In Alicandro et al. (J Mech Phys Solids 92: 87-104, 2016) a simple discrete scheme for the motion of screw dislocations toward low energy configurations has been proposed. There, a formal limit of such a scheme, as the lattice spacing and the time step tend to zero, has been described. The limiting dynamics agrees with the maximal dissipation criterion introduced in Cermelli and Gurtin (Arch Ration Mech Anal 148, 1999) and predicts motion along the glide directions of the crystal. In this paper, we provide rigorous proofs of the results in [3], and in particular of the passage from the discrete to the continuous dynamics. The proofs are based on Gamma-convergence techniques.
Minimising movements for the motion of discrete screw dislocations along glide directions / Alicandro, Roberto; De Luca, Lucia; Garroni, Adriana; Ponsiglione, Marcello. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 56:5(2017). [10.1007/s00526-017-1247-0]
Minimising movements for the motion of discrete screw dislocations along glide directions
Garroni, Adriana;Ponsiglione, Marcello
2017
Abstract
In Alicandro et al. (J Mech Phys Solids 92: 87-104, 2016) a simple discrete scheme for the motion of screw dislocations toward low energy configurations has been proposed. There, a formal limit of such a scheme, as the lattice spacing and the time step tend to zero, has been described. The limiting dynamics agrees with the maximal dissipation criterion introduced in Cermelli and Gurtin (Arch Ration Mech Anal 148, 1999) and predicts motion along the glide directions of the crystal. In this paper, we provide rigorous proofs of the results in [3], and in particular of the passage from the discrete to the continuous dynamics. The proofs are based on Gamma-convergence techniques.File | Dimensione | Formato | |
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