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A Plausible Description of Continuum Material Behavior Derived by Swarm Robot Flocking Rules

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Dynamics, Strength of Materials and Durability in Multiscale Mechanics

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 137))

Abstract

In this chapter, we are considering a material continuum, discretized as two-dimensional lattice of particles, undergone a prefixed strain of some its parts, and we calculate its time evolution without using Newton’s laws but using position-based dynamics rules. This means that the new position of a particle is determined by the spatial position of its neighbors without defining forces. The aim of the model is to reproduce the behavior of deformable bodies with standard or generalized (Cauchy or second gradient) deformation energy density. The tool that we have realized gives a plausible simulation of continuum deformation also in fracture case. It can be useful to describe final and sometime intermediate configuration of a continuum material under assigned strain of some of its points; the advantages are in saving computational time, with respect to solving classical differential equation. It is very flexible to be adapted for complex geometry samples. The numerical results suggest that the system can effectively reproduce the behavior of first and second gradient continua. We checked coherence with the principle of Saint Venant, and it is able to manage complex effects like lateral contraction, anisotropy or elastoplasticity. Its origin lies in our experience in evolution and control of robotic swarm; for a swarm robotics, just as for an animal swarm in Nature, one of the aims is to reach and maintain a desired geometric configuration. One of the possibilities to achieve this result is to see what its neighbors are doing. This approach generates a rules system governing the movement of the single robot just by reference to neighbor’s motion that we have used to describe the continuum deformation. Many aspects have to be still investigated, like the relationships describing the interaction rules between particles and constitutive equations and some results, like beam under shear stress, do not sound very good.

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References

  • Abali, B. E., Müller, W. H., & Dell’Isola, F. (2017). Theory and computation of higher gradient elasticity theories based on action principles. Arch. Appl. Mech. 87(9), 1495–1510.

    Google Scholar 

  • Alibert, J.-J., & Della Corte, A. (2015). Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof. Z. Für Angew. Math. Phys., 66(5), 2855–2870.

    Google Scholar 

  • Alibert, J.-J., Della Corte, A., Giorgio, I., & Battista, A. (2017). Extensional Elastica in large deformation as $$\Gamma $$-limit of a discrete 1D mechanical system. Z. Für Angew. Math. Phys., 68(2), 42.

    Google Scholar 

  • Alibert, J.-J., Seppecher, P., & Dell’isola, F. (2003). Truss modular beams with deformation energy depending on higher displacement gradients. Math. Mech. Solids, 8(1), 51–73.

    Google Scholar 

  • Altenbach, J., Altenbach, H., & Eremeyev, V. A. (2010). On generalized Cosserat-type theories of plates and shells: a short review and bibliography. Arch. Appl. Mech., 80(1), 73–92.

    Google Scholar 

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

    Google Scholar 

  • Altenbach, H., & Eremeyev, V. A. (2009). On the linear theory of micropolar plates. ZAMM‐Journal Appl. Math. Mech. Für Angew. Math. Mech., 89(4), 242–256.

    Google Scholar 

  • Altenbach, H., & Eremeyev, V. A. (2013). Generalized Continua From the Theory to Engineering Applications, CISM Courses and Lectures (Vol. 541). Udine: Springer.

    Google Scholar 

  • Altenbach, H., Eremeyev, V. A., Lebedev, L. P., & Rendón, L. A. (2010). Acceleration waves and ellipticity in thermoelastic micropolar media. Arch. Appl. Mech., 80(3), 217–227.

    Google Scholar 

  • Andreaus, U., Colloca, M., & Iacoviello, D. (2012). An optimal control procedure for bone adaptation under mechanical stimulus. Control Eng. Pract., 20(6), 575–583.

    Google Scholar 

  • Andreaus, U., Colloca, M., & Toscano, A. (2008). Mechanical behaviour of physiological and prosthesized human femurs during stair climbing: A comparative analysis via 3D numerical simulation. Minerva Ortop. E Traumatol., 59(4), 213–220.

