Abstract
The new possibilities arisen in the last years in material manufacturing (3D-printing, electrospinning, roll-to-roll processing, self-assembly, etc.) and the theoretical tools made available by generalized continuum mechanics are still far from achieving their full potential. The main thesis of the present paper is that it is necessary a multidisciplinary approach to address the emerging issues in metamaterials’ design. Therefore, an improvement in the degree and the depth of the cooperation between scientists from different areas is required. The advancements needed in mechanics and physics of solids and fluids, mathematical and numerical modeling and advanced technology in material construction can be obtained only as a consequence of a synergic effort.
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- 1.
An example is the recently established M&MoCS International Research Center, see http://memocs.univaq.it/?lang=en.
- 2.
Indeed the establishment of such networks can be traced back to Hellenistic Science (see Russo et al. 2013). In the Mouseion at Alexandria, experts from all disciplines (geometers, physicists, mechanicians, physicians, grammars) were all working together, attacking the same problem from all available point of view.
References
Altenbach, H., Eremeyev, V.A.: On the linear theory of micropolar plates. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 89(4), 242–256 (2009)
Altenbach, H., Eremeyev, V.A.: Vibration analysis of non-linear 6-parameter prestressed shells. Meccanica 49(8), 1751–1761 (2014)
Ancillao, A., Andreaus, U.: Finite element analysis of the stress state produced by an orthodontic skeletal anchorage system based on miniscrews. J. Cranio-Maxillary Dis. 2(1), 28 (2013)
Andreaus, U., Baragatti, P.: Fatigue crack growth, free vibrations, and breathing crack detection of aluminium alloy and steel beams. J. Strain Anal. Eng. Des. 44(7), 595–608 (2009)
Andreaus, U., Baragatti, P.: Cracked beam identification by numerically analysing the nonlinear behaviour of the harmonically forced response. J. Sound Vib. 330(4), 721–742 (2011)
Andreaus, U., dell’isola, F., Porfiri, M.: Piezoelectric passive distributed controllers for beam flexural vibrations. JVC/J. Vib. Control 10(5), 625–659 (2004). doi:10.1177/1077546304038224
Andreaus, U., Giorgio, I., Lekszycki, T.: A 2-D continuum model of a mixture of bone tissue and bio-resorbable material for simulating mass density redistribution under load slowly variable in time. Zeitschrift für Angewandte Mathematik und Mechanik 13, 7 (2013)
Andreaus, U., Giorgio, I., Madeo, A.: Modeling of the interaction between bone tissue and resorbable biomaterial as linear elastic materials with voids. Zeitschrift für angewandte Mathematik und Physik 66(1), 209–237 (2014)
Aristodemo, M., Turco, E.: Boundary element discretization of plane elasticity and plate bending problems. Int. J. Numer. Methods Eng. 37(6), 965–987 (1994)
Ashby, M.F.: Cellular Solids: Structure and Properties. Cambridge university press, Cambridge (1997)
Ashby, M.: Designing architectured materials. Scr. Mater. 68(1), 4–7 (2013)
Assidi, M., Dos Reis, F., Ganghoffer, J.F.: Equivalent mechanical properties of biological membranes from lattice homogenization. J. Mech. Behav. Biomed. Mater. 4(8), 1833–1845 (2011)
Auffray, N., dell’Isola, F., Eremeyev, V.A., Madeo, A., Rosi, G.: Analytical continuum mechanics à la Hamilton-Piola least action principle for second gradient continua and capillary fluids. Math. Mech. Solids 20(4), 375–417 (2015)
Bilotta, A., Turco, E.: Numerical sensitivity analysis of corrosion detection. Math. Mech. Solids (2014). doi:10.1177/1081286514560093
Bouaziz, O., Brechet, Y., Embury, J.D.: Heterogeneous and architectured materials: a possible strategy for design of structural materials. Adv. Eng. Mater. 10(1–2), 24–36 (2008)
Bréchet, Y.: Euromat 99, Microstructures, Mechanical Properties and Processes: Computer Simulation and Modelling. John Wiley & Sons, New York (2000)
Brechet, Y., Embury, J.D.: Architectured materials: expanding materials space. Scr. Mater. 68(1), 1–3 (2013)
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, pp. 1–24 (2015)
Cazzani, A., Malagù, M., Turco, E.: Isogeometric analysis: a powerful numerical tool for the elastic analysis of historical masonry arches. Continuum Mechanics and Thermodynamics, pp. 1–18 (2014a)
Cazzani, A., Malagù, M., Turco, E.: Isogeometric analysis of plane-curved beams. Math. Mech. Solids (2014b). doi:10.1177/1081286514531265
Cazzani, A., Malagù, M., Turco, E., Stochino, F.: Constitutive models for strongly curved beams in the frame of isogeometric analysis. Math. Mech. Solids (2015). doi:10.1177/1081286515577043
Cuomo, M., Contrafatto, L., Greco, L.: A variational model based on isogeometric interpolation for the analysis of cracked bodies. Int. J. Eng. Sci. 80, 173–188 (2014)
D’Agostino, M.V., Giorgio, I., Greco, L., Madeo, A., Boisse, P.: Continuum and discrete models for structures including (quasi-) inextensible elasticae with a view to the design and modeling of composite reinforcements. Int. J. Solids Struct. 59, 1–17 (2015)
Del Vescovo, D., Giorgio, I.: Dynamic problems for metamaterials: review of existing models and ideas for further research. Int. J. Eng. Sci. 80, 153–172 (2014)
Della Corte, A., Battista, A., Dell’Isola, F.: Referential description of the evolution of a 2D swarm of robots interacting with the closer neighbors: perspectives of continuum modeling via higher gradient continua. Int. J. Non-Linear Mech. (2015). doi:10.1016/j.ijnonlinmec.2015.06.016
dell’Isola, F., Placidi, L.: Variational principles are a powerful tool also for formulating field theories. Variational Models and Methods in Solid and Fluid Mechanics. Springer Science & Business Media, New York (2012)
dell’Isola, F., Steigmann, D.: A two-dimensional gradient-elasticity theory for woven fabrics. J. Elast. 118(1), 113–125 (2015)
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. Math. Mech. Solids 20(8), 887–928 (2015a)
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. Int. J. Solids Struct. 81, 1–12 (2015b)
dell’Isola, F., Giorgio, I., Andreaus, U.: Elastic pantographic 2D lattices: a numerical analysis on static response and wave propagation. Proc. Est. Acad. Sci. 64, 219–225 (2015c)
dell’Isola, F., Lekszycki, T., Pawlikowski, M., Grygoruk, R., Greco, L.: Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence. Zeitschrift für angewandte Mathematik und Physik 66(6), 3473–3498 (2015d)
dell’Isola, F., Seppecher, P., Della Corte, A.: The postulations á la D’Alembert and á la Cauchy for higher gradient continuum theories are equivalent: a review of existing results. Proc. R. Soc. A, R. Soc. 471, 20150415 (2015e)
dell’Isola, F., Steigmann, D., Della Corte, A.: Synthesis of fibrous complex structures: designing microstructure to deliver targeted macroscale response. Appl. Mech. Rev. 67(6), 060804 (2015f)
dell’Isola, F., Della Corte, A., Giorgio, I.: Higher-gradient continua: the legacy of piola, mindlin, sedov and toupin and some future research perspectives. Math. Mech. Solids 1081 (2016a). doi:10.1177/1081286515616034
dell’Isola, F., Giorgio, I., Pawlikowski, M., Rizzi, N.L.: Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium. Proc. R. Soc. A, R. Soc. 472, 20150790 (2016b)
Di Egidio, A., Luongo, A., Paolone, A.: Linear and non-linear interactions between static and dynamic bifurcations of damped planar beams. Int. J. Non-Linear Mech. 42(1), 88–98 (2007)
Dos Reis, F., Ganghoffer, J.F.: Discrete homogenization of architectured materials: implementation of the method in a simulation tool for the systematic prediction of their effective elastic properties. Technische Mechanik 30, 85–109 (2010)
Dos Reis, F., Ganghoffer, J.F.: Equivalent mechanical properties of auxetic lattices from discrete homogenization. Comput. Mater. Sci. 51(1), 314–321 (2012)
Dunlop, J.W.C., Fratzl, P.: Multilevel architectures in natural materials. Scr. Mater. 68(1), 8–12 (2013)
Ebinger, T., Steeb, H., Diebels, S.: Modeling macroscopic extended continua with the aid of numerical homogenization schemes. Comput. mater. sci. 32(3), 337–347 (2005)
Enakoutsa, K., Del Vescovo, D., Scerrato, D.: Combined polarization field gradient and strain field gradient effects in elastic flexoelectric materials. Math. Mech. Solids (2015). doi:10.1177/1081286515616048
Eringen, A.C.: Mechanics of Micromorphic Continua. Springer, Berlin (1968)
Federico, S., Grillo, A.: Elasticity and permeability of porous fibre-reinforced materials under large deformations. Mech. Mater. 44, 58–71 (2012)
