Skip to main content
Top
Published in: Continuum Mechanics and Thermodynamics 4/2023

07-12-2022 | Original Article

A new block-based approach for the analysis of damage in masonries undergoing large deformations

Authors: C. A. Tran, E. Barchiesi

Published in: Continuum Mechanics and Thermodynamics | Issue 4/2023

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

A new block-based elasto-damage model for describing masonry structures has been recently proposed (Tran et al. in Mech Res Commun 118:103802, 2021), where the used constitutive elastic and damage behavioral laws were inspired from granular micromechanics. Preliminary results hinted at the realistic masonry deformation modes which could be obtained, as well as the importance of the damaging characteristic lengths featured in the model. The present work is an extension of that previous paper and presents a more detailed derivation of the model, along with a finer parametric study of the damaging characteristic lengths. Qualitative results hint at how those characteristic lengths allow to model interactions between normal and tangential deformations of the mortar, thus opening the way for future development and quantitative studies of the model.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Appendix
Available only for authorised users
Footnotes
1
Which may or may not be homogeneous to an energy in the physical sense; instead, such quantities may be akin to works, powers,...
 
2
More specifically in the numerical incremental formulation, the damages are non-decreasing with respect to the load parameter.
 
Literature
1.
go back to reference D’Altri, A.M., Sarhosis, V., Milani, G., Rots, J., Cattari, S., Lagomarsino, S., Sacco, E., Tralli, A., Castellazzi, G., de Miranda, S.: Modeling strategies for the computational analysis of unreinforced masonry structures: review and classification. Arch. Comput. Methods Eng. 27, 1–33 (2019) D’Altri, A.M., Sarhosis, V., Milani, G., Rots, J., Cattari, S., Lagomarsino, S., Sacco, E., Tralli, A., Castellazzi, G., de Miranda, S.: Modeling strategies for the computational analysis of unreinforced masonry structures: review and classification. Arch. Comput. Methods Eng. 27, 1–33 (2019)
2.
go back to reference Lourenço, P.B.: Computations on historic masonry structures. Progress Struct. Eng. Mater. 4(3), 301–319 (2002) Lourenço, P.B.: Computations on historic masonry structures. Progress Struct. Eng. Mater. 4(3), 301–319 (2002)
3.
go back to reference Berdichevsky, V.L.: Variational principles. In: Variational Principles of Continuum Mechanics, pp. 3–44. Springer (2009) Berdichevsky, V.L.: Variational principles. In: Variational Principles of Continuum Mechanics, pp. 3–44. Springer (2009)
4.
go back to reference dell’Isola, F., Eugster, S.R., Spagnuolo, M., Barchiesi, E.: Evaluation of Scientific Sources in Mechanics: Heiberg’s Prolegomena to the Works of Archimedes and Hellinger’s Encyclopedia Article on Continuum Mechanics, Vol. 152. Springer Nature (2021) dell’Isola, F., Eugster, S.R., Spagnuolo, M., Barchiesi, E.: Evaluation of Scientific Sources in Mechanics: Heiberg’s Prolegomena to the Works of Archimedes and Hellinger’s Encyclopedia Article on Continuum Mechanics, Vol. 152. Springer Nature (2021)
5.
go back to reference dell’Isola, F., Corte, A.D.: History of the Principle of Virtual Work. In: Encyclopedia of Continuum Mechanics, pp. 1190–1197. Springer (2020) dell’Isola, F., Corte, A.D.: History of the Principle of Virtual Work. In: Encyclopedia of Continuum Mechanics, pp. 1190–1197. Springer (2020)
6.
go back to reference 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) 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)
7.
go back to reference 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 (2015)MathSciNetMATH 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 (2015)MathSciNetMATH
8.
go back to reference dell’Isola, F., Corte, A.D., Giorgio, I.: Higher-gradient continua: the legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives. Math. Mech. Solids 22(4), 852–872 (2017)MathSciNetMATH dell’Isola, F., Corte, A.D., Giorgio, I.: Higher-gradient continua: the legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives. Math. Mech. Solids 22(4), 852–872 (2017)MathSciNetMATH
9.
go back to reference Barchiesi, E., Ciallella, A., Scerrato, D.: A partial report on the controversies about the principle of virtual work: From Archytas of Tarentum to Lagrange, Piola, Mindlin and Toupin. In: Evaluation of Scientific Sources in Mechanics, pp. 341–377. Springer (2022) Barchiesi, E., Ciallella, A., Scerrato, D.: A partial report on the controversies about the principle of virtual work: From Archytas of Tarentum to Lagrange, Piola, Mindlin and Toupin. In: Evaluation of Scientific Sources in Mechanics, pp. 341–377. Springer (2022)
10.
