My research interests concern the Calculus of Variations and its application to Materials Science. In particular I have worked on models for quasistatic evolution of elastoplasticity coupled with damage, and of cohesive and brittle fractures. I am interested also in the mathematical treatment of fatigue, that may cause damage and rupture.

Publications and preprints

⁠⁠⁠All preprint versions and my PhD thesis are available on my CVGMT profile (see also arXiv profile)
  1. A. Chambolle, V. Crismale, A general compactness theorem in G(S)BD, Submitted
  2. V. Crismale, G.Lazzaroni, R. Rossi, Singular limits of a coupled elasto-plastic damage system as viscosity and hardening vanish, Ann. Mat. Pura Appl.
  3. V. Crismale, A. Kubin, A. Ninno, M. Ponsiglione, Failure of crystallization for generalized Lennard-Jones potentials and coarse graining to a rotating stars problem in one dimension, Nonlinear Analysis, Art. 113046 (2022)
  4. V. Crismale, Energetic solutions for the coupling of associative plasticity with damage in geomaterials, Nonlinear Analysis 222, Art. 112957 (2022)
  5. V. Crismale, L. De Luca, A. Kubin, A. Ninno, M. Ponsiglione, The variational approach to s-fractional heat flows and the limit cases s--> 0+ and s--> 1+, J. Funct. Anal. 284, Art. 109851 (2022)
  6. A. Chambolle, V. Crismale, Equilibrium configurations for nonhomogeneous linearly elastic materials with surface discontinuities, Published online on Ann. Sc. Norm. Super. Pisa Cl. Sci.
  7. V. Crismale, M. Friedrich, F. Solombrino, Integral representation for energies in linear elasticity with surface discontinuities, Adv. Calc. Var. 15, 705-733 (2020)
  8. V. Crismale, G. Scilla, F. Solombrino, A derivation of Griffith functionals from discrete finite-difference models
    Calc. Var. Partial Differ. Equ. 59 : Art. 193 (2020)
  9. J.-F. Babadjian, V. Crismale, Dissipative boundary conditions and entropic solutions in dynamical perfect plasticity
    J. Math. Pures Appl. 148, 75-127 (2021)
  10. V. Crismale, R. Rossi, Balanced Viscosity solutions to a rate-independent coupled elasto-plastic damage system
    SIAM J. Math. Anal. 53, 3420-3492 (2021)
  11. V. Crismale, M. Friedrich, Equilibrium configurations for epitaxially strained films and material voids in three-dimensional linear elasticity, Arch. Ration. Mech. Anal. 237, 1041-1098 (2020)
  12. V. Crismale, G. Orlando, A lower semicontinuity result for linearised elasto-plasticity coupled with damage in W1,γ, γ > 1,
    Mathematics in Engineering 2 , 101-118 (2019)
  13. A. Chambolle, V. Crismale, Phase-field approximation for a class of cohesive fracture energies with an activation threshold
    Adv. Calc. Var. 14, 475-497 (2021)
  14. A. Chambolle, V. Crismale, Existence of strong solutions to the Dirichlet problem for the Griffith energy
    Calc. Var. Partial Differ. Equ. 58 : Art. 136 (2019)
  15. V. Crismale, Density in SBD and approximation of fracture energies
    Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30, 533-542 (2019)
  16. R. Alessi, V. Crismale, G. Orlando, Fatigue effects in elastic materials with variational damage models: A vanishing viscosity approach, J. Nonlinear Sci. 29, 1041-1094 (2019)
  17. V. Crismale, On the approximation of SBD functions and some applications
    SIAM J. Math. Anal. 51, 5011-5048 (2019)
  18. A. Chambolle, V. Crismale, Compactness and lower semicontinuity in GSBD
    J. Eur. Math. Soc. (JEMS) 23, 701-719 (2021)
  19. A. Chambolle, V. Crismale, A density result in GSBDp with applications to the approximation of brittle fracture energies
    Arch. Ration. Mech. Anal. 232, 1329-1378 (2019)
  20. V. Crismale, G. Orlando, A Reshetnyak-type lower semicontinuity result for linearised elasto-plasticity coupled with damage in W1,n, Nonl. Diff. Eqns. Appl. (NoDEA) 25 : Art. 16 (2018)
  21. V. Crismale, G. Lazzaroni, G. Orlando, Cohesive fracture with irreversibility: quasistatic evolution for a model subject to fatigue, Math. Models Methods Appl. Sci. (M3AS) 28, 1371-1412 (2018)
  22. V. Crismale, G. Lazzaroni, Quasistatic crack growth based on viscous approximation: a model with branching and kinking, Nonl. Diff. Eqns. Appl. (NoDEA) 24 : Art. 7 (2017)
  23. V. Crismale, Globally stable quasistatic evolutions for strain gradient plasticity coupled with damage
    Ann. Mat. Pura Appl. 196, 641-685 (2017)
  24. V. Crismale, G. Lazzaroni, Viscous approximation of quasistatic evolutions for a coupled elastoplastic damage model
    Calc. Var. Partial Differ. Equ. 55 : Art. 17 (2016)
  25. V. Crismale, Globally stable quasistatic evolution for a coupled elastoplastic–damage model
    ESAIM Control Optim. Calc. Var. 22, 883-912 (2016)