Inelasticity: Ultimate Load and Localized Failure

Abstract

AbstractWe here deal with another class of nonlinear problems in structural engineering that is brought about by the inelastic constitutive behavior of structural material. The main interest is in quantifying the risk of pre-mature structure failure due to the accumulation of internal material damage that reduced the load-bearing capacity from elastic behavior. Here, we provide the inelastic constitutive model in terms of stress resultants, which is much more suitable for keeping the computational efficiency of structural engineering models. We first study the inelastic behavior of the Reissner-Mindlin plate model, seeking to illustrate different plasticity criteria characterizing the inelastic behavior of typical structural materials, such as reinforced concrete, steel or masonry. For each model we define corresponding plasticity criterion expressed directly in terms of stress resultants, bending moments and shear forces. Moreover, we again seek to illustrate the effect of combined loading requiring us to solve the time-evolution of non-stationary heat transfer. In the final part of this chapter we tackle the combined effect of large deformation and inelastic constitutive behavior that jointly can push the structure into softening regime and pre-mature failure. This development is illustrated on the Reissner beam model.