Feyel, F.: A multilevel finite element method (fe 2) to describe the response of highly non-linear structures using generalized continua. Comput. Methods Appl. Mech. Eng. 192(28), 3233–3244 (2003)
Fleck, N.A., Deshpande, V.S., Ashby, M.F.: Micro-architectured materials: past, present and future. Proc. R. Soc. Lond. A: Math., Phys. Eng. Sci., R. Soc. 466, 2495–2516 (2010)
Gabriele, S., Rizzi, N., Varano, V.: On the imperfection sensitivity of thin-walled frames. Civil-Comp Proceedings 99 (2012)
Germain, P.: The method of virtual power in continuum mechanics. part 2: microstructure. SIAM J. Appl. Math. 25(3), 556–575 (1973)
Giorgio, I., Scerrato, D.: Multi-scale concrete model with rate-dependent internal friction. Eur. J. Environ. Civil Eng. 1–19 (2016). doi:10.1080/19648189.2016.1144539
Giorgio, I., Culla, A., Del Vescovo, D.: Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network. Arch. Appl. Mech. 79(9), 859–879 (2009)
Giorgio, I., Andreaus, U., Lekszycki, T., Della Corte, A.: The influence of different geometries of matrix/scaffold on the remodeling process of a bone and bioresorbable material mixture with voids. Math. Mech. Solids (2015). doi:10.1177/1081286515616052
Giorgio, I., Andreaus, U., Madeo, A.: The influence of different loads on the remodeling process of a bone and bioresorbable material mixture with voids. Contin. Mech. Thermodyn. 28(1–2), 21–40 (2016)
Goda, I., Assidi, M., Belouettar, S., Ganghoffer, J.F.: A micropolar anisotropic constitutive model of cancellous bone from discrete homogenization. J. mech. behav. biomed. mater. 16, 87–108 (2012)
Greco, L., Cuomo, M.: B-spline interpolation of Kirchhoff-Love space rods. Comput. Methods Appl. Mech. Eng. 256, 251–269 (2013)
Greco, L., Cuomo, M.: An implicit G1 multi patch B-spline interpolation for Kirchhoff-Love space rod. Comput. Methods Appl. Mech. Eng. 269, 173–197 (2014)
Greco, L., Cuomo, M.: An isogeometric implicit G1 mixed finite element for Kirchhoff space rods. Comput. Methods Appl. Mech. Eng. 298, 325–349 (2016)
Green, A.E., Naghdi, P.M.: A unified procedure for construction of theories of deformable media. ii. generalized continua. Proc. R. Soc. Lond. A: Math., Phys. Eng. Sci., R. Soc. 448, 357–377 (1995)
Javili, A., dell’Isola F, Steinmann P.: Geometrically nonlinear higher-gradient elasticity with energetic boundaries. J. Mech. Phys. Solids 61(12), 2381–2401 (2013)
Lekszycki, T., Dell’Isola F.: A mixture model with evolving mass densities for describing synthesis and resorption phenomena in bones reconstructed with bio-resorbable materials. Zeitschrift für Angewandte Mathematik und Mechanik 92(6), 426–444 (2012)
Luongo, A.: A unified perturbation approach to static/dynamic coupled instabilities of nonlinear structures. Thin-Walled Struct. 48(10), 744–751 (2010)
Luongo, A.: On the use of the multiple scale method in solving “difficult” bifurcation problems. Math. Mech. Solids (2015). doi:10.1177/1081286515616053
Luongo, A., Piccardo, G.: Linear instability mechanisms for coupled translational galloping. J. Sound Vib. 288(4), 1027–1047 (2005)
Masiani, R., Rizzi, N., Trovalusci, P.: Masonry as structured continuum. Meccanica 30(6), 673–683 (1995)
Misra, A., Roberts, L.A., Levorson, S.M.: Reliability analysis of drilled shaft behavior using finite difference method and Monte Carlo simulation. Geotech. Geol. Eng. 25(1), 65–77 (2007)
Neff, P., Forest, S.: A geometrically exact micromorphic model for elastic metallic foams accounting for affine microstructure. modelling, existence of minimizers, identification of moduli and computational results. J. Elast. 87(2–3), 239–276 (2007)
Pagnini, L.C.: Reliability analysis of wind-excited structures. J. Wind Eng. Ind. Aerodyn. 98(1), 1–9 (2010)
Papka, S.D., Kyriakides, S.: Experiments and full-scale numerical simulations of in-plane crushing of a honeycomb. Acta mater. 46(8), 2765–2776 (1998)
Piccardo, G., Tubino, F., Luongo, A.: A shear–shear torsional beam model for nonlinear aeroelastic analysis of tower buildings. Zeitschrift für angewandte Mathematik und Physik, pp 1–19 (2014)
Piccardo, G., Pagnini, L.C., Tubino, F.: Some research perspectives in galloping phenomena: critical conditions and post-critical behavior. Contin. Mech. Thermodyn. 27(1–2), 261–285 (2015)