    Google Scholar 

  • Andreaus, U., Giorgio, I., & Lekszycki, T. (2013). 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 [Online]. Available at: http://www.scopus.com/inward/record.url?eid=2-s2.0-84882523299&partnerID=40&md5=e34b49c6b02b11f8e584e3cb57b5db43.

  • Andreaus, U., Giorgio, I., & Madeo, A. (2015). Modeling of the interaction between bone tissue and resorbable biomaterial as linear elastic materials with voids. Z. Für Angew. Math. Phys., 66(1), 209–237.

    Google Scholar 

  • Andreaus, U., & Placidi, L. (2013). At the origins and in the vanguard of peri-dynamics, non-local and higher gradient continuum mechanics. An underestimated and still topical contribution of Gabrio Piola. ArXiv Prepr. ArXiv13105599 [Online]. Available at: http://arxiv.org/abs/1310.5599. Consultato: 17-gen-2014.

  • Andreaus, U., Spagnuolo, M., Lekszycki, T., & Eugster, S. R. (2018). A Ritz approach for the static analysis of planar pantographic structures modeled with nonlinear Euler–Bernoulli beams. Contin. Mech. Thermodyn., 30(5), 1103–1123.

    Google Scholar 

  • Auffray, N., dell’Isola, F., Eremeyev, V. A., Madeo, A., & Rosi, G. (2015). Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids. Math. Mech. Solids, 20(4), 375–417.

    Google Scholar 

  • Barchiesi, E., Spagnuolo, M., & Placidi, L. (2018). Mechanical metamaterials: A state of the art. Math. Mech. Solids, 24(1), 212–234.

    Google Scholar 

  • Battista, A., Rosa, L., dell’Erba, R., & Greco, L. (2016). Numerical investigation of a particle system compared with first and second gradient continua: Deformation and fracture phenomena. Math. Mech. Solids, p. 1081286516657889.

    Google Scholar 

  • Bender, J., Koschier, D., Charrier, P., & Weber, D. (2014). Position-based simulation of continuous materials. Comput. Graph, 44, 1–10.

    Google Scholar 

  • Bender, J., Müller, M., & Macklin, M. (2015). Position-based simulation methods in computer graphics. In Eurographics (Tutorials) [Online]. Available at: https://www.researchgate.net/profile/Jan_Bender/publication/274940214_Position-Based_Simulation_Methods_in_Computer_Graphics/links/552cc4a40cf29b22c9c466df/Position-Based-Simulation-Methods-in-Computer-Graphics.pdf. Consultato: 06-set-2017.

  • Berezovski, A., Giorgio, I., & Corte, A. D. (2016). Interfaces in micromorphic materials: Wave transmission and reflection with numerical simulations. Math. Mech. Solids, 21(1), 37–51.

    Google Scholar 

  • Bilotta, A., & Turco, E. (2009). A numerical study on the solution of the Cauchy problem in elasticity. Int. J. Solids Struct., 46(25–26), 4451–4477.

    Google Scholar 

  • Boutin, C., Giorgio, I., & Placidi, L. (2017). Linear pantographic sheets: Asymptotic micro-macro models identification. Math. Mech. Complex Syst., 5(2), 127–162.

    Google Scholar 

  • Bückmann, T., et al. (2012). Tailored 3D mechanical metamaterials made by dip‐in direct‐laser‐writing optical lithography. Adv. Mater., 24(20), 2710–2714.

    Google Scholar 

  • Carcaterra, A., Dell’Isola, F., Esposito, R., & Pulvirenti, M. (2015). Macroscopic description of microscopically strongly inhomogenous systems: A mathematical basis for the synthesis of higher gradients metamaterials. Arch. Ration. Mech. Anal., 218(3), 1239–1262.

    Google Scholar 

  • Cazzani, A., Stochino, F., & Turco, E. (2016). An analytical assessment of finite element and isogeometric analyses of the whole spectrum of Timoshenko beams. ZAMM‐Journal Appl. Math. Mech. Für Angew. Math. Mech., 96(10), 1220–1244.