go back to reference Maugin, G.A.: The principle of virtual power: from eliminating metaphysical forces to providing an efficient modelling tool. Contin. Mech. Thermodyn. 25(2), 127–146 (2013)ADSMathSciNetMATH Maugin, G.A.: The principle of virtual power: from eliminating metaphysical forces to providing an efficient modelling tool. Contin. Mech. Thermodyn. 25(2), 127–146 (2013)ADSMathSciNetMATH
11.
go back to reference Tran, C.A., Gołaszewski, M., Barchiesi, E.: Symmetric-in-plane compression of polyamide pantographic fabrics-modelling, experiments and numerical exploration. Symmetry 12(5), 1 (2020) Tran, C.A., Gołaszewski, M., Barchiesi, E.: Symmetric-in-plane compression of polyamide pantographic fabrics-modelling, experiments and numerical exploration. Symmetry 12(5), 1 (2020)
12.
go back to reference Abali, B.E., Müller, W.H., dell’Isola, F.: Theory and computation of higher gradient elasticity theories based on action principles. Arch. Appl. Mech. 87(9), 1495–1510 (2017)ADS Abali, B.E., Müller, W.H., dell’Isola, F.: Theory and computation of higher gradient elasticity theories based on action principles. Arch. Appl. Mech. 87(9), 1495–1510 (2017)ADS
13.
go back to reference 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)MathSciNetMATH 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)MathSciNetMATH
14.
go back to reference Nejadsadeghi, N., Misra, A.: Extended granular micromechanics approach: a micromorphic theory of degree n. Math. Mech. Solids 25(2), 407–429 (2020)MathSciNetMATH Nejadsadeghi, N., Misra, A.: Extended granular micromechanics approach: a micromorphic theory of degree n. Math. Mech. Solids 25(2), 407–429 (2020)MathSciNetMATH
15.
go back to reference Giorgio, I.: A variational formulation for one-dimensional linear thermoviscoelasticity. Math. Mech. Complex Syst. 9(4), 397–412 (2022)MathSciNetMATH Giorgio, I.: A variational formulation for one-dimensional linear thermoviscoelasticity. Math. Mech. Complex Syst. 9(4), 397–412 (2022)MathSciNetMATH
16.
go back to reference dell’Isola, F., Seppecher, P., Placidi, L., Barchiesi, E., Misra, A.: Least action and virtual work principles for the formulation of generalized continuum models. Discret. Contin. Models Complex Metamater. 1, 327 (2020) dell’Isola, F., Seppecher, P., Placidi, L., Barchiesi, E., Misra, A.: Least action and virtual work principles for the formulation of generalized continuum models. Discret. Contin. Models Complex Metamater. 1, 327 (2020)
17.
go back to reference Germain, P.: The method of virtual power in continuum mechanics. Part 2: microstructure. SIAM J. Appl. Math. 25(3), 556–575 (1973)MATH Germain, P.: The method of virtual power in continuum mechanics. Part 2: microstructure. SIAM J. Appl. Math. 25(3), 556–575 (1973)MATH
18.
go back to reference Germain, P.: The method of virtual power in the mechanics of continuous media, I: Second-gradient theory. Math. Mech. Complex Syst. 8(2), 153–190 (2020)MathSciNetMATH Germain, P.: The method of virtual power in the mechanics of continuous media, I: Second-gradient theory. Math. Mech. Complex Syst. 8(2), 153–190 (2020)MathSciNetMATH
19.
go back to reference Maugin, G.A.: The method of virtual power in continuum mechanics: application to coupled fields. Acta Mech. 35(1), 1–70 (1980)ADSMathSciNetMATH Maugin, G.A.: The method of virtual power in continuum mechanics: application to coupled fields. Acta Mech. 35(1), 1–70 (1980)ADSMathSciNetMATH
20.
go back to reference Placidi, L., Barchiesi, E., dell’Isola, F., Maksimov, V., Misra, A., Rezaei, N., Scrofani, A., Timofeev, D.: On a hemi-variational formulation for a 2D elasto-plastic-damage strain gradient solid with granular microstructure. Math. Eng. 5(1), 1–24 (2022)MathSciNet Placidi, L., Barchiesi, E., dell’Isola, F., Maksimov, V., Misra, A., Rezaei, N., Scrofani, A., Timofeev, D.: On a hemi-variational formulation for a 2D elasto-plastic-damage strain gradient solid with granular microstructure. Math. Eng. 5(1), 1–24 (2022)MathSciNet
21.
go back to reference Barchiesi, E., Hamila, N.: Maximum mechano-damage power release-based phase-field modeling of mass diffusion in damaging deformable solids. Z. Angew. Math. Phys. 73(1), 1–21 (2022)MathSciNetMATH Barchiesi, E., Hamila, N.: Maximum mechano-damage power release-based phase-field modeling of mass diffusion in damaging deformable solids. Z. Angew. Math. Phys. 73(1), 1–21 (2022)MathSciNetMATH
22.
