D. Sumarac et S. Stosic, THE PREISACH MODEL FOR THE CYCLIC BENDING OF ELASTOPLASTIC BEAMS, European journal of mechanics. A, Solids, 15(1), 1996, pp. 155-172
In the present paper, the Preisach model, already successfully impleme
nted for the problem of axially loaded members, has been extended to t
he cyclic bending of elasto-plastic beams. Starting from Hooke's and S
t. Venant's element, very well known in the theory of plasticity, usin
g the Preisach model the stress at an arbitrary fiber of the cross sec
tion, and at an arbitrary instant of time can be found for a precribed
history of curvarure change. The solutions for pure bending of symmet
rical cross sections (rectangular and I-section) are presented. Also p
ure bending of an unsymmetrical (triangular) cross section, and the be
nding of a symmetrical (rectangular) cross section due to the simultan
eous action of axial stretching of the neutral fiber and curvature cha
nge are considered.