Pietraszkiewicz, W., Eremeyev, V.A.: On natural strain measures of the non-linear micropolar continuum. Int. J. Solids Struct. 46(3), 774–787 (2009a)
Pietraszkiewicz, W., Eremeyev, V.A.: On vectorially parameterized natural strain measures of the non-linear Cosserat continuum. Int. J. Solids Struct. 46(11), 2477–2480 (2009b)
Placidi, L.: A variational approach for a nonlinear one-dimensional damage-elasto-plastic second-gradient continuum model. Contin. Mech. Thermodyn. (2014). doi:10.1007/s00161-014-0405-2
Placidi, L.: A variational approach for a nonlinear 1-dimensional second gradient continuum damage model. Contin. Mech. Thermodyn. 27(4), 623–638 (2015)
Placidi, L., Hutter, K.: An anisotropic flow law for incompressible polycrystalline materials. Zeitschrift für angewandte Mathematik und Physik ZAMP 57(1), 160–181 (2005)
Placidi, L., Hutter, K.: Thermodynamics of polycrystalline materials treated by the theory of mixtures with continuous diversity. Contin. Mech. Thermodyn. 17(6), 409–451 (2006)
Placidi, L., Andreaus, U., Della Corte, A., Lekszycki, T.: Gedanken experiments for the determination of two-dimensional linear second gradient elasticity coefficients. Zeitschrift für angewandte Mathematik und Physik 66(6), 3699–3725 (2015a)
Placidi, L., Giorgio, I., Della Corte, A., Scerrato, D.: Euromech 563 cisterna di latina 17–21 march 2014 generalized continua and their applications to the design of composites and metamaterials: a review of presentations and discussions. Math. Mech. Solids (2015b). doi:10.1177/1081286515576948
Rahali, Y., Giorgio, I., Ganghoffer, J.F., dell’Isola F, : Homogenization à la Piola produces second gradient continuum models for linear pantographic lattices. Int. J. Eng. Sci. 97, 148–172 (2015)
Rinaldi, A., Placidi, L.: A microscale second gradient approximation of the damage parameter of quasi-brittle heterogeneous lattices. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 94(10), 862–877 (2014)
Rizzi, N.L., Varano, V., Gabriele, S.: Initial postbuckling behavior of thin-walled frames under mode interaction. Thin-Walled Struct. 68, 124–134 (2013). doi:10.1016/j.tws.2013.03.004
Russo, L., et al.: The Forgotten Revolution: How Science was Born in 300 BC and Why it had to be Reborn. Springer Science & Business Media, Berlin (2013)
Scerrato, D., Giorgio, I., Madeo, A., Limam, A., Darve, F.: A simple non-linear model for internal friction in modified concrete. Int. J. Eng. Sci. 80, 136–152 (2014)
Scerrato, D., Giorgio, I., Della Corte, A., Madeo, A., Limam, A.: A micro-structural model for dissipation phenomena in the concrete. Int. J. Numer. Anal. Methods Geomech. 39(18), 2037–2052 (2015)
Steigmann, D.J., Dell’Isola, F.: Mechanical response of fabric sheets to three-dimensional bending, twisting, and stretching. Acta Mech. Sinica 31(3), 373–382 (2015)
Thiagarajan, G., Misra, A.: Fracture simulation for anisotropic materials using a virtual internal bond model. Int. J. Solids Struct. 41(11), 2919–2938 (2004)
Tomic, A., Grillo, A., Federico, S.: Poroelastic materials reinforced by statistically oriented fibres—numerical implementation and application to articular cartilage. IMA J. Appl. Math. 79, 1027–1059 (2014)
Trinh, D.K., Janicke, R., Auffray, N., Diebels, S., Forest, S.: Evaluation of generalized continuum substitution models for heterogeneous materials. Int. J. Multiscale Comput. Eng. 10(6), (2012)
Turco, E.: An effective algorithm for reconstructing boundary conditions in elastic solids. Comput. Methods Appl. Mech. Eng. 190(29), 3819–3829 (2001)
Verhoosel, C.V., Scott, M.A., Borden, M.J., Hughes, T.J., de Borst, R.: Discretization of higher-order gradient damage models using isogeometric finite elements. Technical report DTIC Document (2011)
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dell’Isola, F., Bucci, S., Battista, A. (2016). Against the Fragmentation of Knowledge: The Power of Multidisciplinary Research for the Design of Metamaterials. In: Naumenko, K., Aßmus, M. (eds) Advanced Methods of Continuum Mechanics for Materials and Structures. Advanced Structured Materials, vol 60. Springer, Singapore. https://doi.org/10.1007/978-981-10-0959-4_28
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