go back to reference Nodargi, N.A., Intrigila, C., Bisegna, P.: A variational-based fixed-point algorithm for the limit analysis of dry-masonry block structures with non-associative Coulomb friction. Int. J. Mech. Sci. 161, 105078 (2019) Nodargi, N.A., Intrigila, C., Bisegna, P.: A variational-based fixed-point algorithm for the limit analysis of dry-masonry block structures with non-associative Coulomb friction. Int. J. Mech. Sci. 161, 105078 (2019)
23.
go back to reference Ainsworth, M., Mihai, L.A.: Modeling and numerical analysis of masonry structures. Numer. Methods Part. Differ. Equ.: Int. J. 23(4), 798–816 (2007)MathSciNetMATH Ainsworth, M., Mihai, L.A.: Modeling and numerical analysis of masonry structures. Numer. Methods Part. Differ. Equ.: Int. J. 23(4), 798–816 (2007)MathSciNetMATH
24.
go back to reference Giorgio, I.: A discrete formulation of Kirchhoff rods in large-motion dynamics. Math. Mech. Solids 25(5), 1081–1100 (2020)MathSciNetMATH Giorgio, I.: A discrete formulation of Kirchhoff rods in large-motion dynamics. Math. Mech. Solids 25(5), 1081–1100 (2020)MathSciNetMATH
25.
go back to reference 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. Int. J. Non-linear Mech. 123, 1 (2020) 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. Int. J. Non-linear Mech. 123, 1 (2020)
26.
go back to reference Alibert, J.-J., Seppecher, P., dell’Isola, F.: Truss modular beams with deformation energy depending on higher displacement gradients. Math. Mech. Solids 8(1), 51–73 (2003)MathSciNetMATH Alibert, J.-J., Seppecher, P., dell’Isola, F.: Truss modular beams with deformation energy depending on higher displacement gradients. Math. Mech. Solids 8(1), 51–73 (2003)MathSciNetMATH
27.
go back to reference Baroudi, D., Giorgio, I., Battista, A., Turco, E., Igumnov, L.A.: Nonlinear dynamics of uniformly loaded elastica: experimental and numerical evidence of motion around curled stable equilibrium configurations. ZAMM-J. Appl. Math. Mech. 99(7), 1 (2019)MathSciNet Baroudi, D., Giorgio, I., Battista, A., Turco, E., Igumnov, L.A.: Nonlinear dynamics of uniformly loaded elastica: experimental and numerical evidence of motion around curled stable equilibrium configurations. ZAMM-J. Appl. Math. Mech. 99(7), 1 (2019)MathSciNet
28.
go back to reference Turco, E., Barchiesi, E.: Equilibrium paths of Hencky pantographic beams in a three-point bending problem. Math. Mech. Complex Syst. 7(4), 287–310 (2019)MathSciNetMATH Turco, E., Barchiesi, E.: Equilibrium paths of Hencky pantographic beams in a three-point bending problem. Math. Mech. Complex Syst. 7(4), 287–310 (2019)MathSciNetMATH
29.
go back to reference Misra, A., Placidi, L., Turco, E.: Variational methods for discrete models of granular materials. In: Encyclopedia of Continuum Mechanics, pp. 2621–2634 (2020) Misra, A., Placidi, L., Turco, E.: Variational methods for discrete models of granular materials. In: Encyclopedia of Continuum Mechanics, pp. 2621–2634 (2020)
30.
go back to reference Turco, E., Misra, A., Pawlikowski, M., dell’Isola, F., Hild, F.: Enhanced Piola–Hencky discrete models for pantographic sheets with pivots without deformation energy: numerics and experiments. Int. J. Solids Struct. 147, 94–109 (2018) Turco, E., Misra, A., Pawlikowski, M., dell’Isola, F., Hild, F.: Enhanced Piola–Hencky discrete models for pantographic sheets with pivots without deformation energy: numerics and experiments. Int. J. Solids Struct. 147, 94–109 (2018)
31.
go back to reference 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: Math. Phys. Eng. Sci. 472(2185), 1 (2016) 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: Math. Phys. Eng. Sci. 472(2185), 1 (2016)
32.
go back to reference Barchiesi, E., Yang, H., Tran, C.A., Placidi, L., Müller, W.H.: Computation of brittle fracture propagation in strain gradient materials by the FEniCS library. Math. Mech. Solids 26, 325 (2020)MathSciNetMATH Barchiesi, E., Yang, H., Tran, C.A., Placidi, L., Müller, W.H.: Computation of brittle fracture propagation in strain gradient materials by the FEniCS library. Math. Mech. Solids 26, 325 (2020)MathSciNetMATH
33.
