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Quasistatic and Dynamic Evolution Problems in Plasticity and Fracture

 

 

 

 

Papers

 

Alicandro R., Lazzaroni G., Palombaro M.: Interactions beyond nearest neighbours and rigidity of discrete energies: a compactness result and an application to dimension reduction. Preprint SISSA, Trieste, 2016.

 

Conti S., Focardi M., Iurlano F.: Integral representation for functionals defined on SBDp in dimension two. Preprint 2016.

 

Crismale V., Lazzaroni G.: Quasistatic crack growth based on viscous approximation: a model with branching and kinking. Preprint SISSA, Trieste, 2016.

 

Crismale V., Lazzaroni G., Orlando G.: Cohesive fracture with irreversibility: quasistatic evolution for a model subject to fatigue. Preprint SISSA, Trieste, 2016.

 

Fonseca I., Leoni G, Mora M.G: A second order minimality condition for water-waves functionals. Preprint May 2016.

 

Freddi L., Hornung P., Mora M.G., Paroni R.: A variational model for anisotropic and naturally twisted ribbons. Preprint May 2016.

 

Knees D., Negri M.: Convergence of alternate minimization schemes for phase field fracture and damage. Preprint, 2016

 

Lucardesi I., Morandotti M., Scala R., Zucco D.: Confinement of dislocations inside a crystal with a prescribed external strain. Preprint SISSA, Trieste, 2016.

 

Matias J., Morandotti M., Zappale E.: Optimal design of fractured media with prescribed macroscopic strain. Preprint SISSA, Trieste, 2016, arXiv:1607.08728.

 

Negri M.: An L2 gradient flow and its quasi-static limit in phase-field fracture by alternate minimization. Preprint, 2016.

 

Artina M., Cagnetti F., Fornasier M., Solombrino F.: Linearly constrained evolutions of critical points and an application to cohesive fractures. Preprint, 2015.

 

Barroso A.C., Matias J., Morandotti M., Owen D.R.: Explicit formulas for relaxed disarrangement densities arising from structured deformations. Preprint SISSA, Trieste, 2015, arXiv:1508.06908.

 

Lazzaroni G., Rossi R., Thomas M., Toader R.: Rate-independent damage in thermo-viscoelastic materials with inertia. Preprint SISSA 52/2014/MATE, Trieste, 2014.

 

Mora M.G., Peletier M., Scardia L.: Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement. Preprint Univ. Pavia, 2014.

 

Scala R., Van Goethem N.: Functions whose curl is an integral 1-current, with application to a variational model for dislocations. Preprint CVGMT, Pisa, 2014.

 

Almi S., Dal Maso G., Toader R.:  A lower semicontinuity result for a free discontinuity functional with a boundary term. J. Math. Pures Appl., to appear.

 

Barroso A.C., Matias J., Morandotti M., Owen D.R.: Second-order structured deformations: relaxation, integral representation and applications. Math. Mech. Complex Syst., to appear.

 

Blass T., Morandotti M.: Renormalized energy and Peach-Kšhler forces for screw dislocations with antiplane shear. J. Convex Anal. 24 (2017), to appear.

 

Bonaschi G., van Meurs P., Morandotti M.: Dynamics of screw dislocations: a generalised minimising-movements scheme approach. Eur. J. Appl. Math., to appear.

 

Conti S., Focardi M., Iurlano F.: Which special functions of bounded deformation have bounded variation? Proc. Edinb. Math. Soc. (2), to appear.

 

Dal Maso G., Lucardesi I.: The wave equation on domains with cracks growing on a prescribed path: existence, uniqueness, and continuous dependence on the data. Appl. Math. Res. Express. AMRX, to appear.

 

Dal Maso G., Morandotti M.: A model for the quasistatic growth of cracks with fractional dimension. Nonlinear Anal., to appear.

 

Dal Maso G., Orlando G., Toader R.: Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation. Adv. Cal. Var., to appear.

 

Freddi F., Iurlano F.: Numerical insight of a variational smeared approach to cohesive fracture. J. Mech. Phys. Solids, to appear.

 

Lazzaroni G., Palombaro M., Schlšmerkemper A.: Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires. Discrete Contin. Dyn. Syst. Ser. S, to appear. 

 

Negri M.: A simple derivation and classical representations of energy variations for curved cracks. Appl. Math. Optim. (online first)

 

Barchiesi M., Lazzaroni G.,  Zeppieri C.I.: A bridging mechanism in the homogenisation of brittle composites with soft inclusions. SIAM J. Math. Anal. 48 (2016), 1178-1209.