    Google Scholar 

  • Cecchi, A., & Rizzi, N. L. (2001). Heterogeneous elastic solids: A mixed homogenization-rigidification technique. Int. J. Solids Struct., 38(1), 29–36.

    Google Scholar 

  • Chang, C. S., & Misra, A. (1990). Application of uniform strain theory to heterogeneous granular solids. J. Eng. Mech., 116(10), 2310–2328.

    Google Scholar 

  • Contrafatto, L., Cuomo, M., & Fazio, F. (2012). An enriched finite element for crack opening and rebar slip in reinforced concrete members. Int. J. Fract., 178(1–2), 33–50.

    Google Scholar 

  • Cuomo, M., Dell’Isola, F., Greco, L., & Rizzi, N. L. (2017). First versus second gradient energies for planar sheets with two families of inextensible fibres: investigation on deformation boundary layers, discontinuities and geometrical instabilities. Compos. Part B Eng., 115, 423–448.

    Google Scholar 

  • Cuomo, M., & Greco, L. (2012). Isogeometric Analysis of Space Rods: Considerations on Stress Locking (pp. 5094–5112) [Online]. Available at: http://www.scopus.com/inward/record.url?eid=2-s2.0-84871627441&partnerID=40&md5=48d09dd7e5493bafe0ef2bb10904d094.

  • d’Agostino, M. V., Giorgio, I., Greco, L., Madeo, A., & Boisse, P. (2015). 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.

    Google Scholar 

  • De Angelo, M., et al. (2019). The macroscopic behavior of pantographic sheets depends mainly on their microstructure: Experimental evidence and qualitative analysis of damage in metallic specimens. Contin. Mech. Thermodyn., 1–23.

    Google Scholar 

  • Del Vescovo, D., & Giorgio, I. (2014). Dynamic problems for metamaterials: review of existing models and ideas for further research. Int. J. Eng. Sci., 80, 153–172.

    Google Scholar 

  • dell’Erba, R. (2015). Determination of spatial configuration of an underwater swarm with minimum data. Int. J. Adv. Robot. Syst., 12(7), 97.

    Google Scholar 

  • dell’Erba, R. (2018a). Swarm robotics and complex behaviour of continuum material. Contin. Mech. Thermodyn., Mag. 2018 (Online). Available at: https://doi.org/10.1007/s00161-018-0675-1.

  • dell’Erba, R. (2018b). Position-based dynamic of a particle system: a configurable algorithm to describe complex behaviour of continuum material starting from swarm robotics. Contin. Mech. Thermodyn., 1–22.

    Google Scholar 

  • dell’Erba, R. (2018c). Position-based dynamic of a particle system: A configurable algorithm to describe complex behaviour of continuum material starting from swarm robotics., Contin. Mech. Thermodyn., 30(5), 1069–1090.

    Google Scholar 

  • Dell’Erba, R., & Moriconi, C. Bio-inspired Robotics — it. [Online]. Available at: http://www.enea.it/it/produzione-scientifica/edizioni-enea/2014/bio-inspirede-robotics-proceedings. Consultato: 15-dic-2014.

  • Dell’Isola, F., et al. (2019). Pantographic metamaterials: An example of mathematically driven design and of its technological challenges. Contin. Mech. Thermodyn., 31(4), 851–884.

    Google Scholar 

  • dell’Isola, F., Auffray, N., Eremeyev, V. A., Madeo, A., Placidi, L., & Rosi, G. (2014). Least action principle for second gradient continua and capillary fluids: A Lagrangian approach following Piola’s point of view. In The Complete Works of Gabrio Piola: Volume I (pp. 606–694). Heidelberg: Springer.

    Google Scholar 

  • Dell’Isola, F., Bucci, S., & Battista, A. (2016). 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). Heidelberg: Springer.

    Google Scholar 

  • Dell’Isola, F., d’Agostino, M. V., Madeo, A., Boisse, P., & Steigmann, D. (2016). Minimization of shear energy in two dimensional continua with two orthogonal families of inextensible fibers: The case of standard bias extension test. J. Elast., 122(2), 131–155.