go back to reference Abali, B.E., Klunker, A., Barchiesi, E., Placidi, L.: A novel phase-field approach to brittle damage mechanics of gradient metamaterials combining action formalism and history variable (2021) Abali, B.E., Klunker, A., Barchiesi, E., Placidi, L.: A novel phase-field approach to brittle damage mechanics of gradient metamaterials combining action formalism and history variable (2021)
34.
go back to reference Cuomo, M., dell’Isola, F., Greco, L., Rizzi, N.L.: First versus second gradient energies for planar sheets with two families of inextensible fibres: investigation on deformation boundary layers, discontinuities and geometrical instabilities. Compos. B Eng. 115, 423–448 (2017) Cuomo, M., dell’Isola, F., Greco, L., Rizzi, N.L.: First versus second gradient energies for planar sheets with two families of inextensible fibres: investigation on deformation boundary layers, discontinuities and geometrical instabilities. Compos. B Eng. 115, 423–448 (2017)
35.
go back to reference Giorgio, I.: Lattice shells composed of two families of curved Kirchhoff rods: an archetypal example, topology optimization of a cycloidal metamaterial. Contin. Mech. Thermodyn. 33(4), 1063–1082 (2021)ADSMathSciNet Giorgio, I.: Lattice shells composed of two families of curved Kirchhoff rods: an archetypal example, topology optimization of a cycloidal metamaterial. Contin. Mech. Thermodyn. 33(4), 1063–1082 (2021)ADSMathSciNet
36.
go back to reference De Angelo, M., Barchiesi, E., Giorgio, I., Abali, B.E.: Numerical identification of constitutive parameters in reduced-order bi-dimensional models for pantographic structures: application to out-of-plane buckling. Arch. Appl. Mech. 89(7), 1333–1358 (2019) De Angelo, M., Barchiesi, E., Giorgio, I., Abali, B.E.: Numerical identification of constitutive parameters in reduced-order bi-dimensional models for pantographic structures: application to out-of-plane buckling. Arch. Appl. Mech. 89(7), 1333–1358 (2019)
37.
go back to reference Giorgio, I., Andreaus, U., dell’Isola, F., Lekszycki, T.: Viscous second gradient porous materials for bones reconstructed with bio-resorbable grafts. Extreme Mech. Lett. 13, 141–147 (2017) Giorgio, I., Andreaus, U., dell’Isola, F., Lekszycki, T.: Viscous second gradient porous materials for bones reconstructed with bio-resorbable grafts. Extreme Mech. Lett. 13, 141–147 (2017)
38.
go back to reference Barchiesi, E., Spagnuolo, M., Placidi, L.: Mechanical metamaterials: a state of the art. Math. Mech. Solids 24(1), 212–234 (2019)MathSciNetMATH Barchiesi, E., Spagnuolo, M., Placidi, L.: Mechanical metamaterials: a state of the art. Math. Mech. Solids 24(1), 212–234 (2019)MathSciNetMATH
39.
go back to reference Barchiesi, E., Di Cosmo, F., Laudato, M.: A review of some selected examples of mechanical and acoustic metamaterials. Discret. Contin. Models Complex Metamater. (2020) Barchiesi, E., Di Cosmo, F., Laudato, M.: A review of some selected examples of mechanical and acoustic metamaterials. Discret. Contin. Models Complex Metamater. (2020)
40.
go back to reference dell’Isola, F., Seppecher, P., Alibert, J.J., Lekszycki, T., Grygoruk, R., Pawlikowski, M., Steigmann, D., Giorgio, I., Andreaus, U., Turco, E., et al.: Pantographic metamaterials: an example of mathematically driven design and of its technological challenges. Contin. Mech. Thermodyn. 31(4), 851–884 (2019)ADSMathSciNet dell’Isola, F., Seppecher, P., Alibert, J.J., Lekszycki, T., Grygoruk, R., Pawlikowski, M., Steigmann, D., Giorgio, I., Andreaus, U., Turco, E., et al.: Pantographic metamaterials: an example of mathematically driven design and of its technological challenges. Contin. Mech. Thermodyn. 31(4), 851–884 (2019)ADSMathSciNet
41.
go back to reference dell’Isola, F., Seppecher, P., Spagnuolo, M., Barchiesi, E., Hild, F., Lekszycki, T., Giorgio, I., Placidi, L., Andreaus, U., Cuomo, M., et al.: Advances in pantographic structures: design, manufacturing, models, experiments and image analyses. Contin. Mech. Thermodyn. 31(4), 1231–1282 (2019)ADS dell’Isola, F., Seppecher, P., Spagnuolo, M., Barchiesi, E., Hild, F., Lekszycki, T., Giorgio, I., Placidi, L., Andreaus, U., Cuomo, M., et al.: Advances in pantographic structures: design, manufacturing, models, experiments and image analyses. Contin. Mech. Thermodyn. 31(4), 1231–1282 (2019)ADS
42.
