The stress distribution on the midsection of a pure bending beam where tensile strain
localization band initiates on the tensile side of the beam and propagates within the beam is analyzed.
Using the static equilibrium condition on the section of the midspan of the beam and the assumption
of plane section as well as the linear softening constitutive relation beyond the tensile strength, the
expressions for the length of tensile strain localization band and the distance from the tip of the band
to the neutral axis are derived. After superimposing a linear unloading stress distribution over the
initial stress distribution, the residual stress distribution on the midsection of the beam is investigated.
In the process of strain localization band’s propagation, strain-softening behavior of the band occurs
and neutral axis will shift. When the unloading moment is lower, the length of tensile strain
localization band remains a constant since the stress on the base side of the beam is tensile stress.
While, for larger unloading moment, with an increase of unloading moment, the length of tensile
strain localization band decreases and the distance from the initial neutral axis to the unloading
neutral axis increases. The neutral axis of midsection of the beam will shift in the unloading process.
The present analysis is applicable to some metal materials and many quasi-brittle geomaterials (rocks
and concrete, etc) in which tensile strength is lower than compressive strength. The present
investigation is limited to the case of no real crack. Moreover, the present investigation is limited to
the case that the length of strain localization band before unloading is less than half of depth of the
beam. Otherwise, the residual tensile stress above the elastic neutral axis will be greater than the
tensile strength, leading to the further development of tensile strain localization band in the unloading
process.