Homogenization of elasto-plastic evolutions driven by the flow of dislocations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916661379989504 |
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| author | Bonicatto, Paolo Rindler, Filip |
| author_facet | Bonicatto, Paolo Rindler, Filip |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02906 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homogenization of elasto-plastic evolutions driven by the flow of dislocations Bonicatto, Paolo Rindler, Filip Analysis of PDEs 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. |
| title | Homogenization of elasto-plastic evolutions driven by the flow of dislocations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.02906 |