go back to reference Barchiesi, E., Placidi, L.: A review on models for the 3D statics and 2D dynamics of pantographic fabrics. In: Wave dynamics and composite mechanics for microstructured materials and metamaterials, pp. 239–258. Springer (2017) Barchiesi, E., Placidi, L.: A review on models for the 3D statics and 2D dynamics of pantographic fabrics. In: Wave dynamics and composite mechanics for microstructured materials and metamaterials, pp. 239–258. Springer (2017)
43.
go back to reference Placidi, L., Barchiesi, E., Della Corte, A.: Identification of two-dimensional pantographic structures with a linear \(D_4\) orthotropic second gradient elastic model accounting for external bulk double forces. In: Mathematical Modelling in Solid Mechanics, pp. 211–232. Springer (2017) Placidi, L., Barchiesi, E., Della Corte, A.: Identification of two-dimensional pantographic structures with a linear \(D_4\) orthotropic second gradient elastic model accounting for external bulk double forces. In: Mathematical Modelling in Solid Mechanics, pp. 211–232. Springer (2017)
44.
go back to reference Barchiesi, E., dell’Isola, F., Laudato, M., Placidi, L., Seppecher, P.: A 1D continuum model for beams with pantographic microstructure: asymptotic micro-macro identification and numerical results. In: Advances in Mechanics of Microstructured Media and Structures, pp. 43–74. Springer (2018) Barchiesi, E., dell’Isola, F., Laudato, M., Placidi, L., Seppecher, P.: A 1D continuum model for beams with pantographic microstructure: asymptotic micro-macro identification and numerical results. In: Advances in Mechanics of Microstructured Media and Structures, pp. 43–74. Springer (2018)
45.
go back to reference Spagnuolo, M., Barcz, K., Pfaff, A., dell’Isola, F., Franciosi, P.: Qualitative pivot damage analysis in aluminum printed pantographic sheets: numerics and experiments. Mech. Res. Commun. 83, 47–52 (2017) Spagnuolo, M., Barcz, K., Pfaff, A., dell’Isola, F., Franciosi, P.: Qualitative pivot damage analysis in aluminum printed pantographic sheets: numerics and experiments. Mech. Res. Commun. 83, 47–52 (2017)
46.
go back to reference dell’Isola, F., Lekszycki, T., Spagnuolo, M., Peyre, P., Dupuy, C., Hild, F., Misra, A., Barchiesi, E., Turco, E., Dirrenberger, J.: Experimental Methods in Pantographic Structures. Discrete and Continuum Models for Complex Metamaterials, p 263 (2020) dell’Isola, F., Lekszycki, T., Spagnuolo, M., Peyre, P., Dupuy, C., Hild, F., Misra, A., Barchiesi, E., Turco, E., Dirrenberger, J.: Experimental Methods in Pantographic Structures. Discrete and Continuum Models for Complex Metamaterials, p 263 (2020)
47.
go back to reference Yildizdag, M.E., Tran, C.A., Barchiesi, E., Spagnuolo, M., dell’Isola, F., Hild, F.: A multi-disciplinary approach for mechanical metamaterial synthesis: a hierarchical modular multiscale cellular structure paradigm. In: State of the Art and Future Trends in Material Modeling, pp. 485–505. Springer (2019) Yildizdag, M.E., Tran, C.A., Barchiesi, E., Spagnuolo, M., dell’Isola, F., Hild, F.: A multi-disciplinary approach for mechanical metamaterial synthesis: a hierarchical modular multiscale cellular structure paradigm. In: State of the Art and Future Trends in Material Modeling, pp. 485–505. Springer (2019)
48.
go back to reference Trzepieciński, T., dell’Isola, F., Lemu, H.G.: Multiphysics modeling and numerical simulation in computer-aided manufacturing processes. Metals 11(1), 175 (2021) Trzepieciński, T., dell’Isola, F., Lemu, H.G.: Multiphysics modeling and numerical simulation in computer-aided manufacturing processes. Metals 11(1), 175 (2021)
49.
go back to reference Hild, F., Misra, A., dell’Isola, F.: Multiscale DIC applied to pantographic structures. Exp. Mech. 61, 431–443 (2021) Hild, F., Misra, A., dell’Isola, F.: Multiscale DIC applied to pantographic structures. Exp. Mech. 61, 431–443 (2021)
50.
go back to reference Barchiesi, E., Bouterf, A., Hild, F., Dell’Isola, F., Misra, A., Neggers, J., Pawlikowski, M., Spagnuolo, M., Turco, E.: On the use of fe-based dic to measure the kinematics of metamaterials at different scales. In: Joint MEMOCS Workshop on Models of Complex Materials and Systems (2019) Barchiesi, E., Bouterf, A., Hild, F., Dell’Isola, F., Misra, A., Neggers, J., Pawlikowski, M., Spagnuolo, M., Turco, E.: On the use of fe-based dic to measure the kinematics of metamaterials at different scales. In: Joint MEMOCS Workshop on Models of Complex Materials and Systems (2019)
51.
