Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Variational models in elasticity

1 IAC-CNR, Via dei Taurini, 19 I-00185 Rome, Italy
2 Dipartimento di Matematica “G. Castelnuovo”, Sapienza Università di Roma, Piazzale A. Moro 2, I-00185, Rome, Italy

This contribution is part of the Special Issue: Variational Models in Elasticity
Guest Editors: Lucia De Luca; Marcello Ponsiglione
Link: www.aimspress.com/mine/article/5510/special-articles

Special Issues: Variational Models in Elasticity

  Figure/Table
  Supplementary
  Article Metrics

Citation: L. De Luca, M. Ponsiglione. Variational models in elasticity. Mathematics in Engineering, 2021, 3(2): 1-4. doi: 10.3934/mine.2021015

References

  • 1. Alicandro R, De Luca L, Garroni A, et al. (2014) Metastability and dynamics of discrete topological singularities in two dimensions: A Γ-convergence approach. Arch Ration Mech Anal 214: 269-330.    
  • 2. Allaire G (2012) Shape Optimization by the Homogenization Method, Springer Science & Business Media.
  • 3. Almi S, Lazzaroni G, Lucardesi I (2020) Crack growth by vanishing viscosity in planar elasticity. Mathematics in Engineering 2: 141-173.    
  • 4. Ambrosio L (1990) Existence theory for a new class of variational problems. Arch Ration Mech Anal 111: 291-322.    
  • 5. Ball JM (1976) Convexity conditions and existence theorems in nonlinear elasticity. Arch Ration Mech Anal 63: 337-403.    
  • 6. Ball JM, James RD (1987) Fine phase mixtures as minimizers of energy. Arch Ration Mech Anal 100: 13-52.    
  • 7. Bellettini G, Coscia A, Dal Maso G (1998) Compactness and lower semicontinuity properties in S BD(Ω). Math Z 228: 337-351.    
  • 8. Bethuel F, Brezis H, Hélein F (1994) Ginzburg-Landau Vortices, Boston: Birkhäuser.
  • 9. Braides A, Defranceschi A (1998) Homogenization of Multiple Integrals, New York: Oxford University Press.
  • 10. Canevari G, Zarnescu A (2020) Polydispersity and surface energy strength in nematic colloids. Mathematics in Engineering 2: 290-312.    
  • 11. Crismale V, Orlando G (2020) A lower semicontinuity result for linearised elasto-plasticity coupled with damage in W1,γ, γ > 1. Mathematics in Engineering 2: 101-118.    
  • 12. Dal Maso G (2012) An Introduction to Γ-Convergence, Springer Science & Business Media.
  • 13. Dal Maso G (2013) Generalised functions of bounded deformation. J Eur Math Soc 15: 1943-1997.    
  • 14. De Philippis G, Rindler F (2020) Fine properties of functions of bounded deformation - an approach via linear PDEs, Mathematics in Engineering 2: 386-422.
  • 15. Franfcfort GA, Marigo JJ (1998) Revisiting brittle fracture as an energy minimization problem. J Mech Phys Sol 46: 1319-1342.    
  • 16. Friedrich M (2020) Griffith energies as small strain limit of nonlinear models for nonsimple brittle materials. Mathematics in Engineering 2: 75-100.    
  • 17. Friesecke G, James RD, Müller S (2002) A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. Commun Pure Appl Math 55: 1461-1506.    
  • 18. Giacomini A, Ponsiglione M (2006) A Γ-convergence approach to stability of unilateral minimality properties in fracture mechanics and applications. Arch Ration Mech Anal 180: 399-447.    
  • 19. Griffith AA (1921) The phenomena of rupture and flow in solids. Philos Trans Royal Soc A 221: 163-198.
  • 20. Mateu J, Mora MG, Rondi L, et al. (2020) A maximum-principle approach to the minimisation of a nonlocal dislocation energy. Mathematics in Engineering 2: 253-263.    
  • 21. Novaga M, Pozzetta M (2020) Connected surfaces with boundary minimizing the Willmore energy. Mathematics in Engineering 2: 527-556.    
  • 22. Suquet PM (1978) Existence et régularité des solutions des équations de la plasticité. C R Acad Sci Paris Sér A 286: 1201-1204.
  • 23. Tartar L (2009) The general theory of homogenization: A personalized introduction, Springer Science & Business Media.
  • 24. Zeppieri CI (2020) Homogenisation of high-contrast brittle materials. Mathematics in Engineering 2: 174-202.    

 

Reader Comments

your name: *   your email: *  

© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved