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We extend the recent existence result of [9] for quasistatic evolutions of cracks in finite elasticity, allowing for boundary conditions and external forces with discontinuous first derivatives.

In the setting of antiplane linearized elasticity, we show the existence of the stress intensity factor and its relation with the energy release rate when the crack path is a C curve. Finally, we show that the energy release rate is continuous with respect to the Hausdorff convergence in a class of admissible cracks.

In the context of nanowire heterostructures we perform a discrete to continuum limit of the corresponding free energy by means of Γ-convergence techniques. Nearest neighbours are identified by employing the notions of Voronoi diagrams and Delaunay triangulations. The scaling of the nanowire is done in such a way that we perform not only a continuum limit… (More)

We discuss an atomistic model for heterogeneous nanowires, allowing for dislocations at the interface. We study the limit as the atomic distance converges to zero, considering simultaneously a dimension reduction and the passage from discrete to continuum. Employing the notion of Gamma-convergence, we establish the minimal energies associated to defect-free… (More)

- C Almici, Alfredo Cordoni, Paolo D'Adda, M R Inzoli, Giuliano Lazzaroni, Andrea Zambruni
- Giornale di clinica medica
- 1976

Epitaxially grown heterogeneous nanowires present dislocations at the interface between the phases if their radius is big. We consider a corresponding variational discrete model with quadratic pairwise atomic interaction energy. By employing the notion of Gamma-convergence and a geometric rigidity estimate, we perform a discrete to continuum limit and a… (More)

We present a recent existence result concerning the quasistatic evolution of cracks in hyperelastic brittle materials, in the framework of finite elasticity with non-interpenetration. In particular, here we consider the problem where no Dirichlet conditions are imposed, the boundary is traction-free, and the body is subject only to time-dependent volume… (More)

- Giuliano Lazzaroni, R. Bargellini, Pierre Dumouchel, Jean-Jacques Marigo, Renaud Bargellini
- 2017

We study the dynamic debonding of a onedimensional inextensible film, subject to a monotonic loading and under the hypothesis that the toughness of the glue can take only two values. We first consider the case of a single defect of small length in the glue where the toughness is lower than in the remaining part. The dynamic solution is obtained in a closed… (More)

- Marco Barchiesi, Giuliano Lazzaroni, Caterina Ida Zeppieri
- SIAM J. Math. Analysis
- 2016

We describe an existence result for quasistatic evolutions of cracks in antiplane elasticity obtained in [16] by a vanishing viscosity approach, with free (but regular enough) crack path. We underline in particular the motivations for the choice of the class of admissible cracks and of the dissipation potential. Moreover, we extend the result to a model… (More)