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arXiv · 2410.02906

Homogenization of elasto-plastic evolutions driven by the flow of dislocations

Paolo Bonicatto·Filip Rindler
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Abstract

Starting from a prototypical model of elasto-plasticity in the small-strain and quasi-static setting, where the evolution of the plastic distortion is driven exclusively by the motion of discrete dislocations, this work performs a rigorous homogenization procedure to a model involving continuously-distributed dislocation fields. Our main result shows the existence of rate-independent evolutions driven by the motion of dislocation fields, obtained as limits of discrete dislocation evolutions. For all notions of solutions we employ the recent concepts of space-time integral and normal currents, which is richer than the classical approach using the Kröner dislocation density tensor. The key technical challenge is to find discrete dislocation evolutions approximating a given dislocation field evolution, which requires a careful recovery construction of space-time slip trajectories and associated displacements. These methods enable one to transfer the properties, most importantly the quasi-static stability, from the discrete to the field regime.

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Paolo Bonicatto, Filip Rindler. 2025-03-25. Homogenization of elasto-plastic evolutions driven by the flow of dislocations. https://arxiv.org/abs/2410.02906

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