Research


Research Areas


I am interested in several applications in material science:

Industrial Partners


PhD students


Publications

Preprints available here
  1. L. Scardia: The nonlinear bending-torsion theory for curved rods as Gamma-limit of three-dimensional elasticity. Asymptot. Anal., 47 (2006) 317-343.
  2. L. Scardia: Damage as Gamma-limit of microfractures in anti-plane linearized elasticity. Math. Models Methods Appl. Sci., 18 (2008) 1703-1740.
  3. L. Scardia: Asymptotic models for curved rods derived from nonlinear elasticity by Gamma-convergence. Proc. Roy. Edinb. Soc. A, 139 (2009), 1037-1070.
  4. T. Roubicek, L. Scardia and C. Zanini: Quasistatic delamination problem. Contin. Mech. Thermodyn., 21 (2009), 223-235.
  5. L. Scardia: Damage as the Gamma-limit of microfractures in linearized elasticity under the non-interpenetration constraint. Adv. Calc. Var., 3 (2010), 423-458.
  6. F. Cagnetti and L. Scardia: An extension theorem in SBV and an application to the homogenization of the Mumford-Shah functional in perforated domains. J. Math. Pures Appl., 95 (2011), 349-381.
  7. L. Scardia, A. Schloemerkemper and C. Zanini: Boundary layer energies for nonconvex discrete energies. Math. Models Methods Appl. Sci., 21 (2011), 777-817.
  8. M.G. Mora and L. Scardia: Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density. J. Differential Equations, 252 (2012), 35-55.
  9. L. Scardia, A. Schloemerkemper and C. Zanini: Towards uniformly Gamma-equivalent theories for non-convex discrete systems. Discrete Contin. Dyn. Syst. Ser. B, 17/2 (2012), 661-686.
  10. L. Scardia and C.I. Zeppieri: Line Tension for Plasticity as the Gamma-limit of a nonlinear dislocation energy. SIAM J. Math. Anal., 44/4 (2012), 2372-2400.
  11. M.G.D. Geers, R.H.J. Peerlings, M.A. Peletier and L. Scardia: Asymptotic behaviour of a pile-up of infinite walls of edge dislocations. Arch. Rational Mech. Anal., 209/2 (2013), 495-539.
  12. L. Scardia, R.H.J. Peerlings, M.A. Peletier and M.G.D. Geers: Mechanics of dislocation pile-up: A unification of scaling regimes. J. Mech. Phys. Solids, 70 (2014), 42-61.
  13. S. Mueller, L. Scardia and C.I. Zeppieri: Geometric rigidity for incompatible fields and an application to stain-gradient plasticity. Indiana Univ. Math. J., 63 (2014), 1365-1396.
  14. S. Mueller, L. Scardia and C.I. Zeppieri: Gradient theory for geometrically nonlinear plasticity via the homogenization of dislocations. In: Conti, S. and Hackl, K., eds. Analysis and Computation of Microstructure in Finite Plasticity. Switzerland: Springer (2015), 175-204.
  15. A. Garroni, P. van Meurs, M.A. Peletier and L. Scardia: Boundary-layer analysis of a pile-up of walls of edge dislocations at a lock. Math. Models Methods Appl. Sci., 21 (2016).
  16. L. Scardia: Continuum limits of discrete models via Gamma-convergence. In: Muntean et al eds. Macroscopic and large scale phenomena: coarse graining, mean field limits and ergodicity. Lect. Notes Appl. Math. Mech., 3, Springer (2016), 145-186.
  17. M.G. Mora, M.A. Peletier and L. Scardia: Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement. SIAM J. Math. Anal., in press.
  18. M.G. Mora, L. Rondi and L. Scardia: The equilibrium measure for a nonlocal dislocation energy. Comm. Pure Appl. Math., in press.
  19. J.A. Carrillo, J. Mateu, M.G. Mora, L. Rondi L. Scardia and J. Verdera: The ellipse law: Kirchhoff meets dislocations. Submitted.
  20. F. Cagnetti, G. Dal Maso, L. Scardia and C.I. Zeppieri: Gamma-convergence of free discontinuity problems. Submitted.
  21. F. Cagnetti, G. Dal Maso, L. Scardia and C.I. Zeppieri: Stochastic Homogenisation of Free-Discontinuity Problems. Submitted.

Recent conferences, seminars and visits


Organisation of conferences

Nonlocal interactions: Dislocations and beyond, University of Bath, 11-14 June 2018 (co-organised with Maria Giovanna Mora).

Workshop Young Applied Analysts in the UK, University of Bath, 26-27 May 2016 (co-organised with David Bourne).

Third Scottish PDE Colloquium, University of Strathclyde, 1-2 June 2015 (co-organised with G. Barrenechea).

Workshop Young Applied Analysts in the UK, University of Glasgow, 29-30 May 2014 (co-organised with David Bourne).

Current seminar organisation


Grants