Strain Localization in the Series Coupling Model
Whenever a structure contains elements that may soften, localization of the strain can take place. This section analyzes this phenomenon for the simple, yet important, quasi-static uniaxial case. The case of two nominally identical elements coupled in series is first presented and studied from the point of view of the imperfection approach to bifurcation (no two elements can be exactly identical), and then from the
Figure 8.1.1 (a) Series coupling of two softening elements, (b) Load-displacement curve of one clement, (c) Resulting load-displacement curve (full line).
point of view of the more general thermodynamic analysis of bifurcations. Next, as a simple extension, a chain of many softening elements is analyzed to show that, after reaching the peak load, only one element will be stretched further, while all the remaining elements unload. This is the starting point for the analysis of a softening continuous homogeneous bar, considered in the next section.