Reformulating plastic instabilities within a damage-like variational framework
Abstract
Yield point phenomena in metals, anticracks in soils and snows, or planewise collapses in lattice metamaterials, are different manifestations of plastic instabilities characterized by stress softening and strain localization. Several independent constitutive descriptions exist and suffer from similar challenges: experimental difficulties to link local events to global measurements, and computational lack of convergence, spurious localization and mesh sensitivity. This work proposes a minimal field-agnostic constitutive framework where plastic softening is represented by a damage-like internal variable which explicitly separates stable hardening behavior from unstable softening. The resulting formulation admits a variational structure and can leverage regularization tools originally developed by the ductile fracture community. The framework aims at emphasizing similarities within plastic instability phenomena and establishing a bridge with continuum damage mechanics, to open a path towards regularized variational formulations of localized plastic flows.
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BibTeX
@misc{reyne2026reformulating,
title = {{Reformulating plastic instabilities within a damage-like variational framework}},
author = {Baptiste Reyne},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03328},
eprint = {2610.03328},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03328},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reformulating plastic instabilities within a damage-like variational framework
AU - Baptiste Reyne
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03328
UR - https://arxiv.org/abs/2610.03328
AB - Yield point phenomena in metals, anticracks in soils and snows, or planewise collapses in lattice metamaterials, are different manifestations of plastic instabilities characterized by stress softening and strain localization. Several independent constitutive descriptions exist and suffer from similar challenges: experimental difficulties to link local events to global measurements, and computational lack of convergence, spurious localization and mesh sensitivity. This work proposes a minimal field-agnostic constitutive framework where plastic softening is represented by a damage-like internal variable which explicitly separates stable hardening behavior from unstable softening. The resulting formulation admits a variational structure and can leverage regularization tools originally developed by the ductile fracture community. The framework aims at emphasizing similarities within plastic instability phenomena and establishing a bridge with continuum damage mechanics, to open a path towards regularized variational formulations of localized plastic flows.
ER -