    Google Scholar 

  • Dell’Isola, F., Della Corte, A., Greco, L., & Luongo, A. (2016). 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.

    Google Scholar 

  • Dell’Isola, F., & Gavrilyuk, S. (2012). Variational Models and Methods in Solid and Fluid Mechanics (Vol. 535). Springer Science & Business Media.

    Google Scholar 

  • dell’Isola, F., Giorgio, I., & Andreaus, U. (2015). Elastic pantographic 2D lattices: A numerical analysis on the static response and wave propagation. In Proc. Est. Acad. Sci. (Vol. 64, N. 3, p. 219).

    Google Scholar 

  • Dell’Isola, F., Giorgio, I., Pawlikowski, M., & Rizzi, N. L. (2016). Large deformations of planar extensible beams and pantographic lattices: Heuristic homogenization, experimental and numerical examples of equilibrium. In Proc. R. Soc. Math. Phys. Eng. Sci. (Vol. 472, No 2185, p. 20150790).

    Google Scholar 

  • Dell’Isola, F., Madeo, A., & Placidi, L. (2011). Linear plane wave propagation and normal transmission and reflection at discontinuity surfaces in second gradient 3D continua. ZAMM Z. Angew. Math. Mech., 92(1), 52–71.

    Google Scholar 

  • Dell’Isola, F., Madeo, A., & Seppecher, P. (2016). Cauchy tetrahedron argument applied to higher contact interactions. Arch. Ration. Mech. Anal., 219(3), 1305–1341.

    Google Scholar 

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

    Google Scholar 

  • Dell’Isola, F., Sciarra, G., & Vidoli, S. (2009). Generalized hooke’s law for isotropic second gradient materials. Proc. R. Soc. Math. Phys. Eng. Sci., 465(2107), 2177–2196.

    Google Scholar 

  • Dell’Isola, F., & Seppecher, P. (1995). The Relationship Between Edge Contact Forces, Double Forces and Interstitial Working Allowed by the Principle of Virtual Power.

    Google Scholar 

  • Dell’isola, F., & Seppecher, P. (1997). Edge contact forces and quasi-balanced power. Meccanica, 32(1), 33–52.

    Google Scholar 

  • Dell’Isola, F., Seppecher, P., & Corte, A. D. (2015). The postulations á la D’Alembert and á la Cauchy for higher gradient continuum theories are equivalent: A review of existing results. In Proc. R. Soc. Math. Phys. Eng. Sci., 471(2183), 20150415.

    Google Scholar 

  • dell’Isola, F., Seppecher, P., & Madeo, A. (2012). How contact interactions may depend on the shape of Cauchy cuts in Nth gradient continua: Approach “à la D’Alembert”. Z. Angew. Math. Phys., 63(6), 1119–1141.

    Google Scholar 

  • Dell’Isola, F., Steigmann, D., & Della Corte, A. (2015). Synthesis of fibrous complex structures: Designing microstructure to deliver targeted macroscale response. Appl. Mech. Rev., 67(6), 060804.

    Google Scholar 

  • Della Corte, A., dell’Isola, F., Esposito, R., & Pulvirenti, M. (2017). Equilibria of a clamped Euler beam (Elastica) with distributed load: Large deformations. Math. Models Methods Appl. Sci., 27(08), 1391–1421.

    Google Scholar 

  • Diziol, R., Bender, J., & Bayer, D. (2011). Robust real-time deformation of incompressible surface meshes. In Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, New York, NY, USA (pp. 237–246) [Online]. Available at: http://doi.acm.org/10.1145/2019406.2019438.

  • Dong, Y., Zhang, G., Xu, A., & Gan, Y. (2013). Cellular automata model for elastic solid material. Commun. Theor. Phys., 59(1), 59–67.

    Google Scholar 

  • Dos Reis, F., & Ganghoffer, J.-F. (2011). Construction of micropolar continua from the homogenization of repetitive planar lattices. In Mechanics of generalized continua (pp. 193–217). Heidelberg: Springer.

