Rezaei, A. Scrofani, D. Timofeev “On a hemi-variational formulation for a 2D elasto-plastic-damage strain gradient solid with granular microstructure” Mathematics in Engineering, 2023, vol. 5 (1), pp. 1-24. [DOI: 10.3934/mine.2023021]. Download Pdf
[257]* R. Fedele, F. dell’Isola, P. Seppecher and S. R. Eugster “Which kind of external loading second gradient materials can sustain?” International Conference of Numerical Analysis and Applied Mathematics ICNAAM 2021 AIP Conf. Proc. 2849, 2023, pp. 420003-1–420003-4. [DOI: https://doi.org/10.1063/5.0162225]. Download Pdf
[258] F. dell’Isola, V. A. Eremeyev, V. A. Korolenko and Y. O. Solyaev “Deformation of an elastic second gradient spherical body under equatorial line density of dead forces” European Journal of Mechanics – A/Solids Volume 103, January–February 2024, 105153 [Available online 5 October 2023]. Download Pdf