An analysis of strong discontinuities in thermo-elasto-plastic solids

The failure of many engineering materials often follows the development of large plastic strains in a narrow zone. In typical metals, this zone of strain localization generates heat from the dissipated energy during the plastic deformation process. In general, the heat in the localized zone increases the temperature of the material and that temperature increase weakens the material strength, which is called thermal softening. The overall reduction of the load capacity of the solid with the increase of strain observed at these stages is often modelled through a constitutive relation with strain softening.; In this dissertation, we model this localization phenomenon through a multiscale strong discontinuity approach. This approach considers surfaces of discontinuity of the displacement field to model the localized zone, and its small scale effects, in the large scale problem. The temperature field remains continuous, a fact that is shown to be consistent with a positive thermal conductivity.; This approach is motivated by the deficiencies of classical continuum thermoplastic models. Linearized spectral analyses of a one-dimensional problem reveal that strain softening results in solutions which do not depend continuously on the boundary and initial conditions, that is, the problem is ill-posed. The thermal coupling does not define a length scale regularizing the localization in the continuum thermoplastic problem. An exact solution of the problem of wave propagation is presented in this context, showing its physically meaningless characteristics: no energy dissipation is observed. This solution leads to the pathological mesh-size dependence of the finite element solutions of the problem. The application of the strong discontinuity approach introducing a thermoplastic localized mechanism yields a physically meaningful analytic solution with the proper energy dissipation. Its finite element solution is not affected by the pathological mesh-size dependence.; The application of the strong discontinuity approach to general two and three dimensional thermoplastic solids is also presented. The formulation of enhanced strain finite elements incorporating the singular fields of the strong discontinuity is developed in detail. This includes the propagation of the surfaces of discontinuity through the finite element mesh. Several numerical simulations are presented to evaluate the performance of the proposed approach.