go back to reference Barchiesi, E., dell’Isola, F., Hild, F.: On the validation of homogenized modeling for bi-pantographic metamaterials via digital image correlation. Int. J. Solids Struct. 208, 49–62 (2021) Barchiesi, E., dell’Isola, F., Hild, F.: On the validation of homogenized modeling for bi-pantographic metamaterials via digital image correlation. Int. J. Solids Struct. 208, 49–62 (2021)
52.
go back to reference Placidi, L., Barchiesi, E., Misra, A., Andreaus, U.: Variational methods in continuum damage and fracture mechanics. In: Encyclopedia of Continuum Mechanics, pp. 2634–2643 (2020) Placidi, L., Barchiesi, E., Misra, A., Andreaus, U.: Variational methods in continuum damage and fracture mechanics. In: Encyclopedia of Continuum Mechanics, pp. 2634–2643 (2020)
53.
go back to reference Solyaev, Y., Lurie, S., Barchiesi, E., Placidi, L.: On the dependence of standard and gradient elastic material constants on a field of defects. Math. Mech. Solids 25(1), 35–45 (2020)MathSciNetMATH Solyaev, Y., Lurie, S., Barchiesi, E., Placidi, L.: On the dependence of standard and gradient elastic material constants on a field of defects. Math. Mech. Solids 25(1), 35–45 (2020)MathSciNetMATH
54.
go back to reference Placidi, L., Barchiesi, E., Misra, A.: A strain gradient variational approach to damage: a comparison with damage gradient models and numerical results. Math. Mech. Complex Syst. 6(2), 77–100 (2018)MathSciNetMATH Placidi, L., Barchiesi, E., Misra, A.: A strain gradient variational approach to damage: a comparison with damage gradient models and numerical results. Math. Mech. Complex Syst. 6(2), 77–100 (2018)MathSciNetMATH
55.
go back to reference Placidi, L., Barchiesi, E.: Energy approach to brittle fracture in strain-gradient modelling. Proc. R. Soc. A: Math. Phys. Eng. Sci. 474(2210), 1 (2018)MathSciNetMATH Placidi, L., Barchiesi, E.: Energy approach to brittle fracture in strain-gradient modelling. Proc. R. Soc. A: Math. Phys. Eng. Sci. 474(2210), 1 (2018)MathSciNetMATH
56.
go back to reference Eremeyev, V.A., Lebedev, L.P., Altenbach, H.: Foundations of Micropolar Mechanics. Springer, Berlin (2012)MATH Eremeyev, V.A., Lebedev, L.P., Altenbach, H.: Foundations of Micropolar Mechanics. Springer, Berlin (2012)MATH
57.
go back to reference Pietraszkiewicz, W., Eremeyev, V.A.: On natural strain measures of the non-linear micropolar continuum. Int. J. Solids Struct. 46(3–4), 774–787 (2009)MathSciNetMATH Pietraszkiewicz, W., Eremeyev, V.A.: On natural strain measures of the non-linear micropolar continuum. Int. J. Solids Struct. 46(3–4), 774–787 (2009)MathSciNetMATH
58.
go back to reference Eremeyev, V.A., Lebedev, L.P.: Existence theorems in the linear theory of micropolar shells. ZAMM-J. Appl. Math. Mech. 91(6), 468–476 (2011)MathSciNetMATH Eremeyev, V.A., Lebedev, L.P.: Existence theorems in the linear theory of micropolar shells. ZAMM-J. Appl. Math. Mech. 91(6), 468–476 (2011)MathSciNetMATH
59.
go back to reference Eremeyev, V., Altenbach, H.: Basics of mechanics of micropolar shells. In: Shell-Like Structures, pp. 63–111. Springer (2017) Eremeyev, V., Altenbach, H.: Basics of mechanics of micropolar shells. In: Shell-Like Structures, pp. 63–111. Springer (2017)
60.
go back to reference Yeremeyev, V.A., Zubov, L.M.: The theory of elastic and viscoelastic micropolar liquids. J. Appl. Math. Mech. 63(5), 755–767 (1999)MathSciNet Yeremeyev, V.A., Zubov, L.M.: The theory of elastic and viscoelastic micropolar liquids. J. Appl. Math. Mech. 63(5), 755–767 (1999)MathSciNet
61.
go back to reference Giorgio, I., De Angelo, M., Turco, E., Misra, A.: A Biot-Cosserat two-dimensional elastic nonlinear model for a micromorphic medium. Contin. Mech. Thermodyn. 1, 1–13 (2019) Giorgio, I., De Angelo, M., Turco, E., Misra, A.: A Biot-Cosserat two-dimensional elastic nonlinear model for a micromorphic medium. Contin. Mech. Thermodyn. 1, 1–13 (2019)
62.
