Calculus of Variations and Geometric Measure Theory

S. Conti - A. Garroni - S. Müller

Derivation of strain-gradient plasticity from a generalized Peierls-Nabarro model

created by garroni on 18 Sep 2020
modified by garroni1 on 24 Mar 2022


Accepted Paper

Inserted: 18 sep 2020
Last Updated: 24 mar 2022

Journal: JEMS
Year: 2022

ArXiv: 2009.03072 PDF


We derive strain-gradient plasticity from a nonlocal phase-field model of dislocations in a plane. Both a continuous energy with linear growth depending on a measure which characterizes the macroscopic dislocation density and a nonlocal effective energy representing the far-field interaction between dislocations arise naturally as scaling limits of the nonlocal elastic interaction. Relaxation and formation of microstructures at intermediate scales are automatically incorporated in the limiting procedure based on Γ-convergence.