    Google Scholar 

  • Dos Reis, F., & Ganghoffer, J. F. (2012). Equivalent mechanical properties of auxetic lattices from discrete homogenization. Comput. Mater. Sci., 51(1), 314–321.

    Google Scholar 

  • Enakoutsa, K., Corte, A. D., & Giorgio, I. (2016). A model for elastic flexoelectric materials including strain gradient effects. Math. Mech. Solids, 21(2), 242–254.

    Google Scholar 

  • Eremeyev, V. A., Ivanova, E. A., & Indeitsev, D. A. (2010). Wave processes in nanostructures formed by nanotube arrays or nanosize crystals. J. Appl. Mech. Tech. Phys., 51(4), 569–578.

    Google Scholar 

  • Eremeyev, V. A., Ivanova, E. A., Morozov, N. F., & Solov’ev, A. N. (2006). On the determination of eigenfrequencies for nanometer-size objects. Doklady Physics, 51, 93–97.

    Google Scholar 

  • Eremeyev, V. A., Ivanova, E. A., Morozov, N. F., & Strochkov, S. E. (2007). The spectrum of natural oscillations of an array of micro-or nanospheres on an elastic substrate. Doklady Physics, 52, 699–702.

    Google Scholar 

  • Eremeyev, V. A., Lebedev, L. P., & Altenbach, H. (2012). Foundations of Micropolar Mechanics. Springer Science & Business Media.

    Google Scholar 

  • Eremeyev, V. A., & Pietraszkiewicz, W. (2012). Material symmetry group of the non-linear polar-elastic continuum. Int. J. Solids Struct., 49(14), 1993–2005.

    Google Scholar 

  • Eringen, A. C. (2012). Microcontinuum Field Theories: I. Foundations and Solids. Springer Science & Business Media.

    Google Scholar 

  • Ern, A., & Guermond, J.-L. (2013). Theory and Practice Of Finite Elements (vol. 159). Springer Science & Business Media.

    Google Scholar 

  • Forest, S. (2009). Micromorphic approach for gradient elasticity, viscoplasticity, and damage. J. Eng. Mech., 135(3), 117–131.

    Google Scholar 

  • Forest, S., Cordero, N. M., & Busso, E. P. (2011). First vs. second gradient of strain theory for capillarity effects in an elastic fluid at small length scales. Comput. Mater. Sci., 50(4), 1299–1304.

    Google Scholar 

  • Gabriele, S., Rizzi, N. L., & Varano, V. (2014). A one-dimensional nonlinear thin walled beam model derived from Koiter shell theory. Civ.-Comp Proc. 106.

    Google Scholar 

  • Germain, P. (1973). The method of virtual power in continuum mechanics. Part 2: Microstructure. SIAM J. Appl. Math., 25(3), 556–575.

    Google Scholar 

  • Giorgio, I., Andreaus, U., Scerrato, D., & Dell’Isola, F. (2016). A visco-poroelastic model of functional adaptation in bones reconstructed with bio-resorbable materials. Biomech. Model. Mechanobiol., 15(5), 1325–1343.

    Google Scholar 

  • Giorgio, I., Della Corte, A., dell’Isola, F., & Steigmann, D. J. (2016). Buckling modes in pantographic lattices. Comptes Rendus Mécanique, 344(7), 487–501.

    Google Scholar 

  • Giorgio, I., Galantucci, L., Della Corte, A., & Del Vescovo, D. (2015). Piezo-electromechanical smart materials with distributed arrays of piezoelectric transducers: Current and upcoming applications. Int. J. Appl. Electromagn. Mech., 47(4), 1051–1084.

    Google Scholar 

  • Giorgio, I., Harrison, P., Dell’Isola, F., Alsayednoor, J., & Turco, E. (2018). Wrinkling in engineering fabrics: A comparison between two different comprehensive modelling approaches. Proc. R. Soc. Math. Phys. Eng. Sci., 474(2216), 20180063.

