3 papers
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
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.AP2024
Stress solution of static linear elasticity with mixed boundary conditions via adjoint linear operators
Ivan Gudoshnikov, Michal Křížek
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…