 

Cicalese M., Ruf M., Solombrino F.: Chirality transitions in frustrated S2-valued spin systems. Math. Models Methods Appl. Sci. 26 (2016), 1481-1529.

 

Conti S., Focardi M., Iurlano F.: Phase field approximation of cohesive fracture models. Ann. Inst. H. PoincarŽ Anal. Non LinŽaire 33 (2016), 1033-1067.

 

Crismale V., Lazzaroni G.: Viscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model. Calc. Var. Partial Differential Equations 55 (2016), article 17.

 

Dal Maso G., Larsen C.J., Toader R.: Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition. J. Mech. Phys. Solids 95 (2016), 697-707.

 

Dal Maso G., Lazzaroni G., Nardini L.: Existence and uniqueness of dynamic evolutions for a peeling test in dimension one. J. Differential Equations 261 (2016), 4897-4923.

 

Dal Maso G., Orlando G., Toader R.: Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case. Calc. Var. Partial Differential Equations 55 (2016), Article 45.

 

Freddi L., Hornung  P., Mora M.G., Paroni R.: A corrected Sadowsky functional for inextensible elastic ribbons. J. Elasticity 123 (2016), 125-136.

 

Lazzaroni G., Rossi R., Thomas M., Toader R.: Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics. Proceedings of MURPHYS-HSFS-2014, J. Phys. Conf. Ser. 727 (2016), 012009.

 

Maggiani G.B., Mora M.G: A dynamic evolution model for perfectly plastic plates. Math. Models Methods Appl. Sci. 26 (2016), 1825-1864.

 

Mora M.G: Relaxation of the Hencky model in perfect plasticity.  J. Math. Pures Appl. 106 (2016), 725-743.

 

Negri M.: Quasi-static evolutions in brittle fracture generated by gradient flows: sharp crack and phase-field approaches. Innovative Numerical Approaches for Multi-Field and Multi-Scale Problems. In Honor of Michael Ortiz's 60th Birthday. Weinberg K. and Pandolfi A. Editors, 197-216, Lecture Notes in Applied and Computational Mechanics 81, Springer, New York, 2016,.

 

Agostiniani V., Dal Maso G., DeSimone A.: Attainment results for nematic elastomers. Proc. Roy. Soc. Edinburgh Sect. A 145 (2015), 669-701.

 

Babadjian J.-F., Mora M.G.: Approximation of dynamic and quasi-static evolution problems in elasto-plasticity by cap models. Q. Appl. Math. 73 (2015), 265-316.

 

Blass T., Fonseca I., Leoni G., Morandotti M.: Dynamics for systems of screw dislocations. SIAM J. Appl. Math. 75 (2015), 393-419.

 

Braides A., Cicalese M., Solombrino F.: Q-tensor continuum energies as limits of head-to-tail symmetric spin systems. SIAM J. Math. Anal. 47 (2015), 2832-2867.

 

Chenchiah I.V., Larsen C.J.: Quasi-static brittle damage evolution in elastic materials with multiple damaged states. Arch. Ration. Mech. Anal. 215 (2015), 831-866.

 

Cicalese M., Solombrino F.: Frustrated ferromagnetic spin chains: a variational approach to chirality transitions. J. Nonlinear Sci. 25 (2015), 291-313.

 

Dal Maso G., Orlando G., Toader R.: Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length. NoDEA Nonlinear Differential Equations Appl. 22 (2015), 449-476.

 

Davoli E., Mora  M.G.: Stress regularity for a new quasistatic evolution model of perfectly plastic plates. Calc. Var. Partial Differential Equations 54 (2015), 2581-2614.

 

Lazzaroni G., Palombaro M., Schlšmerkemper A.: A discrete to continuum analysis of dislocations in nanowire heterostructures. Commun. Math. Sci. 13 (2015), 1105-1133.

 

Maggiani, G., Scala R., Van Goethem N.: A compatible-incompatible decomposition of symmetric tensors in Lp with application to elasticity. Math. Meth. Appl. Sci. 38 (2015), 5217-5230.

 

Matias J., Morandotti M.: Homogenization problems in the Calculus of Variations: an overview. S‹o Paulo J. Math. Sci. 9 (2015), 162-180.

