3 papers
math.AP2025
Regularity lost: the fundamental limitations and constraint qualifications in the problems of elastoplasticity
Ivan Gudoshnikov
We investigate the existence and non-existence of a function-valued strain solution in various models of elastoplasticity from the perspective of the constraint-based ``dual'' form…
math.OC2025
Elastoplasticity with softening as a state-dependent sweeping process: non-uniqueness of solutions and emergence of shear bands in lattices of springs
Ivan Gudoshnikov
Plasticity with softening and fracture mechanics lead to ill-posed mathematical problems due to the loss of monotonicity. Multiple co-existing solutions are possible when softening…
math.AP2024
Stress solution of static linear elasticity with mixed boundary conditions via adjoint linear operators
Ivan Gudoshnikov, Michal KÅÞek
We revisit stress problems in linear elasticity to provide a perspective from the geometrical and functionalanalytic points of view. For the static stress problem of linear elastic…