The current state of structural engineering is leading to an increasing demand for lighter and more efficient structures and engineering components, which in turn is resulting in designs that reach the limitations of materials' strength. These technological advancements generally rely on extensive experimental investigation in order to determine material’s behavior under loading conditions. However, experimentation is generally expensive, not only financially but also in research time. Besides, many structures or components cannot be tested under workloads, due to being inaccessible or the test being economically unfeasible. These difficulties associated with experimentation inevitably lead to the need of using numerical tools to obtain solutions, such as the stress fields in a component. Therefore, it becomes more and more crucial to develop numerical models capable of adequately describing the material’s behavior under a given loading.


In this project, I implemented Lemaitre’s mathematical/numerical continuous damage mechanics model and evaluated its performance in determining fatigue life and stress amplitudes under multiaxial loading. Chaboche's kinematic hardening model was used to model kinematic hardening.

The proposed model was implemented in a FORTRAN subroutine and then subjected to proportional and non-proportional loading to compare the numeric fatigue life prediction with experimental data for three distinct materials.


From the fatigue life data, it was seen that the model adequately described fatigue life for all materials under various proportional and non-proportional loading. The model described better, as expected, low cycle fatigue – characterized by the dominance of the macroscopic plastic strain. When lower strain amplitudes are applied, however, the model predicts conservative lives.

A limitation of the study was that only kinematic hardening was modelled; there was no mechanism to account for isotropic hardening.


Fatigue life estimates under non-proportional loading through continuum damage evolution law