go back to reference 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. Meth. Geomech. 39(18), 2037–2052 (2015) 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. Meth. Geomech. 39(18), 2037–2052 (2015)
63.
go back to reference Giorgio, I., dell’Isola, F., Misra, A.: Chirality in 2D Cosserat media related to stretch-micro-rotation coupling with links to granular micromechanics. Int. J. Solids Struct. 202, 28–38 (2020) Giorgio, I., dell’Isola, F., Misra, A.: Chirality in 2D Cosserat media related to stretch-micro-rotation coupling with links to granular micromechanics. Int. J. Solids Struct. 202, 28–38 (2020)
64.
go back to reference La Valle, G.: A new deformation measure for the nonlinear micropolar continuum. Z. Angew. Math. Phys. 73(2), 1–26 (2022)MathSciNetMATH La Valle, G.: A new deformation measure for the nonlinear micropolar continuum. Z. Angew. Math. Phys. 73(2), 1–26 (2022)MathSciNetMATH
65.
go back to reference Abali, B.E., Barchiesi, E.: Additive manufacturing introduced substructure and computational determination of metamaterials parameters by means of the asymptotic homogenization. Contin. Mech. Thermodyn. 33(4), 993–1009 (2021)ADSMathSciNet Abali, B.E., Barchiesi, E.: Additive manufacturing introduced substructure and computational determination of metamaterials parameters by means of the asymptotic homogenization. Contin. Mech. Thermodyn. 33(4), 993–1009 (2021)ADSMathSciNet
66.
go back to reference Barchiesi, E., dell’Isola, F., Hild, F., Seppecher, P.: Two-dimensional continua capable of large elastic extension in two independent directions: asymptotic homogenization, numerical simulations and experimental evidence. Mech. Res. Commun. 103, 1 (2020) Barchiesi, E., dell’Isola, F., Hild, F., Seppecher, P.: Two-dimensional continua capable of large elastic extension in two independent directions: asymptotic homogenization, numerical simulations and experimental evidence. Mech. Res. Commun. 103, 1 (2020)
67.
go back to reference Barchiesi, E., Harsch, J., Ganzosch, G., Eugster, S.R.: Discrete versus homogenized continuum modeling in finite deformation bias extension test of bi-pantographic fabrics. Contin. Mech. Thermodyn. 1, 1–14 (2020) Barchiesi, E., Harsch, J., Ganzosch, G., Eugster, S.R.: Discrete versus homogenized continuum modeling in finite deformation bias extension test of bi-pantographic fabrics. Contin. Mech. Thermodyn. 1, 1–14 (2020)
68.
go back to reference Barchiesi, E., Eugster, S.R., dell’Isola, F., Hild, F.: Large in-plane elastic deformations of bi-pantographic fabrics: asymptotic homogenization and experimental validation. Math. Mech. Solids 25(3), 739–767 (2020)MathSciNetMATH Barchiesi, E., Eugster, S.R., dell’Isola, F., Hild, F.: Large in-plane elastic deformations of bi-pantographic fabrics: asymptotic homogenization and experimental validation. Math. Mech. Solids 25(3), 739–767 (2020)MathSciNetMATH
69.
go back to reference Placidi, L., Barchiesi, E., Misra, A., Timofeev, D.: Micromechanics-based elasto-plastic-damage energy formulation for strain gradient solids with granular microstructure. Contin. Mech. Thermodyn. 1, 1–29 (2021)MathSciNet Placidi, L., Barchiesi, E., Misra, A., Timofeev, D.: Micromechanics-based elasto-plastic-damage energy formulation for strain gradient solids with granular microstructure. Contin. Mech. Thermodyn. 1, 1–29 (2021)MathSciNet
70.
go back to reference Placidi, L., Misra, A., Barchiesi, E.: Simulation results for damage with evolving microstructure and growing strain gradient moduli. Contin. Mech. Thermodyn. 31(4), 1143–1163 (2019)ADSMathSciNet Placidi, L., Misra, A., Barchiesi, E.: Simulation results for damage with evolving microstructure and growing strain gradient moduli. Contin. Mech. Thermodyn. 31(4), 1143–1163 (2019)ADSMathSciNet
71.
go back to reference Misra, A., Singh, V.: Nonlinear granular micromechanics model for multi-axial rate-dependent behavior. Int. J. Solids Struct. 51(13), 2272–2282 (2014) Misra, A., Singh, V.: Nonlinear granular micromechanics model for multi-axial rate-dependent behavior. Int. J. Solids Struct. 51(13), 2272–2282 (2014)
72.
