Preprint

Inserted: 10 oct 2023
Last Updated: 2 nov 2023

Year: 2023

Abstract:

We derive a quantitative rigidity estimate for a multiwell problem in nonlinear elasticity with dislocations. Precisely, we show that the $L^{1^{*}}$-distance of a possibly incompatible strain field $\beta$ from a single well is controlled in terms of the $L^{1^{*}}$-distance from a finite set of wells, of ${\rm curl}\beta$, and of ${\rm div}\beta$. As a consequence, we derive a strain-gradient plasticity model as $\Gamma$-limit of a nonlinear finite dislocation model, containing a singular perturbation term accounting for the divergence of the strain field. This can also be seen as a generalization of the result of Alicandro et al. (2018) to the case of incompatible vector fields.

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• Almi_Reggiani_Solombrino_23.01.01.pdf