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PreprintCC BY 4.0HAL

A VARIATIONAL FRAMEWORK FOR INCOMPATIBILITY-DRIVEN DEFORMATIONS

  • Samuel Amstutz
  • Thien-Nga Le
  • Nicolas van Goethem
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Abstract

We propose an incremental, variational model for elasto-plastic deformations in which a newly constructed incompatible strain tensor, linked to dislocation density through Kr¨oner’s relation, serves as the primary kinematical descriptor. The model also introduces a scalar internal variable, the compatibility modulus, governing both dissipation and the tangent elastic response, thereby providing a rate-independent framework capable of describing strain hardening. Numerical simulations exhibit localized deformation patterns and residual stresses consistent with dislocation-mediated plasticity. The higher-order structure arises intrinsically from strain incompatibility, providing a geometrically natural and unified framework for size-dependent effects.

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Cite

BibTeXRIS
BibTeX
@misc{amstutz2026variational,
  title = {{A VARIATIONAL FRAMEWORK FOR INCOMPATIBILITY-DRIVEN DEFORMATIONS}},
  author = {Samuel Amstutz and Thien-Nga Le and Nicolas van Goethem},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  url = {https://hal.science/hal-05361307v4},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A VARIATIONAL FRAMEWORK FOR INCOMPATIBILITY-DRIVEN DEFORMATIONS
AU  - Samuel Amstutz
AU  - Thien-Nga Le
AU  - Nicolas van Goethem
PY  - 2026
DA  - 2026/10/23
PB  - HAL
UR  - https://hal.science/hal-05361307v4
AB  - We propose an incremental, variational model for elasto-plastic deformations in which a newly constructed incompatible strain tensor, linked to dislocation density through Kr¨oner’s relation, serves as the primary kinematical descriptor. The model also introduces a scalar internal variable, the compatibility modulus, governing both dissipation and the tangent elastic response, thereby providing a rate-independent framework capable of describing strain hardening. Numerical simulations exhibit localized deformation patterns and residual stresses consistent with dislocation-mediated plasticity. The higher-order structure arises intrinsically from strain incompatibility, providing a geometrically natural and unified framework for size-dependent effects.
ER  -