    Google Scholar 

  • Goda, I., Assidi, M., Belouettar, S., & Ganghoffer, J. F. (2012). A micropolar anisotropic constitutive model of cancellous bone from discrete homogenization. J. Mech. Behav. Biomed. Mater., 16, 87–108.

    Google Scholar 

  • Goda, I., Assidi, M., & Ganghoffer, J.-F. (2013). Equivalent mechanical properties of textile monolayers from discrete asymptotic homogenization. J. Mech. Phys. Solids, 61(12), 2537–2565.

    Google Scholar 

  • Goda, I., Assidi, M., & Ganghoffer, J.-F. (2014). A 3D elastic micropolar model of vertebral trabecular bone from lattice homogenization of the bone microstructure. Biomech. Model. Mechanobiol., 13(1), 53–83.

    Google Scholar 

  • Greco, L., & Cuomo, M. (2013). B-Spline interpolation of Kirchhoff-Love space rods. Comput. Methods Appl. Mech. Eng., 256, 251–269.

    Google Scholar 

  • Greco, L., & Cuomo, M. (2014). An implicit G1 multi patch B-spline interpolation for Kirchhoff-Love space rod. Comput. Methods Appl. Mech. Eng., 269, 173–197.

    Google Scholar 

  • Janson, S., Middendorf, M., & Beekman, M. (2005). Honeybee swarms: how do scouts guide a swarm of uninformed bees? Anim. Behav., 70(2), 349–358.

    Google Scholar 

  • Javili, A., Dell’Isola, F., & Steinmann, P. (2013). Geometrically nonlinear higher-gradient elasticity with energetic boundaries. J. Mech. Phys. Solids, 61(12), 2381–2401.

    Google Scholar 

  • Karaboga, D. (2005). An Idea Based on Honey Bee Swarm for Numerical Optimization. Technical Report-tr06, Erciyes University, Engineering Faculty, Computer Engineering Department, [Online]. Available at: http://www-lia.deis.unibo.it/Courses/SistInt/articoli/bee-colony1.pdf. Consultato: 07-nov-2014.

  • Khatib, O, Kumar, V., & Rus, D. (2008). Experimental Robotics: The 10th International Symposium on Experimental Robotics. Heidelberg: Springer.

    Google Scholar 

  • Ladevèze, P. (2012). Nonlinear Computational Structural Mechanics: New Approaches and Non-incremental Methods of Calculation. Springer Science & Business Media.

    Google Scholar 

  • Lanczos, C. (2012). The Variational Principles of Mechanics. Courier Corporation.

    Google Scholar 

  • Lekszycki, T., & Dell’Isola, F. (2012). A mixture model with evolving mass densities for describing synthesis and resorption phenomena in bones reconstructed with bio-resorbable materials. ZAMM Z. Angew. Math. Mech., 92(6), 426–444.

    Google Scholar 

  • Macklin, M., Müller, M., & Chentanez, N. (2016). XPBD: Position-Based Simulation of Compliant Constrained Dynamics (pp. 49–54) [Online]. Available at: http://dl.acm.org/citation.cfm?doid=2994258.2994272. Consultato: 06-ott-2017.

  • Madeo, A., Dell’Isola, F., & Darve, F. (2013). A continuum model for deformable, second gradient porous media partially saturated with compressible fluids. J. Mech. Phys. Solids, 61(11), 2196–2211.

    Google Scholar 

  • Madeo, A., Dell’Isola, F., Ianiro, N., & Sciarra, G. (2008). A variational deduction of second gradient poroelasticity II: An application to the consolidation problem. J. Mech. Mater. Struct., 3(4), 607–625.

    Google Scholar 

  • Madeo, A., Placidi, L., & Rosi, G. (2014). Towards the design of metamaterials with enhanced damage sensitivity: second gradient porous materials. Res. Nondestruct. Eval., 25(2), 99–124.

    Google Scholar 

  • Masiani, R., Rizzi, N. & Trovalusci, P. (1995). Masonry as structured continuum. Meccanica, 30(6), 673–683.

    Google Scholar 

  • Milton, G., & Seppecher, P. (2012). A metamaterial having a frequency dependent elasticity tensor and a zero effective mass density. Phys. Status Solidi B, 249(7), 1412–1414.

