Sweeping Process in Stress-Based Models of Elastoplasticity
Ivan Gudoshnikov1*
1 Institute of Mathematics, Czech Academy of Sciences
Keywords: elastoplasticity, sweeping process, convex analysis, strain softening
The connection between plasticity phenomenon in mechanics and the sweeping process was noticed since the very discovery of the sweeping process as a mathematical problem. Specifically, when the stress distribution is considered as a state variable, the "moving set" of a sweeping process reflects the interplay between the "elastic range" characteristic of an elastoplastic material, and the constraint of quasistatic equilibrium. In the presentation we will discuss the implications of this idea for various types of plasticity (strain hardening, perfect plasticity [1], strain softening [2]), and pay attention to the accompanying challenges.
References
- I. Gudoshnikov, Regularity lost: the fundamental limitations and constraint qualifications in the problems of elastoplasticity, Discrete Contin. Dyn. Sys., 51(0):370-438, 2026, https://doi.org/10.3934/dcds.2026034.
- I. Gudoshnikov, Elastoplasticity with softening as a state-dependent sweeping process: non-uniqueness of solutions and emergence of shear bands in lattices of springs, 2026, https://doi.org/10.48550/arXiv.2508.16333.