On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems

Abstract In this work the finite element (FE) implementation of small strain cyclic plasticity is discussed. The family elastoplastic constitutive models considered which uses mixed, kinematic-isotropic hardening rule. It assumed that kinematic governed by Armstrong–Frederick law. radial return mapping algorithm utilized to discretize general form equation. A relation for consistent tangent operator derived. To best author’s knowledge, formula has not been presented in literature yet. obtained set equations can be used implement into numerous commercial or non-commercial FE packages. user subroutine UMAT (User’s MATerial) developed order model Yoshida open-source program CalculiX. coding included Appendix. easily modified any isotropic rule yield stress a function effective plastic strain. number backstress variables increased as well. Several validation tests have performed verify code’s performance are