 

Matias J., Morandotti M., Santos P.M.: Homogenization of functionals with linear growth in the context of A-quasiconvexity. Appl. Math. Optim. 72 (2015), 523-547.

 

Negri M., Toader R.: Scaling in fracture mechanics by BažantŐs law: from finite to linearized elasticity. Math. Models Methods Appl. Sci. 25 (2015), 1389-1420.

 

Solombrino F.: A priori time-regularity estimates and a simplified proof of existence in perfect plasticity. Math. Nachr. 288 (2015), 1786-1800.

 

Almi S., Dal Maso G., Toader R.: Quasi-static crack growth in hydraulic fracture. Nonlinear Anal. 109 (2014), 301-318.

 

Amstutz S., Novotny A.A., Van Goethem N.: Minimal partitions and image classification using a gradient-free perimeter approximation. Inverse Probl. Imaging 8 (2014), 361-387.

 

Amstutz S., Novotny A.A., Van Goethem N.: Topological sensitivity analysis for high order elliptic operators. J. Differential Equations 256 (2014), 1735-1770.

 

Ansini N., Dal Maso G., Zeppieri C.I.: New results on Gamma-limits of integral functionals. Ann. Inst. H. PoincarŽ Anal. Non LinŽaire 31 (2014), 185-202.

 

Dal Maso G., Scala R.: Quasistatic evolution in perfect plasticity as limit of dynamic processes. J. Dynam. Differential Equations 26 (2014) 915-954.

 

Focardi M., Iurlano F.: Asymptotic analysis of Ambrosio–Tortorelli energies in linearized elasticity. SIAM J. Math. Anal. 46 (2014), 2936-2955.

 

Iurlano F.:  A density result for GSBD and its application to the approximation of brittle fracture energies. Calc. Var. Partial Differential Equations 51 (2014), 315–342.

 

Larsen C.J.: A new variational principle for cohesive fracture and elastoplasticity. Mech. Res. Commun. 58 (2014), 33-38.

 

Larsen C.J., Slastikov V.: Dynamic cohesive fracture: models and analysis. Math. Models Methods Appl. Sci. 24 (2014), 1857-1875.

 

Negri M.: Quasi-static rate-independent evolutions: characterization, existence, approximation and application to fracture mechanics. ESAIM Control Optim. Calc. Var. 20 (2014) 983-1008.

 

Negri M., Zanini C.: From finite to linear elastic fracture mechanics by scaling. Calc. Var. Partial Differential Equations 50 (2014) 525-548.

 

Racca S.: A model for crack growth with branching and kinking. Asymptotic Anal. 89 (2014), 63-110.

 

Racca S., Toader R.: A variational model for the quasi-static growth of fractional dimensional brittle fractures. Interfaces Free Bound. 16 (2014), 509-538.

 

Solombrino F.: Quasistatic evolution in perfect plasticity for general heterogeneous materials. Arch. Ration. Mech. Anal. 212 (2014), 283-300.

 

Van Goethem N.: Fields of bounded deformation for mesoscopic dislocations. Math. Mech. Solids, 19 (2014), 579-600.

 

Van Goethem N.: Thermodynamic forces in single crystals with dislocations. Z. Angew. Math. Phys. 65 (2014), 549-586.

 

Ansini N., Dal Maso G., Zeppieri C.I.: Gamma-convergence and H-convergence of linear elliptic operators. J. Math. Pures Appl. 99 (2013), 321-329.

 

Dal Maso G.: Generalised functions of bounded deformation. J. Eur. Math. Soc. (JEMS) 15 (2013), 1943-1997.

 

Davoli E., Mora M.G.: A quasistatic evolution model for perfectly plastic plates derived by Gamma-convergence. Ann. Inst. H. PoincarŽ Anal. Non LinŽaire 30 (2013), 615-660.

 

Larsen C.J.: Local minimality and crack prediction in quasi-static Griffith fracture evolution. Discrete Contin. Dyn. Syst. Ser. S 6 (2013), 121-129.

 

Negri M.: From phase-field to sharp crack: convergence of quasi-static evolutions in a special setting. Appl. Math. Lett. 26 (2013), 219-224.

 

Racca S.: A viscosity-driven crack evolution. Adv. Calc. Var. 5 (2012), 433-483.

 

Babadjian J.-F., Francfort G.A., Mora M.G.: Quasi-static evolution in nonassociative plasticity: the cap model. SIAM J. Math. Anal. 44 (2012), 245-292.