go back to reference Barchiesi, E., Misra, A., Placidi, L., Turco, E.: Granular micromechanics-based identification of isotropic strain gradient parameters for elastic geometrically nonlinear deformations. ZAMM-J. Appl. Math. Mech. 1, 1 (2021) Barchiesi, E., Misra, A., Placidi, L., Turco, E.: Granular micromechanics-based identification of isotropic strain gradient parameters for elastic geometrically nonlinear deformations. ZAMM-J. Appl. Math. Mech. 1, 1 (2021)
73.
go back to reference Maksimov, V., Barchiesi, E., Misra, A., Placidi, L., Timofeev, D.: Two-dimensional analysis of size effects in strain-gradient granular solids with damage-induced anisotropy evolution. J. Eng. Mech. 147(11), 1 (2021) Maksimov, V., Barchiesi, E., Misra, A., Placidi, L., Timofeev, D.: Two-dimensional analysis of size effects in strain-gradient granular solids with damage-induced anisotropy evolution. J. Eng. Mech. 147(11), 1 (2021)
74.
go back to reference Misra, A., Poorsolhjouy, P.: Grain-and macro-scale kinematics for granular micromechanics based small deformation micromorphic continuum model. Mech. Res. Commun. 81, 1–6 (2017) Misra, A., Poorsolhjouy, P.: Grain-and macro-scale kinematics for granular micromechanics based small deformation micromorphic continuum model. Mech. Res. Commun. 81, 1–6 (2017)
75.
go back to reference Timofeev, D., Barchiesi, E., Misra, A., Placidi, L.: Hemivariational continuum approach for granular solids with damage-induced anisotropy evolution. Math. Mech. Solids 26(5), 738–770 (2021)MathSciNetMATH Timofeev, D., Barchiesi, E., Misra, A., Placidi, L.: Hemivariational continuum approach for granular solids with damage-induced anisotropy evolution. Math. Mech. Solids 26(5), 738–770 (2021)MathSciNetMATH
76.
go back to reference Misra, A., Singh, V.: Thermomechanics-based nonlinear rate-dependent coupled damage-plasticity granular micromechanics model. Contin. Mech. Thermodyn. 27(4), 787–817 (2015)ADSMathSciNetMATH Misra, A., Singh, V.: Thermomechanics-based nonlinear rate-dependent coupled damage-plasticity granular micromechanics model. Contin. Mech. Thermodyn. 27(4), 787–817 (2015)ADSMathSciNetMATH
77.
go back to reference Zhao, C.-F., Yin, Z.-Y., Misra, A., Hicher, P.-Y.: Thermomechanical formulation for micromechanical elasto-plasticity in granular materials. Int. J. Solids Struct. 138, 64–75 (2018) Zhao, C.-F., Yin, Z.-Y., Misra, A., Hicher, P.-Y.: Thermomechanical formulation for micromechanical elasto-plasticity in granular materials. Int. J. Solids Struct. 138, 64–75 (2018)
78.
go back to reference Misra, A., Poorsolhjouy, P.: Granular micromechanics model for damage and plasticity of cementitious materials based upon thermomechanics. Math. Mech. Solids 25(10), 1778–1803 (2020)MathSciNetMATH Misra, A., Poorsolhjouy, P.: Granular micromechanics model for damage and plasticity of cementitious materials based upon thermomechanics. Math. Mech. Solids 25(10), 1778–1803 (2020)MathSciNetMATH
79.
go back to reference Bryant, E.C., Bennett, K.C., Miller, N.A., Misra, A.: Multiscale plasticity of geomaterials predicted via constrained optimization-based granular micromechanics. Int. J. Numer. Anal. Meth. Geomech. 46(4), 739–778 (2022) Bryant, E.C., Bennett, K.C., Miller, N.A., Misra, A.: Multiscale plasticity of geomaterials predicted via constrained optimization-based granular micromechanics. Int. J. Numer. Anal. Meth. Geomech. 46(4), 739–778 (2022)
80.
go back to reference Tran, C.A., Barchiesi, E., Placidi, L., Trujillo, F.J.L.: A block-based variational elasto-damage model for masonry analysis inspired from granular micromechanics: preliminary study. Mech. Res. Commun. 118, 103802 (2021) Tran, C.A., Barchiesi, E., Placidi, L., Trujillo, F.J.L.: A block-based variational elasto-damage model for masonry analysis inspired from granular micromechanics: preliminary study. Mech. Res. Commun. 118, 103802 (2021)
Metadata
Title
A new block-based approach for the analysis of damage in masonries undergoing large deformations
Authors
C. A. Tran
E. Barchiesi
Publication date
07-12-2022
Publisher
Springer Berlin Heidelberg
Published in
Continuum Mechanics and Thermodynamics / Issue 4/2023
Print ISSN: 0935-1175
Electronic ISSN: 1432-0959
DOI
https://doi.org/10.1007/s00161-022-01178-5

Other articles of this Issue 4/2023

Continuum Mechanics and Thermodynamics 4/2023 Go to the issue

Premium Partners