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)

- A. Chambolle, V. Crismale,
*A general compactness theorem in G(S)BD*, Submitted - V. Crismale, G.Lazzaroni, R. Rossi,
*Singular limits of a coupled elasto-plastic damage system as viscosity and hardening vanish*,**Ann. Mat. Pura Appl.** - 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) - V. Crismale,
*Energetic solutions for the coupling of associative plasticity with damage in geomaterials*,**Nonlinear Analysis 222**, Art. 112957 (2022) - 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) - A. Chambolle, V. Crismale,
*Equilibrium configurations for nonhomogeneous linearly elastic materials with surface discontinuities*, Published online on**Ann. Sc. Norm. Super. Pisa Cl. Sci.** - V. Crismale, M. Friedrich, F. Solombrino,
*Integral representation for energies in linear elasticity with surface discontinuities*,**Adv. Calc. Var. 15**, 705-733 (2020) - 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) - J.-F. Babadjian, V. Crismale,
*Dissipative boundary conditions and entropic solutions in dynamical perfect plasticity*

**J. Math. Pures Appl. 148**, 75-127 (2021) - V. Crismale, R. Rossi,
*Balanced Viscosity solutions to a rate-independent coupled elasto-plastic damage system*

**SIAM J. Math. Anal. 53**, 3420-3492 (2021) - 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) - V. Crismale, G. Orlando,
*A lower semicontinuity result for linearised elasto-plasticity coupled with damage in W*,^{1,γ}, γ > 1**Mathematics in Engineering 2**, 101-118 (2019) - 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) - 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) - V. Crismale,
*Density in SBD and approximation of fracture energies*

**Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30**, 533-542 (2019) - 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) - V. Crismale,
*On the approximation of SBD functions and some applications*

**SIAM J. Math. Anal. 51**, 5011-5048 (2019) - A. Chambolle, V. Crismale,
*Compactness and lower semicontinuity in GSBD*

**J. Eur. Math. Soc. (JEMS) 23**, 701-719 (2021) - A. Chambolle, V. Crismale,
*A density result in GSBD*^{p}with applications to the approximation of brittle fracture energies**Arch. Ration. Mech. Anal. 232**, 1329-1378 (2019) - V. Crismale, G. Orlando,
*A Reshetnyak-type lower semicontinuity result for linearised elasto-plasticity coupled with damage in W*,^{1,n}**Nonl. Diff. Eqns. Appl. (NoDEA) 25 : Art. 16**(2018) - 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) - 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) - V. Crismale,
*Globally stable quasistatic evolutions for strain gradient plasticity coupled with damage*

**Ann. Mat. Pura Appl. 196**, 641-685 (2017) - V. Crismale, G. Lazzaroni,
*Viscous approximation of quasistatic evolutions for a coupled elastoplastic damage model*

**Calc. Var. Partial Differ. Equ. 55 : Art. 17**(2016) - V. Crismale,
*Globally stable quasistatic evolution for a coupled elastoplastic–damage model*

**ESAIM Control Optim. Calc. Var. 22**, 883-912 (2016)