    Google Scholar 

  • Mindlin, R. D. (1964). Micro-structure in linear elasticity. Arch. Ration. Mech. Anal., 16(1), 51–78.

    Google Scholar 

  • Moriconi,C., & dell’Erba, R. (2012). The localization problem for harness: A multipurpose robotic swarm. In SENSORCOMM 2012, The Sixth International Conference on Sensor Technologies and Applications (pp. 327–333) [Online]. Available at: http://www.thinkmind.org/index.php?view=article&articleid=sensorcomm_2012_14_20_10138. Consultato: 04-apr-2014.

  • Passino, K. M., Seeley, T. D., & Visscher, P. K. (2007). Swarm cognition in honey bees. Behav. Ecol. Sociobiol., 62(3), 401–414.

    Google Scholar 

  • Pietraszkiewicz, W. & Eremeyev, V. A. (2009). On natural strain measures of the non-linear micropolar continuum. Int. J. Solids Struct., 46(3), 774–787.

    Google Scholar 

  • Pietraszkiewicz, W., & Eremeyev, V. A. (2009). On vectorially parameterized natural strain measures of the non-linear Cosserat continuum. Int. J. Solids Struct., 46(11–12), 2477–2480.

    Google Scholar 

  • Placidi, L. (2015). A variational approach for a nonlinear 1-dimensional second gradient continuum damage model. Contin. Mech. Thermodyn., 27(4–5), 623–638.

    Google Scholar 

  • Placidi, L., Dell’Isola, F., Ianiro, N., & Sciarra, G. (2008). Variational formulation of pre-stressed solid-fluid mixture theory, with an application to wave phenomena. Eur. J. Mech. ASolids, 27(4), 582–606.

    Google Scholar 

  • Placidi, L., Faria, S. H., & Hutter, K. (2004). On the role of grain growth, recrystallization and polygonization in a continuum theory for anisotropic ice sheets. Ann. Glaciol., 39, 49–52.

    Google Scholar 

  • Placidi, L., Giorgio, I., Della Corte, A., & Scerrato, D. (2017). 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, 22(2), 144–157.

    Google Scholar 

  • Placidi, L., Greve, R., Seddik, H., & Faria, S. H. (2010). Continuum-mechanical, Anisotropic Flow model for polar ice masses, based on an anisotropic flow enhancement factor. Contin. Mech. Thermodyn., 22(3), 221–237.

    Google Scholar 

  • Placidi, L., & Hutter, K. (2006). Thermodynamics of polycrystalline materials treated by the theory of mixtures with continuous diversity. Contin. Mech. Thermodyn., 17(6), 409–451.

    Google Scholar 

  • Placidi, L., Rosi, G., Giorgio, I., & Madeo, A. (2013). Reflection and transmission of plane waves at surfaces carrying material properties and embedded in second-gradient materials. Math. Mech. Solids, 19(5), 555–578.

    Google Scholar 

  • Konovalenko, Ig. S., Smolin, A. Yu., & Psakhie, S. G. (2010). Multilevel simulation of deformation and fracture of brittle porous materials in the method of movable cellular automata. Phys. Mesomech., 13(1–2), 47–53.

    Google Scholar 

  • Rahali, Y., Giorgio, I., Ganghoffer, J. F., & Dell’Isola, F. (2015). Homogenization à la Piola produces second gradient continuum models for linear pantographic lattices. Int. J. Eng. Sci., 97, 148–172.

    Google Scholar 

  • Rivers, A. R., & James, D. (2007). FastLSM: Fast Lattice Shape Matching for Robust Real-Time Deformation (Vol. 26).

    Google Scholar 

  • Rosi, G., Giorgio, I., & Eremeyev, V. A. (2013). Propagation of linear compression waves through plane interfacial layers and mass adsorption in second gradient fluids. ZAMM‐Journal Appl. Math. Mech. Für Angew. Math. Mech., 93(12), 914–927.

