Evolution of nonlocal damage in steel under cyclic straining

For high dynamic excitation, e.g. by earthquakes, the vibrations of steel structures lead to inelastic material behavior. Hystereses, developing under cyclic loading, are responsible for the dissipation of energy. Additionally, stress concentration at small defects results in the nucleation and the growth of microvoids which is referred to as damage, here especially as ultra low cycle fatigue. The material damage influences the stiffness of a structure and its response to dynamic excitation. With increasing load the voids can coalesce and form a macrocrack which destroys the structural integrity and peril the overall safety. A material model is proposed which describes the evolution and distribution of inelastic strains and isotropic ductile damage for mild construction steel by means of a set of internal variables. Viscoplasticity as well as isotropic and kinematic hardening are taken into account. The evolution of isotropic hardening is related to the growth of a strain memory surface which accounts for the strain amplitude history of the material. Under tension isotropic ductile damage develops for significant inelastic strains [1]. The material model is implemented in the frameworks of the finite element method with displacement based ansatz functions. The equation of motion is solved with the Newmark method. To overcome the phenomenon of vanishing dissipation energy in case of mesh refinement due to strain localization a nonlocal extension in the form of an implicit gradient formulation is applied. The presented model is used to analyse 3D structures subjected to seismic excitation