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The second part deals with hysteresis modelling during unloading path using a fractional derivative approach.
While the reloading path in all specimens was almost linear, the unloading path was highly nonlinear and was affected by unconfined concrete strength.
Following this, two hypotheses are given for the derivation of the subcycle delamination growth model: (1) delamination growth does not happen during the unloading path and (2) delamination growth does not happen when the applied loading is below a reference level during the loading path.
The proposed stress-strain model is composed of three main components: (1) a monotonic stress-strain model for the envelope curve of cyclic response; (2) a parabolic expression for the unloading path; and (3) a straight line for the reloading path.
These differences in following the unloading path cause a large difference in the displacement history at the post-peak structural response, as shown in Fig. 10.
This result is induced by the fact that concrete and reinforcing steel under the unloading path represent larger stiffness, which is not substantially different from the initial stiffness.
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The effects of different unloading paths and different confining stresses can be characterised by the SED rate.
The results show that there are clear differences in the state of stress and deformation behavior of the clay along different unloading paths.
The proposed model consists of three main components, namely (i) a monotonically ascending portion to describe the envelope curve, (ii) a polynomial equation to describe unloading paths, and (iii) a straight line to describe reloading paths.
The study also indicates other important results such as, linearity of relationship between the plastic strain and the envelope unloading strain, increase of the axial strain in the early stage of envelope unloading paths, and the cumulative effect of loading history on the plastic strain and stress deterioration.
Accidental loadings due to blast or impact may easily cause failure of the elements exposed or located in the vicinity of the hazard; therefore, assessment of the structural over strength is critical for structural engineers to ensure a certain level of security and validate alternative unloading paths.
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