    Google Scholar 

  • Scerrato, D., Giorgio, I., Della Corte, A., Madeo, A., & Limam, A. (2015). A micro‐structural model for dissipation phenomena in the concrete. Int. J. Numer. Anal. Methods Geomech., 39(18), 2037–2052.

    Google Scholar 

  • Seddik, H., Greve, R., Placidi, L., Hamann, I., & Gagliardini, O. (2008). Application of a continuum-mechanical model for the flow of anisotropic polar ice to the EDML core, Antarctica. J. Glaciol., 54(187), 631–642.

    Google Scholar 

  • Seppecher, P., Alibert, J.-J., & Isola, F. D. (2011). Linear elastic trusses leading to continua with exotic mechanical interactions. Journal of Physics: Conference Series, 319, 012018.

    Google Scholar 

  • Spagnuolo, M., Barcz, K., Pfaff, A., Dell’Isola, F., & Franciosi, P. (2017). Qualitative pivot damage analysis in aluminum printed pantographic sheets: Numerics and experiments. Mech. Res. Commun., 83, 47–52.

    Google Scholar 

  • Steigmann, D. J. (2008). Two-dimensional models for the combined bending and stretching of plates and shells based on three-dimensional linear elasticity. Int. J. Eng. Sci., 46(7), 654–676.

    Google Scholar 

  • Steigmann, D. J. (2009). A concise derivation of membrane theory from three-dimensional nonlinear elasticity. J. Elast., 97(1), 97–101.

    Google Scholar 

  • Steigmann, D. J. (2010). Applications of polyconvexity and strong ellipticity to nonlinear elasticity and elastic plate theory. In Poly-, Quasi-and rank-one convexity in applied mechanics (pp. 265–299). Heidelberg: Springer.

    Google Scholar 

  • Steigmann, D. J. (2013). Koiter’s shell theory from the perspective of three-dimensional nonlinear elasticity. J. Elast., 111(1), 91–107.

    Google Scholar 

  • Steigmann, D. J., & Pipkin, A. C. (1991). Equilibrium of elastic nets. Philos. Trans. R. Soc. Lond. Ser. Phys. Eng. Sci., 335(1639), 419–454.

    Google Scholar 

  • Turco, E., Barcz, K., Pawlikowski, M., & Rizzi, N. L. (2016). Non-standard coupled extensional and bending bias tests for planar pantographic lattices. Part I: numerical simulations. Z. Für Angew. Math. Phys., 67(5), 122.

    Google Scholar 

  • Turco, E., Dell’Isola, F., Cazzani, A., & Rizzi, N. L. (2016). Hencky-type discrete model for pantographic structures: Numerical comparison with second gradient continuum models. Z. Für Angew. Math. Phys., 67(4), 85.

    Google Scholar 

  • Turco, E., Giorgio, I., Misra, A., & Dell’Isola, F. (2017). King post truss as a motif for internal structure of (meta) material with controlled elastic properties. R. Soc. Open Sci., 4(10), 171153.

    Google Scholar 

  • Turco, E., & Rizzi, N. L. (2016). Pantographic structures presenting statistically distributed defects: Numerical investigations of the effects on deformation fields. Mech. Res. Commun., 77, 65–69.

    Google Scholar 

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Authors and Affiliations

  1. ENEA Technical Unit Technologies for Energy and Industry—Robotics Laboratory, Rome, Italy

    Ramiro dell’Erba

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  1. Ramiro dell’Erba
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  1. Dipartimento di Ingegneria Strutturale, Università degli Studi dell’Aquila MEMOCS, L’Aquila, Italy

    Francesco dell'Isola

  2. Research Institute for Mechanics, National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    Leonid Igumnov

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dell’Erba, R. (2021). A Plausible Description of Continuum Material Behavior Derived by Swarm Robot Flocking Rules. In: dell'Isola, F., Igumnov, L. (eds) Dynamics, Strength of Materials and Durability in Multiscale Mechanics. Advanced Structured Materials, vol 137. Springer, Cham. https://doi.org/10.1007/978-3-030-53755-5_18

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